Publications
2020 |
Bardin, Joseph C; Slichter, Daniel H; Reilly, David J Microwaves in Quantum Computing Journal Article arXiv preprint arXiv:2011.01480, 2020. BibTeX | Links: @article{bardin2020microwaves, title = {Microwaves in Quantum Computing}, author = {Joseph C Bardin and Daniel H Slichter and David J Reilly}, url = {https://arxiv.org/abs/2011.01480}, year = {2020}, date = {2020-11-03}, journal = {arXiv preprint arXiv:2011.01480}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Carvalho, Andre RR; Ball, Harrison; Biercuk, Michael J; Hush, Michael R; Thomsen, Felix Error-robust quantum logic optimization using a cloud quantum computer interface Journal Article arXiv preprint arXiv:2010.08057, 2020. BibTeX | Links: @article{carvalho2020error, title = {Error-robust quantum logic optimization using a cloud quantum computer interface}, author = {Andre RR Carvalho and Harrison Ball and Michael J Biercuk and Michael R Hush and Felix Thomsen}, url = {https://arxiv.org/abs/2010.08057}, year = {2020}, date = {2020-10-15}, journal = {arXiv preprint arXiv:2010.08057}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Pauka, SJ; Witt, JDS; Allen, CN; Harlech-Jones, B; Jouan, A; Gardner, GC; Gronin, S; Wang, T; Thomas, C; Manfra, MJ; others, Repairing the surface of InAs-based topological heterostructures Journal Article Journal of Applied Physics, 128 (11), pp. 114301, 2020. BibTeX | Links: @article{pauka2020repairing, title = {Repairing the surface of InAs-based topological heterostructures}, author = {SJ Pauka and JDS Witt and CN Allen and B Harlech-Jones and A Jouan and GC Gardner and S Gronin and T Wang and C Thomas and MJ Manfra and others}, url = {https://aip.scitation.org/doi/abs/10.1063/5.0014361}, year = {2020}, date = {2020-09-21}, journal = {Journal of Applied Physics}, volume = {128}, number = {11}, pages = {114301}, publisher = {AIP Publishing LLC}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Gupta, Riddhi Swaroop; Edmunds, Claire L; Milne, Alistair R; Hempel, Cornelius; Biercuk, Michael J Adaptive characterization of spatially inhomogeneous fields and errors in qubit registers Journal Article npj Quantum Information, 6 (1), pp. 53, 2020. @article{Gupta.2020, title = {Adaptive characterization of spatially inhomogeneous fields and errors in qubit registers}, author = {Riddhi Swaroop Gupta and Claire L Edmunds and Alistair R Milne and Cornelius Hempel and Michael J Biercuk}, doi = {10.1038/s41534-020-0286-0}, year = {2020}, date = {2020-06-12}, journal = {npj Quantum Information}, volume = {6}, number = {1}, pages = {53}, abstract = {New quantum computing architectures consider integrating qubits as sensors to provide actionable information useful for calibration or decoherence mitigation on neighboring data qubits, but little work has addressed how such schemes may be efficiently implemented in order to maximize information utilization. Techniques from classical estimation and dynamic control, suitably adapted to the strictures of quantum measurement, provide an opportunity to extract augmented hardware performance through automation of low-level characterization and control. In this work, we present an adaptive learning framework, Noise Mapping for Quantum Architectures (NMQA), for scheduling of sensor–qubit measurements and efficient spatial noise mapping (prior to actuation) across device architectures. Via a two-layer particle filter, NMQA receives binary measurements and determines regions within the architecture that share common noise processes; an adaptive controller then schedules future measurements to reduce map uncertainty. Numerical analysis and experiments on an array of trapped ytterbium ions demonstrate that NMQA outperforms brute-force mapping by up to 20× (3×) in simulations (experiments), calculated as a reduction in the number of measurements required to map a spatially inhomogeneous magnetic field with a target error metric. As an early adaptation of robotic control to quantum devices, this work opens up exciting new avenues in quantum computer science.}, keywords = {}, pubstate = {published}, tppubtype = {article} } New quantum computing architectures consider integrating qubits as sensors to provide actionable information useful for calibration or decoherence mitigation on neighboring data qubits, but little work has addressed how such schemes may be efficiently implemented in order to maximize information utilization. Techniques from classical estimation and dynamic control, suitably adapted to the strictures of quantum measurement, provide an opportunity to extract augmented hardware performance through automation of low-level characterization and control. In this work, we present an adaptive learning framework, Noise Mapping for Quantum Architectures (NMQA), for scheduling of sensor–qubit measurements and efficient spatial noise mapping (prior to actuation) across device architectures. Via a two-layer particle filter, NMQA receives binary measurements and determines regions within the architecture that share common noise processes; an adaptive controller then schedules future measurements to reduce map uncertainty. Numerical analysis and experiments on an array of trapped ytterbium ions demonstrate that NMQA outperforms brute-force mapping by up to 20× (3×) in simulations (experiments), calculated as a reduction in the number of measurements required to map a spatially inhomogeneous magnetic field with a target error metric. As an early adaptation of robotic control to quantum devices, this work opens up exciting new avenues in quantum computer science. |
Marciniak, Ch. D; Rischka, A; Wolf, R N; Biercuk, M J High-power spectral beamsplitter for closely spaced frequencies Journal Article Optics Express, 28 (8), pp. 11372, 2020. BibTeX | Links: @article{Marciniak2020, title = {High-power spectral beamsplitter for closely spaced frequencies}, author = {Ch. D Marciniak and A Rischka and R N Wolf and M J Biercuk}, doi = {10.1364/oe.390956}, year = {2020}, date = {2020-04-01}, journal = {Optics Express}, volume = {28}, number = {8}, pages = {11372}, publisher = {The Optical Society}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Edmunds, C L; Hempel, C; Harris, R J; Frey, V; Stace, T M; Biercuk, M J Dynamically corrected gates suppressing spatiotemporal error correlations as measured by randomized benchmarking Journal Article Physical Review Research, 2 (1), pp. 013156, 2020. @article{Edmunds.2020, title = {Dynamically corrected gates suppressing spatiotemporal error correlations as measured by randomized benchmarking}, author = {C L Edmunds and C Hempel and R J Harris and V Frey and T M Stace and M J Biercuk}, doi = {10.1103/physrevresearch.2.013156}, year = {2020}, date = {2020-01-01}, journal = {Physical Review Research}, volume = {2}, number = {1}, pages = {013156}, abstract = {Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of statistically independent errors in quantum logic operations is at odds with realistic environments where error sources may exhibit strong temporal and spatial correlations. We present experiments using trapped ions to demonstrate that the use of dynamically corrected gates (DCGs), generally considered for the reduction of error magnitudes, can also suppress error correlations in space and time throughout quantum circuits. We present a first-principles analysis of the manifestation of error correlations in randomized benchmarking and validate this model through experiments performed using engineered errors. We find that standard DCGs can reduce error correlations by ∼50× while increasing the magnitude of uncorrelated errors by a factor scaling linearly with the extended DCG duration compared to a primitive gate. We then demonstrate that the correlation characteristics of intrinsic errors in our system are modified by the use of DCGs, consistent with a picture in which DCGs whiten the effective error spectrum induced by external noise.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of statistically independent errors in quantum logic operations is at odds with realistic environments where error sources may exhibit strong temporal and spatial correlations. We present experiments using trapped ions to demonstrate that the use of dynamically corrected gates (DCGs), generally considered for the reduction of error magnitudes, can also suppress error correlations in space and time throughout quantum circuits. We present a first-principles analysis of the manifestation of error correlations in randomized benchmarking and validate this model through experiments performed using engineered errors. We find that standard DCGs can reduce error correlations by ∼50× while increasing the magnitude of uncorrelated errors by a factor scaling linearly with the extended DCG duration compared to a primitive gate. We then demonstrate that the correlation characteristics of intrinsic errors in our system are modified by the use of DCGs, consistent with a picture in which DCGs whiten the effective error spectrum induced by external noise. |
Bentley, Christopher D B; Ball, Harrison; Biercuk, Michael J; Carvalho, Andre R R; Hush, Michael R; Slatyer, Harry J Numeric Optimization for Configurable, Parallel, Error‐Robust Entangling Gates in Large Ion Registers Journal Article Advanced Quantum Technologies, pp. 2000044, 2020, ISSN: 2511-9044. @article{Bentley.2020, title = {Numeric Optimization for Configurable, Parallel, Error‐Robust Entangling Gates in Large Ion Registers}, author = {Christopher D B Bentley and Harrison Ball and Michael J Biercuk and Andre R R Carvalho and Michael R Hush and Harry J Slatyer}, doi = {10.1002/qute.202000044}, issn = {2511-9044}, year = {2020}, date = {2020-01-01}, journal = {Advanced Quantum Technologies}, pages = {2000044}, abstract = {A class of entangling gates for trapped atomic ions is studied and the use of numeric optimization techniques to create a wide range of fast, error‐robust gate constructions is demonstrated. A numeric optimization framework is introduced targeting maximally‐ and partially‐entangling operations on ion pairs, multi‐ion registers, multi‐ion subsets of large registers, and parallel operations within a single register. Ions are assumed to be individually addressed, permitting optimization over amplitude‐ and phase‐modulated controls. Calculations and simulations demonstrate that the inclusion of modulation of the difference phase for the bichromatic drive used in the Mølmer–Sørensen gate permits approximately time‐optimal control across a range of gate configurations, and when suitably combined with analytic constraints can also provide robustness against key experimental sources of error. The impact of experimental constraints such as bounds on coupling rates or modulation band‐limits on achievable performance is further demonstrated. Using a custom optimization engine based on TensorFlow, for optimizations on ion registers up to 20 ions, time‐to‐solution of order tens of minutes using a local‐instance laptop is also demonstrated, allowing computational access to system‐scales relevant to near‐term trapped‐ion devices. Numeric optimization and control techniques are demonstrated to create a wide range of fast, robust, high‐fidelity gates. Complex drive controls, with both phase and amplitude modulation on the mediating laser field, are applied to enact multi‐body and parallel operations on chains of up to 20 ions. Control solutions incorporate real constraints on modulation hardware and robustness to laser noise sources.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A class of entangling gates for trapped atomic ions is studied and the use of numeric optimization techniques to create a wide range of fast, error‐robust gate constructions is demonstrated. A numeric optimization framework is introduced targeting maximally‐ and partially‐entangling operations on ion pairs, multi‐ion registers, multi‐ion subsets of large registers, and parallel operations within a single register. Ions are assumed to be individually addressed, permitting optimization over amplitude‐ and phase‐modulated controls. Calculations and simulations demonstrate that the inclusion of modulation of the difference phase for the bichromatic drive used in the Mølmer–Sørensen gate permits approximately time‐optimal control across a range of gate configurations, and when suitably combined with analytic constraints can also provide robustness against key experimental sources of error. The impact of experimental constraints such as bounds on coupling rates or modulation band‐limits on achievable performance is further demonstrated. Using a custom optimization engine based on TensorFlow, for optimizations on ion registers up to 20 ions, time‐to‐solution of order tens of minutes using a local‐instance laptop is also demonstrated, allowing computational access to system‐scales relevant to near‐term trapped‐ion devices. Numeric optimization and control techniques are demonstrated to create a wide range of fast, robust, high‐fidelity gates. Complex drive controls, with both phase and amplitude modulation on the mediating laser field, are applied to enact multi‐body and parallel operations on chains of up to 20 ions. Control solutions incorporate real constraints on modulation hardware and robustness to laser noise sources. |
Milne, Alistair R; Edmunds, Claire L; Hempel, Cornelius; Roy, Federico; Mavadia, Sandeep; Biercuk, Michael J Phase-Modulated Entangling Gates Robust to Static and Time-Varying Errors Journal Article Physical Review Applied, 13 (2), pp. 024022, 2020. @article{Milne.2020, title = {Phase-Modulated Entangling Gates Robust to Static and Time-Varying Errors}, author = {Alistair R Milne and Claire L Edmunds and Cornelius Hempel and Federico Roy and Sandeep Mavadia and Michael J Biercuk}, doi = {10.1103/physrevapplied.13.024022}, year = {2020}, date = {2020-01-01}, journal = {Physical Review Applied}, volume = {13}, number = {2}, pages = {024022}, abstract = {Entangling operations are among the most important primitive gates employed in quantum computing, and it is crucial to ensure high-fidelity implementations as systems are scaled up. We experimentally realize and characterize a simple scheme to minimize errors in entangling operations related to the residual excitation of mediating bosonic oscillator modes that both improves gate robustness and provides scaling benefits in larger systems. The technique employs discrete phase shifts in the control field driving the gate operation, determined either analytically or numerically, to ensure all modes are de-excited at arbitrary user-defined times. We demonstrate an average gate fidelity of 99.4(2)% across a wide range of parameters in a system of Yb171+ trapped ion qubits, and observe a reduction of gate error in the presence of common experimental error sources. Our approach provides a unified framework to achieve robustness against both static and time-varying laser amplitude and frequency detuning errors. We verify these capabilities through system-identification experiments revealing improvements in error susceptibility achieved in phase-modulated gates.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Entangling operations are among the most important primitive gates employed in quantum computing, and it is crucial to ensure high-fidelity implementations as systems are scaled up. We experimentally realize and characterize a simple scheme to minimize errors in entangling operations related to the residual excitation of mediating bosonic oscillator modes that both improves gate robustness and provides scaling benefits in larger systems. The technique employs discrete phase shifts in the control field driving the gate operation, determined either analytically or numerically, to ensure all modes are de-excited at arbitrary user-defined times. We demonstrate an average gate fidelity of 99.4(2)% across a wide range of parameters in a system of Yb171+ trapped ion qubits, and observe a reduction of gate error in the presence of common experimental error sources. Our approach provides a unified framework to achieve robustness against both static and time-varying laser amplitude and frequency detuning errors. We verify these capabilities through system-identification experiments revealing improvements in error susceptibility achieved in phase-modulated gates. |
Ball, Harrison; Biercuk, Michael J; Carvalho, Andre; Chen, Jiayin; Hush, Michael; Castro, Leonardo De A; Li, Li; Liebermann, Per J; Slatyer, Harry J; Edmunds, Claire; Frey, Virginia; Hempel, Cornelius; Milne, Alistair Software tools for quantum control: Improving quantum computer performance through noise and error suppression Journal Article arXiv, quant-ph (2001.04060), 2020. @article{ball2020software, title = {Software tools for quantum control: Improving quantum computer performance through noise and error suppression}, author = {Harrison Ball and Michael J Biercuk and Andre Carvalho and Jiayin Chen and Michael Hush and Leonardo De A Castro and Li Li and Per J Liebermann and Harry J Slatyer and Claire Edmunds and Virginia Frey and Cornelius Hempel and Alistair Milne}, url = {https://arxiv.org/abs/2001.04060}, year = {2020}, date = {2020-01-01}, journal = {arXiv}, volume = {quant-ph}, number = {2001.04060}, abstract = {Manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise in particular limits the performance and algorithmic capabilities experienced by end users. Fortunately, in both the NISQ era and beyond, quantum control enables the efficient execution of quantum logic operations and quantum algorithms exhibiting robustness to errors, without the need for complex logical encoding. We introduce the first commercial-grade software tools for quantum control in quantum computing research from Q-CTRL, serving the needs of hardware Rtextbackslash&D teams, algorithm developers, and end users. We survey quantum control and its role in combating noise in near-term devices; our primary focus is on quantum firmware, the low-level software solutions designed to enhance the stability of quantum computational hardware at the physical layer. We explain the benefits of quantum firmware not only in error suppression, but also in simplifying compilation protocols and enhancing the efficiency of quantum error correction. We provide an overview of Q-CTRL's software tools for creating and deploying quantum control solutions at various layers of the quantum computing software stack. We describe our software architecture leveraging both distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other quantum programming languages. We present a detailed technical overview of product features including a control-optimization engine, filter functions for general systems, and noise characterization. Finally, we present a series of case studies demonstrating the utility of quantum control solutions derived from these tools in improving the performance of trapped-ion and superconducting quantum computer hardware.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise in particular limits the performance and algorithmic capabilities experienced by end users. Fortunately, in both the NISQ era and beyond, quantum control enables the efficient execution of quantum logic operations and quantum algorithms exhibiting robustness to errors, without the need for complex logical encoding. We introduce the first commercial-grade software tools for quantum control in quantum computing research from Q-CTRL, serving the needs of hardware Rtextbackslash&D teams, algorithm developers, and end users. We survey quantum control and its role in combating noise in near-term devices; our primary focus is on quantum firmware, the low-level software solutions designed to enhance the stability of quantum computational hardware at the physical layer. We explain the benefits of quantum firmware not only in error suppression, but also in simplifying compilation protocols and enhancing the efficiency of quantum error correction. We provide an overview of Q-CTRL's software tools for creating and deploying quantum control solutions at various layers of the quantum computing software stack. We describe our software architecture leveraging both distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other quantum programming languages. We present a detailed technical overview of product features including a control-optimization engine, filter functions for general systems, and noise characterization. Finally, we present a series of case studies demonstrating the utility of quantum control solutions derived from these tools in improving the performance of trapped-ion and superconducting quantum computer hardware. |
Tuckett, David K; Bartlett, Stephen D; Flammia, Steven T; Brown, Benjamin J Fault-Tolerant Thresholds for the Surface Code in Excess of 5% under Biased Noise Journal Article Physical Review Letters, 124 (13), pp. 130501, 2020, ISSN: 0031-9007. @article{Tuckett.2020, title = {Fault-Tolerant Thresholds for the Surface Code in Excess of 5% under Biased Noise}, author = {David K Tuckett and Stephen D Bartlett and Steven T Flammia and Benjamin J Brown}, doi = {10.1103/physrevlett.124.130501}, issn = {0031-9007}, year = {2020}, date = {2020-01-01}, journal = {Physical Review Letters}, volume = {124}, number = {13}, pages = {130501}, abstract = {Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the noise is biased towards dephasing. Here we introduce an efficient high-threshold decoder for a noise-tailored surface code based on minimum-weight perfect matching. The decoder exploits the symmetries of its syndrome under the action of biased noise and generalizes to the fault-tolerant regime where measurements are unreliable. Using this decoder, we obtain fault-tolerant thresholds in excess of 6% for a phenomenological noise model in the limit where dephasing dominates. These gains persist even for modest noise biases: we find a threshold of ∼5% in an experimentally relevant regime where dephasing errors occur at a rate 100 times greater than bit-flip errors.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the noise is biased towards dephasing. Here we introduce an efficient high-threshold decoder for a noise-tailored surface code based on minimum-weight perfect matching. The decoder exploits the symmetries of its syndrome under the action of biased noise and generalizes to the fault-tolerant regime where measurements are unreliable. Using this decoder, we obtain fault-tolerant thresholds in excess of 6% for a phenomenological noise model in the limit where dephasing dominates. These gains persist even for modest noise biases: we find a threshold of ∼5% in an experimentally relevant regime where dephasing errors occur at a rate 100 times greater than bit-flip errors. |
Roberts, Sam; Bartlett, Stephen D Symmetry-Protected Self-Correcting Quantum Memories Journal Article Physical Review X, 10 (3), pp. 031041, 2020. @article{10.1103/physrevx.10.031041b, title = {Symmetry-Protected Self-Correcting Quantum Memories}, author = {Sam Roberts and Stephen D Bartlett}, doi = {10.1103/physrevx.10.031041}, year = {2020}, date = {2020-01-01}, journal = {Physical Review X}, volume = {10}, number = {3}, pages = {031041}, abstract = {A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D “cluster-state” model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D “cluster-state” model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally. |
Grimsmo, Arne L; Combes, Joshua; Baragiola, Ben Q Quantum computing with rotation-symmetric Bosonic codes Journal Article Physical Review X, 10 (1), pp. 011058, 2020. @article{grimsmo2020quantum, title = {Quantum computing with rotation-symmetric Bosonic codes}, author = {Arne L Grimsmo and Joshua Combes and Ben Q Baragiola}, year = {2020}, date = {2020-01-01}, journal = {Physical Review X}, volume = {10}, number = {1}, pages = {011058}, publisher = {APS}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Milne, Alistair R; Hempel, Cornelius; Li, Li; Edmunds, Claire L; Slatyer, Harry J; Ball, Harrison; Hush, Michael R; Biercuk, Michael J Quantum oscillator noise spectroscopy via displaced Schrödinger cat states Journal Article arXiv preprint arXiv:2010.04375, 2020. BibTeX | Links: @article{milne2020quantum, title = {Quantum oscillator noise spectroscopy via displaced Schrödinger cat states}, author = {Alistair R Milne and Cornelius Hempel and Li Li and Claire L Edmunds and Harry J Slatyer and Harrison Ball and Michael R Hush and Michael J Biercuk}, url = {https://arxiv.org/abs/2010.04375}, year = {2020}, date = {2020-01-01}, journal = {arXiv preprint arXiv:2010.04375}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
2019 |
Ball, H; Marciniak, Ch D; Wolf, R N; Hung, A T -H; Pyka, K; Biercuk, M J Site-resolved imaging of beryllium ion crystals in a high-optical-access Penning trap with inbore optomechanics Journal Article Review of Scientific Instruments, 90 (5), pp. 053103, 2019, ISSN: 0034-6748. @article{Ball.20198bj, title = {Site-resolved imaging of beryllium ion crystals in a high-optical-access Penning trap with inbore optomechanics}, author = {H Ball and Ch D Marciniak and R N Wolf and A T -H Hung and K Pyka and M J Biercuk}, url = {https://aip.scitation.org/doi/10.1063/1.5049506}, doi = {10.1063/1.5049506}, issn = {0034-6748}, year = {2019}, date = {2019-01-01}, journal = {Review of Scientific Instruments}, volume = {90}, number = {5}, pages = {053103}, abstract = {We present the design, construction, and characterization of an experimental system capable of supporting a broad class of quantum simulation experiments with hundreds of spin qubits using 9Be+ ions in a Penning trap. This article provides a detailed overview of the core optical and trapping subsystems and their integration. We begin with a description of a dual-trap design separating loading and experimental zones and associated vacuum infrastructure design. The experimental-zone trap electrodes are designed for wide-angle optical access (e.g., for lasers used to engineer spin-motional coupling across large ion crystals) while simultaneously providing a harmonic trapping potential. We describe a near-zero-loss liquid-cryogen-based superconducting magnet, employed in both trapping and establishing a quantization field for ion spin-states and equipped with a dual-stage remote-motor LN2/LHe recondenser. Experimental measurements using a nuclear magnetic resonance (NMR) probe demonstrate part-per-million homogeneity over 7 mm-diameter cylindrical volume, with no discernible effect on the measured NMR linewidth from pulse-tube operation. Next, we describe a custom-engineered inbore optomechanical system which delivers ultraviolet (UV) laser light to the trap and supports multiple aligned optical objectives for topview and sideview imaging in the experimental trap region. We describe design choices including the use of nonmagnetic goniometers and translation stages for precision alignment. Furthermore, the optomechanical system integrates UV-compatible fiber optics which decouple the system's alignment from remote light sources. Using this system, we present site-resolved images of ion crystals and demonstrate the ability to realize both planar and three-dimensional ion arrays via control of rotating wall electrodes and radial laser beams. Looking to future work, we include interferometric vibration measurements demonstrating root-mean-square trap motion of ∼33 nm (∼117 nm) in the axial (transverse) direction; both values can be reduced when operating the magnet in free-running mode. The paper concludes with an outlook toward extensions of the experimental setup, areas for improvement, and future experimental studies.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present the design, construction, and characterization of an experimental system capable of supporting a broad class of quantum simulation experiments with hundreds of spin qubits using 9Be+ ions in a Penning trap. This article provides a detailed overview of the core optical and trapping subsystems and their integration. We begin with a description of a dual-trap design separating loading and experimental zones and associated vacuum infrastructure design. The experimental-zone trap electrodes are designed for wide-angle optical access (e.g., for lasers used to engineer spin-motional coupling across large ion crystals) while simultaneously providing a harmonic trapping potential. We describe a near-zero-loss liquid-cryogen-based superconducting magnet, employed in both trapping and establishing a quantization field for ion spin-states and equipped with a dual-stage remote-motor LN2/LHe recondenser. Experimental measurements using a nuclear magnetic resonance (NMR) probe demonstrate part-per-million homogeneity over 7 mm-diameter cylindrical volume, with no discernible effect on the measured NMR linewidth from pulse-tube operation. Next, we describe a custom-engineered inbore optomechanical system which delivers ultraviolet (UV) laser light to the trap and supports multiple aligned optical objectives for topview and sideview imaging in the experimental trap region. We describe design choices including the use of nonmagnetic goniometers and translation stages for precision alignment. Furthermore, the optomechanical system integrates UV-compatible fiber optics which decouple the system's alignment from remote light sources. Using this system, we present site-resolved images of ion crystals and demonstrate the ability to realize both planar and three-dimensional ion arrays via control of rotating wall electrodes and radial laser beams. Looking to future work, we include interferometric vibration measurements demonstrating root-mean-square trap motion of ∼33 nm (∼117 nm) in the axial (transverse) direction; both values can be reduced when operating the magnet in free-running mode. The paper concludes with an outlook toward extensions of the experimental setup, areas for improvement, and future experimental studies. |
Yang, C H; Chan, K W; Harper, R; Huang, W; Evans, T; Hwang, J C C; Hensen, B; Laucht, A; Tanttu, T; Hudson, F E; Flammia, S T; Itoh, K M; Morello, A; Bartlett, S D; Dzurak, A S Silicon qubit fidelities approaching incoherent noise limits via pulse engineering Journal Article Nature Electronics, 2 (4), pp. 151–158, 2019. @article{Yang.2019, title = {Silicon qubit fidelities approaching incoherent noise limits via pulse engineering}, author = {C H Yang and K W Chan and R Harper and W Huang and T Evans and J C C Hwang and B Hensen and A Laucht and T Tanttu and F E Hudson and S T Flammia and K M Itoh and A Morello and S D Bartlett and A S Dzurak}, url = {https://www.nature.com/articles/s41928-019-0234-1.epdf?shared_access_token=dwgc0pOWyz17aQfkQBd4wtRgN0jAjWel9jnR3ZoTv0O-UqCO5w04UHpr1iaXzevFLT0JVyPpg9mA3x2230uknqWY4orZ4AuvqFwyDcjiIUIlYS9H_CiaXwr7TrJtnh4_b0MJCLVSEYws_x-aTqCHRw%3D%3D}, doi = {10.1038/s41928-019-0234-1}, year = {2019}, date = {2019-01-01}, journal = {Nature Electronics}, volume = {2}, number = {4}, pages = {151--158}, abstract = {Spin qubits created from gate-defined silicon metal–oxide–semiconductor quantum dots are a promising architecture for quantum computation. The high single qubit fidelities possible in these systems, combined with quantum error correcting codes, could potentially offer a route to fault-tolerant quantum computing. To achieve fault tolerance, however, gate error rates must be reduced to below a certain threshold and, in general, correlated errors must be removed. Here we show that pulse engineering techniques can be used to reduce the average Clifford gate error rates for silicon quantum dot spin qubits down to 0.043%. This represents a factor of three improvement over state-of-the-art silicon quantum dot devices and extends the randomized benchmarking coherence time to 9.4 ms. By including tomographically complete measurements in our randomized benchmarking, we infer a higher-order feature of the noise called the unitarity, which measures the coherence of noise. This, in turn, allows us to theoretically predict that average gate error rates as low as 0.026% may be achievable with further pulse improvements. These spin qubit fidelities are ultimately limited by incoherent noise, which we attribute to charge noise from the silicon device structure or the environment. Pulse engineering techniques can be used to reduce the average Clifford gate error rates for silicon quantum dot spin qubits down to 0.043%, a factor of three improvement over state-of-the-art silicon devices.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Spin qubits created from gate-defined silicon metal–oxide–semiconductor quantum dots are a promising architecture for quantum computation. The high single qubit fidelities possible in these systems, combined with quantum error correcting codes, could potentially offer a route to fault-tolerant quantum computing. To achieve fault tolerance, however, gate error rates must be reduced to below a certain threshold and, in general, correlated errors must be removed. Here we show that pulse engineering techniques can be used to reduce the average Clifford gate error rates for silicon quantum dot spin qubits down to 0.043%. This represents a factor of three improvement over state-of-the-art silicon quantum dot devices and extends the randomized benchmarking coherence time to 9.4 ms. By including tomographically complete measurements in our randomized benchmarking, we infer a higher-order feature of the noise called the unitarity, which measures the coherence of noise. This, in turn, allows us to theoretically predict that average gate error rates as low as 0.026% may be achievable with further pulse improvements. These spin qubit fidelities are ultimately limited by incoherent noise, which we attribute to charge noise from the silicon device structure or the environment. Pulse engineering techniques can be used to reduce the average Clifford gate error rates for silicon quantum dot spin qubits down to 0.043%, a factor of three improvement over state-of-the-art silicon devices. |
Tuckett, David K; Darmawan, Andrew S; Chubb, Christopher T; Bravyi, Sergey; Bartlett, Stephen D; Flammia, Steven T Tailoring Surface Codes for Highly Biased Noise Journal Article Physical Review X, 9 (4), pp. 041031, 2019. @article{Tuckett.2019, title = {Tailoring Surface Codes for Highly Biased Noise}, author = {David K Tuckett and Andrew S Darmawan and Christopher T Chubb and Sergey Bravyi and Stephen D Bartlett and Steven T Flammia}, doi = {10.1103/physrevx.9.041031}, year = {2019}, date = {2019-01-01}, journal = {Physical Review X}, volume = {9}, number = {4}, pages = {041031}, abstract = {The surface code, with a simple modification, exhibits ultrahigh error-correction thresholds when the noise is biased toward dephasing. Here, we identify features of the surface code responsible for these ultrahigh thresholds. We provide strong evidence that the threshold error rate of the surface code tracks the hashing bound exactly for all biases and show how to exploit these features to achieve significant improvement in the logical failure rate. First, we consider the infinite bias limit, meaning pure dephasing. We prove that the error threshold of the modified surface code for pure dephasing noise is 50%, i.e., that all qubits are fully dephased, and this threshold can be achieved by a polynomial time-decoding algorithm. We demonstrate that the subthreshold behavior of the code depends critically on the precise shape and boundary conditions of the code. That is, for rectangular surface codes with standard rough or smooth open boundaries, it is controlled by the parameter g=gcd(j,k), where j and k are dimensions of the surface code lattice. We demonstrate a significant improvement in the logical failure rate with pure dephasing for coprime codes that have g=1 and closely related rotated codes, which have a modified boundary. The effect is dramatic: The same logical failure rate achievable with a square surface code and n physical qubits can be obtained with a coprime or rotated surface code using only O(n) physical qubits. Finally, we use approximate maximum-likelihood decoding to demonstrate that this improvement persists for a general Pauli noise biased toward dephasing. In particular, comparing with a square surface code, we observe a significant improvement in the logical failure rate against biased noise using a rotated surface code with approximately half the number of physical qubits.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The surface code, with a simple modification, exhibits ultrahigh error-correction thresholds when the noise is biased toward dephasing. Here, we identify features of the surface code responsible for these ultrahigh thresholds. We provide strong evidence that the threshold error rate of the surface code tracks the hashing bound exactly for all biases and show how to exploit these features to achieve significant improvement in the logical failure rate. First, we consider the infinite bias limit, meaning pure dephasing. We prove that the error threshold of the modified surface code for pure dephasing noise is 50%, i.e., that all qubits are fully dephased, and this threshold can be achieved by a polynomial time-decoding algorithm. We demonstrate that the subthreshold behavior of the code depends critically on the precise shape and boundary conditions of the code. That is, for rectangular surface codes with standard rough or smooth open boundaries, it is controlled by the parameter g=gcd(j,k), where j and k are dimensions of the surface code lattice. We demonstrate a significant improvement in the logical failure rate with pure dephasing for coprime codes that have g=1 and closely related rotated codes, which have a modified boundary. The effect is dramatic: The same logical failure rate achievable with a square surface code and n physical qubits can be obtained with a coprime or rotated surface code using only O(n) physical qubits. Finally, we use approximate maximum-likelihood decoding to demonstrate that this improvement persists for a general Pauli noise biased toward dephasing. In particular, comparing with a square surface code, we observe a significant improvement in the logical failure rate against biased noise using a rotated surface code with approximately half the number of physical qubits. |
2018 |
Hempel, Cornelius; Maier, Christine; Romero, Jonathan; McClean, Jarrod; Monz, Thomas; Shen, Heng; Jurcevic, Petar; Lanyon, Ben P; Love, Peter; Babbush, Ryan; Aspuru-Guzik, Alán; Blatt, Rainer; Roos, Christian F Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator Journal Article Physical Review X, 8 (3), pp. 031022, 2018. @article{Hempel.2018, title = {Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator}, author = {Cornelius Hempel and Christine Maier and Jonathan Romero and Jarrod McClean and Thomas Monz and Heng Shen and Petar Jurcevic and Ben P Lanyon and Peter Love and Ryan Babbush and Alán Aspuru-Guzik and Rainer Blatt and Christian F Roos}, url = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.031022}, doi = {10.1103/physrevx.8.031022}, year = {2018}, date = {2018-01-01}, journal = {Physical Review X}, volume = {8}, number = {3}, pages = {031022}, abstract = {Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground-state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multiqubit quantum simulators.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground-state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multiqubit quantum simulators. |
Gupta, Riddhi Swaroop; Biercuk, Michael J Machine Learning for Predictive Estimation of Qubit Dynamics Subject to Dephasing Journal Article Physical Review Applied, 9 (6), pp. 064042, 2018. @article{Gupta.2018, title = {Machine Learning for Predictive Estimation of Qubit Dynamics Subject to Dephasing}, author = {Riddhi Swaroop Gupta and Michael J Biercuk}, url = {https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.9.064042?utm_source=email&utm_medium=email&utm_campaign=prapplied-alert}, doi = {10.1103/physrevapplied.9.064042}, year = {2018}, date = {2018-01-01}, journal = {Physical Review Applied}, volume = {9}, number = {6}, pages = {064042}, abstract = {Decoherence remains a major challenge in quantum computing hardware, and a variety of physical-layer controls provide opportunities to mitigate the impact of this phenomenon through feedback and feed-forward control. In this work, we compare a variety of machine-learning algorithms derived from diverse fields for the task of state estimation (retrodiction) and forward prediction of future qubit-state evolution for a single qubit subject to classical, non-Markovian dephasing. Our approaches involve the construction of a dynamical model capturing qubit dynamics via autoregressive or Fourier-type protocols using only a historical record of projective measurements. A detailed comparison of achievable prediction horizons, model robustness, and measurement-noise-filtering capabilities for Kalman filters (KFs) and Gaussian process regression (GPR) algorithms is provided. We demonstrate superior performance from the autoregressive KF relative to Fourier-based KF approaches and focus on the role of filter optimization in achieving suitable performance. Finally, we examine several realizations of GPR using different kernels and discover that these approaches are generally not suitable for forward prediction. We highlight the linkages between predictive performance and kernel structure, and we identify ways in which forward predictions are susceptible to numerical artifacts.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Decoherence remains a major challenge in quantum computing hardware, and a variety of physical-layer controls provide opportunities to mitigate the impact of this phenomenon through feedback and feed-forward control. In this work, we compare a variety of machine-learning algorithms derived from diverse fields for the task of state estimation (retrodiction) and forward prediction of future qubit-state evolution for a single qubit subject to classical, non-Markovian dephasing. Our approaches involve the construction of a dynamical model capturing qubit dynamics via autoregressive or Fourier-type protocols using only a historical record of projective measurements. A detailed comparison of achievable prediction horizons, model robustness, and measurement-noise-filtering capabilities for Kalman filters (KFs) and Gaussian process regression (GPR) algorithms is provided. We demonstrate superior performance from the autoregressive KF relative to Fourier-based KF approaches and focus on the role of filter optimization in achieving suitable performance. Finally, we examine several realizations of GPR using different kernels and discover that these approaches are generally not suitable for forward prediction. We highlight the linkages between predictive performance and kernel structure, and we identify ways in which forward predictions are susceptible to numerical artifacts. |
Mavadia, S; Edmunds, C L; Hempel, C; Ball, H; Roy, F; Stace, T M; Biercuk, M J Experimental quantum verification in the presence of temporally correlated noise Journal Article npj Quantum Information, 4 (1), pp. 7, 2018. @article{Mavadia.2018, title = {Experimental quantum verification in the presence of temporally correlated noise}, author = {S Mavadia and C L Edmunds and C Hempel and H Ball and F Roy and T M Stace and M J Biercuk}, url = {https://doi.org/10.1038/s41534-017-0052-0}, doi = {10.1038/s41534-017-0052-0}, year = {2018}, date = {2018-01-01}, journal = {npj Quantum Information}, volume = {4}, number = {1}, pages = {7}, abstract = {Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171Yb+ ion-qubit and inject engineered noise ∝σtextasciicircumz to probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated σtextasciicircumz errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated σtextasciicircumx or σtextasciicircumy errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments. Experiments reveal that the presence of correlated noise may compromise the interpretation of techniques for the validation of quantum hardware. A team led by Michael Biercuk at Australia’s University of Sydney and National Measurement Institute, carried out experiments on a single trapped 171Yb+ ion to test the reliability of widespread techniques for characterisation, validation and verification of quantum hardware. Although error processes are often assumed to be statistically independent, in practice slowly varying external fields may introduce temporal correlations in noise. The experiments revealed that the outcome of randomised benchmarking and gate-set tomography differ substantially in presence of correlated noise, and reveal an unexpected sequence-dependent behaviour. These results demonstrate that the reliability of standard performance benchmarking techniques is strongly influenced by the statistical properties of the noise affecting the hardware, complicating direct comparisons between experiments.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171Yb+ ion-qubit and inject engineered noise ∝σtextasciicircumz to probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated σtextasciicircumz errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated σtextasciicircumx or σtextasciicircumy errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments. Experiments reveal that the presence of correlated noise may compromise the interpretation of techniques for the validation of quantum hardware. A team led by Michael Biercuk at Australia’s University of Sydney and National Measurement Institute, carried out experiments on a single trapped 171Yb+ ion to test the reliability of widespread techniques for characterisation, validation and verification of quantum hardware. Although error processes are often assumed to be statistically independent, in practice slowly varying external fields may introduce temporal correlations in noise. The experiments revealed that the outcome of randomised benchmarking and gate-set tomography differ substantially in presence of correlated noise, and reveal an unexpected sequence-dependent behaviour. These results demonstrate that the reliability of standard performance benchmarking techniques is strongly influenced by the statistical properties of the noise affecting the hardware, complicating direct comparisons between experiments. |
Tuckett, David K; Bartlett, Stephen D; Flammia, Steven T Ultrahigh Error Threshold for Surface Codes with Biased Noise Journal Article Physical Review Letters, 120 (5), pp. 050505, 2018, ISSN: 0031-9007. @article{Tuckett.2018, title = {Ultrahigh Error Threshold for Surface Codes with Biased Noise}, author = {David K Tuckett and Stephen D Bartlett and Steven T Flammia}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.050505?utm_source=email&utm_medium=email&utm_campaign=prl-alert}, doi = {10.1103/physrevlett.120.050505}, issn = {0031-9007}, year = {2018}, date = {2018-01-01}, journal = {Physical Review Letters}, volume = {120}, number = {5}, pages = {050505}, abstract = {We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara, and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is, in fact, at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara, and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is, in fact, at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes. |
2017 |
Frey, V M; Mavadia, S; Norris, L M; de Ferranti, W; Lucarelli, D; Viola, L; Biercuk, M J Application of optimal band-limited control protocols to quantum noise sensing Journal Article Nature Communications, 8 (1), pp. 2189, 2017. @article{Frey.2017, title = {Application of optimal band-limited control protocols to quantum noise sensing}, author = {V M Frey and S Mavadia and L M Norris and W de Ferranti and D Lucarelli and L Viola and M J Biercuk}, url = {https://www.nature.com/articles/s41467-017-02298-2}, doi = {10.1038/s41467-017-02298-2}, year = {2017}, date = {2017-01-01}, journal = {Nature Communications}, volume = {8}, number = {1}, pages = {2189}, abstract = {Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. However, in common control routines out-of-band spectral leakage complicates interpretation of the sensor’s signal. In this work, we leverage discrete prolate spheroidal sequences (a.k.a. Slepian sequences) to synthesize provably optimal narrowband controls ideally suited to spectral estimation of a qubit’s noisy environment. Experiments with trapped ions demonstrate how spectral leakage may be reduced by orders of magnitude over conventional controls when a near resonant driving field is modulated by Slepians, and how the desired narrowband sensitivity may be tuned using concepts from RF engineering. We demonstrate that classical multitaper techniques for spectral analysis can be ported to the quantum domain and combined with Bayesian estimation tools to experimentally reconstruct complex noise spectra. We then deploy these techniques to identify previously immeasurable frequency-resolved amplitude noise in our qubit’s microwave synthesis chain. Control of qubits’ frequency response by dynamical decoupling is usually vexed by control’s out-of-band harmonics, a problem known in metrology as “spectral leakage”. Here, the authors reduce this problem by orders of magnitude exploiting discrete prolate spheroidal sequences to control a trapped-ion qubit.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. However, in common control routines out-of-band spectral leakage complicates interpretation of the sensor’s signal. In this work, we leverage discrete prolate spheroidal sequences (a.k.a. Slepian sequences) to synthesize provably optimal narrowband controls ideally suited to spectral estimation of a qubit’s noisy environment. Experiments with trapped ions demonstrate how spectral leakage may be reduced by orders of magnitude over conventional controls when a near resonant driving field is modulated by Slepians, and how the desired narrowband sensitivity may be tuned using concepts from RF engineering. We demonstrate that classical multitaper techniques for spectral analysis can be ported to the quantum domain and combined with Bayesian estimation tools to experimentally reconstruct complex noise spectra. We then deploy these techniques to identify previously immeasurable frequency-resolved amplitude noise in our qubit’s microwave synthesis chain. Control of qubits’ frequency response by dynamical decoupling is usually vexed by control’s out-of-band harmonics, a problem known in metrology as “spectral leakage”. Here, the authors reduce this problem by orders of magnitude exploiting discrete prolate spheroidal sequences to control a trapped-ion qubit. |
Bermudez, A; Xu, X; Nigmatullin, R; O’Gorman, J; Negnevitsky, V; Schindler, P; Monz, T; Poschinger, U G; Hempel, C; Home, J; Schmidt-Kaler, F; Biercuk, M; Blatt, R; Benjamin, S; Müller, M Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum Computation Journal Article Physical Review X, 7 (4), pp. 041061, 2017. @article{Bermudez.20174vd, title = {Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum Computation}, author = {A Bermudez and X Xu and R Nigmatullin and J O’Gorman and V Negnevitsky and P Schindler and T Monz and U G Poschinger and C Hempel and J Home and F Schmidt-Kaler and M Biercuk and R Blatt and S Benjamin and M Müller}, url = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.041061}, doi = {10.1103/physrevx.7.041061}, year = {2017}, date = {2017-01-01}, journal = {Physical Review X}, volume = {7}, number = {4}, pages = {041061}, abstract = {A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that will be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC and a physically motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realized in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements described here, this platform is a very promising candidate for fault-tolerant quantum computation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that will be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC and a physically motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realized in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements described here, this platform is a very promising candidate for fault-tolerant quantum computation. |
Mavadia, Sandeep; Frey, Virginia; Sastrawan, Jarrah; Dona, Stephen; Biercuk, Michael J Prediction and real-time compensation of qubit decoherence via machine learning Journal Article Nature Communications, 8 (1), pp. 14106, 2017. @article{Mavadia.2017, title = {Prediction and real-time compensation of qubit decoherence via machine learning}, author = {Sandeep Mavadia and Virginia Frey and Jarrah Sastrawan and Stephen Dona and Michael J Biercuk}, doi = {10.1038/ncomms14106}, year = {2017}, date = {2017-01-01}, journal = {Nature Communications}, volume = {8}, number = {1}, pages = {14106}, abstract = {The wide-ranging adoption of quantum technologies requires practical, high-performance advances in our ability to maintain quantum coherence while facing the challenge of state collapse under measurement. Here we use techniques from control theory and machine learning to predict the future evolution of a qubit’s state; we deploy this information to suppress stochastic, semiclassical decoherence, even when access to measurements is limited. First, we implement a time-division multiplexed approach, interleaving measurement periods with periods of unsupervised but stabilised operation during which qubits are available, for example, in quantum information experiments. Second, we employ predictive feedback during sequential but time delayed measurements to reduce the Dick effect as encountered in passive frequency standards. Both experiments demonstrate significant improvements in qubit-phase stability over ‘traditional’ measurement-based feedback approaches by exploiting time domain correlations in the noise processes. This technique requires no additional hardware and is applicable to all two-level quantum systems where projective measurements are possible. Control engineering techniques are promising for realizing stable quantum systems to counter their extreme fragility. Here the authors use techniques from machine learning to enable real-time feedback suppression of decoherence in a trapped ion qubit by predicting its future stochastic evolution.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The wide-ranging adoption of quantum technologies requires practical, high-performance advances in our ability to maintain quantum coherence while facing the challenge of state collapse under measurement. Here we use techniques from control theory and machine learning to predict the future evolution of a qubit’s state; we deploy this information to suppress stochastic, semiclassical decoherence, even when access to measurements is limited. First, we implement a time-division multiplexed approach, interleaving measurement periods with periods of unsupervised but stabilised operation during which qubits are available, for example, in quantum information experiments. Second, we employ predictive feedback during sequential but time delayed measurements to reduce the Dick effect as encountered in passive frequency standards. Both experiments demonstrate significant improvements in qubit-phase stability over ‘traditional’ measurement-based feedback approaches by exploiting time domain correlations in the noise processes. This technique requires no additional hardware and is applicable to all two-level quantum systems where projective measurements are possible. Control engineering techniques are promising for realizing stable quantum systems to counter their extreme fragility. Here the authors use techniques from machine learning to enable real-time feedback suppression of decoherence in a trapped ion qubit by predicting its future stochastic evolution. |
Marciniak, Christian D; Ball, Harrison B; Hung, Alex T -H; Biercuk, Michael J Towards fully commercial, UV-compatible fiber patch cords Journal Article Optics Express, 25 (14), pp. 15643, 2017. @article{Marciniak.2017, title = {Towards fully commercial, UV-compatible fiber patch cords}, author = {Christian D Marciniak and Harrison B Ball and Alex T -H Hung and Michael J Biercuk}, doi = {10.1364/oe.25.015643}, year = {2017}, date = {2017-01-01}, journal = {Optics Express}, volume = {25}, number = {14}, pages = {15643}, abstract = {We present and analyze two pathways to produce commercial optical-fiber patch cords with stable long-term transmission in the ultraviolet (UV) at powers up to textbackslashtextasciitilde 200 mW, and typical bulk transmission between 66-75 %. Commercial fiber patch cords in the UV are of great interest across a wide variety of scientific applications ranging from biology to metrology, and the lack of availability has yet to be suitably addressed. We provide a guide to producing such solarization-resistant, hydrogen-passivated, polarization-maintaining, connectorized and jacketed optical fibers compatible with demanding scientific and industrial applications. Our presentation describes the fabrication and hydrogen loading procedure in detail and presents a high-pressure vessel design, calculations of required H2 loading times, and information on patch cord handling and the mitigation of bending sensitivities. Transmission at 313 nm is measured over many months for cumulative energy on the fiber output of > 10 kJ with no demonstrable degradation due to UV solarization, in contrast to standard uncured fibers. Polarization sensitivity and stability are characterized yielding polarization extinction ratios between 15 dB and 25 dB at 313 nm, where we find patch cords become linearly polarizing. We observe that particle deposition at the fiber facet induced by high-intensity UV exposure can (reversibly) deteriorate patch cord performance and describe a technique for nitrogen purging of fiber collimators which mitigates this phenomenon.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present and analyze two pathways to produce commercial optical-fiber patch cords with stable long-term transmission in the ultraviolet (UV) at powers up to textbackslashtextasciitilde 200 mW, and typical bulk transmission between 66-75 %. Commercial fiber patch cords in the UV are of great interest across a wide variety of scientific applications ranging from biology to metrology, and the lack of availability has yet to be suitably addressed. We provide a guide to producing such solarization-resistant, hydrogen-passivated, polarization-maintaining, connectorized and jacketed optical fibers compatible with demanding scientific and industrial applications. Our presentation describes the fabrication and hydrogen loading procedure in detail and presents a high-pressure vessel design, calculations of required H2 loading times, and information on patch cord handling and the mitigation of bending sensitivities. Transmission at 313 nm is measured over many months for cumulative energy on the fiber output of > 10 kJ with no demonstrable degradation due to UV solarization, in contrast to standard uncured fibers. Polarization sensitivity and stability are characterized yielding polarization extinction ratios between 15 dB and 25 dB at 313 nm, where we find patch cords become linearly polarizing. We observe that particle deposition at the fiber facet induced by high-intensity UV exposure can (reversibly) deteriorate patch cord performance and describe a technique for nitrogen purging of fiber collimators which mitigates this phenomenon. |
Robertson, Alan; Granade, Christopher; Bartlett, Stephen D; Flammia, Steven T Tailored Codes for Small Quantum Memories Journal Article Physical Review Applied, 8 (6), pp. 064004 EP –, 2017. @article{Robertson.2017, title = {Tailored Codes for Small Quantum Memories}, author = {Alan Robertson and Christopher Granade and Stephen D Bartlett and Steven T Flammia}, year = {2017}, date = {2017-01-01}, journal = {Physical Review Applied}, volume = {8}, number = {6}, pages = {064004 EP --}, abstract = {We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10,000 randomly selected stabilizer codes of comparable experimental complexity. Tailored codes can even outperform the Steane code with realistic experimental noise, and without any increase in the experimental complexity, as we demonstrate by comparison in the observed error model in a recent 7-qubit trapped ion experiment.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10,000 randomly selected stabilizer codes of comparable experimental complexity. Tailored codes can even outperform the Steane code with realistic experimental noise, and without any increase in the experimental complexity, as we demonstrate by comparison in the observed error model in a recent 7-qubit trapped ion experiment. |
2016 |
Ball, Harrison; Oliver, William D; Biercuk, Michael J The role of master clock stability in quantum information processing Journal Article npj Quantum Information, 2 (1), pp. 16033, 2016. @article{Ball.2016lq8, title = {The role of master clock stability in quantum information processing}, author = {Harrison Ball and William D Oliver and Michael J Biercuk}, url = {http://www.nature.com/articles/npjqi201633?WT.ec_id=NPJQI-201611&spMailingID=52876976&spUserID=MTc5OTg2NTM4NTc4S0&spJobID=1048210951&spReportId=MTA0ODIxMDk1MQS2}, doi = {10.1038/npjqi.2016.33}, year = {2016}, date = {2016-01-01}, journal = {npj Quantum Information}, volume = {2}, number = {1}, pages = {16033}, abstract = {Experimentalists seeking to improve the coherent lifetimes of quantum bits have generally focused on mitigating decoherence mechanisms through, for example, improvements to qubit designs and materials, and system isolation from environmental perturbations. In the case of the phase degree of freedom in a quantum superposition, however, the coherence that must be preserved is not solely internal to the qubit, but rather necessarily includes that of the qubit relative to the ‘master clock’ (e.g., a local oscillator) that governs its control system. In this manuscript, we articulate the impact of instabilities in the master clock on qubit phase coherence and provide tools to calculate the contributions to qubit error arising from these processes. We first connect standard oscillator phase-noise metrics to their corresponding qubit dephasing spectral densities. We then use representative lab-grade and performance-grade oscillator specifications to calculate operational fidelity bounds on trapped-ion and superconducting qubits with relatively slow and fast operation times. We discuss the relevance of these bounds for quantum error correction in contemporary experiments and future large-scale quantum information systems, and consider potential means to improve master clock stability.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Experimentalists seeking to improve the coherent lifetimes of quantum bits have generally focused on mitigating decoherence mechanisms through, for example, improvements to qubit designs and materials, and system isolation from environmental perturbations. In the case of the phase degree of freedom in a quantum superposition, however, the coherence that must be preserved is not solely internal to the qubit, but rather necessarily includes that of the qubit relative to the ‘master clock’ (e.g., a local oscillator) that governs its control system. In this manuscript, we articulate the impact of instabilities in the master clock on qubit phase coherence and provide tools to calculate the contributions to qubit error arising from these processes. We first connect standard oscillator phase-noise metrics to their corresponding qubit dephasing spectral densities. We then use representative lab-grade and performance-grade oscillator specifications to calculate operational fidelity bounds on trapped-ion and superconducting qubits with relatively slow and fast operation times. We discuss the relevance of these bounds for quantum error correction in contemporary experiments and future large-scale quantum information systems, and consider potential means to improve master clock stability. |
Ball, Harrison; Stace, Thomas M; Flammia, Steven T; Biercuk, Michael J Effect of noise correlations on randomized benchmarking Journal Article Physical Review A, 93 (2), pp. 022303, 2016, ISSN: 2469-9926. @article{Ball.2016b, title = {Effect of noise correlations on randomized benchmarking}, author = {Harrison Ball and Thomas M Stace and Steven T Flammia and Michael J Biercuk}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.022303}, doi = {10.1103/physreva.93.022303}, issn = {2469-9926}, year = {2016}, date = {2016-01-01}, journal = {Physical Review A}, volume = {93}, number = {2}, pages = {022303}, abstract = {Among the most popular and well-studied quantum characterization, verification, and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in “Pauli space.” Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a Γ distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes—consistent with existing experimental data—highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Among the most popular and well-studied quantum characterization, verification, and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in “Pauli space.” Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a Γ distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes—consistent with existing experimental data—highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation. |
Britton, J W; Bohnet, J G; Sawyer, B C; Uys, H; Biercuk, M J; Bollinger, J J Vibration-induced field fluctuations in a superconducting magnet Journal Article Physical Review A, 93 (6), pp. 062511, 2016, ISSN: 2469-9926. @article{Britton.2016, title = {Vibration-induced field fluctuations in a superconducting magnet}, author = {J W Britton and J G Bohnet and B C Sawyer and H Uys and M J Biercuk and J J Bollinger}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.062511}, doi = {10.1103/physreva.93.062511}, issn = {2469-9926}, year = {2016}, date = {2016-01-01}, journal = {Physical Review A}, volume = {93}, number = {6}, pages = {062511}, abstract = {Superconducting magnets enable precise control of nuclear and electron spins, and are used in experiments that explore biological and condensed-matter systems, and fundamental atomic particles. In high-precision applications, a common view is that slow (<1Hz) drift of the homogeneous magnetic-field limits control and measurement precision. We report on previously undocumented higher-frequency field noise (10–200 Hz) that limits the coherence time of Be+9 electron-spin qubits in the 4.46-T field of a superconducting magnet. We measure a spin-echo T2 coherence time of ∼6ms for the Be+9 electron-spin resonance at 124GHz, limited by part-per-billion fractional fluctuations in the magnet's homogeneous field. Vibration isolation of the magnet improved T2 to ∼50 ms.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Superconducting magnets enable precise control of nuclear and electron spins, and are used in experiments that explore biological and condensed-matter systems, and fundamental atomic particles. In high-precision applications, a common view is that slow (<1Hz) drift of the homogeneous magnetic-field limits control and measurement precision. We report on previously undocumented higher-frequency field noise (10–200 Hz) that limits the coherence time of Be+9 electron-spin qubits in the 4.46-T field of a superconducting magnet. We measure a spin-echo T2 coherence time of ∼6ms for the Be+9 electron-spin resonance at 124GHz, limited by part-per-billion fractional fluctuations in the magnet's homogeneous field. Vibration isolation of the magnet improved T2 to ∼50 ms. |
Ball, Harrison; Nguyen, Trung; Leong, Philip H W; Biercuk, Michael J Functional Basis for Efficient Physical Layer Classical Control in Quantum Processors Journal Article Physical Review Applied, 6 (6), pp. 064009, 2016, ISSN: 2331-7019. @article{Ball.2016gh5, title = {Functional Basis for Efficient Physical Layer Classical Control in Quantum Processors}, author = {Harrison Ball and Trung Nguyen and Philip H W Leong and Michael J Biercuk}, url = {http://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.6.064009?utm_source=email&utm_medium=email&utm_campaign=prapplied-alert}, doi = {10.1103/physrevapplied.6.064009}, issn = {2331-7019}, year = {2016}, date = {2016-01-01}, journal = {Physical Review Applied}, volume = {6}, number = {6}, pages = {064009}, abstract = {The rapid progress seen in the development of quantum-coherent devices for information processing has motivated serious consideration of quantum computer architecture and organization. One topic which remains open for investigation and optimization relates to the design of the classical-quantum interface, where control operations on individual qubits are applied according to higher-level algorithms; accommodating competing demands on performance and scalability remains a major outstanding challenge. In this work, we present a resource-efficient, scalable framework for the implementation of embedded physical layer classical controllers for quantum-information systems. Design drivers and key functionalities are introduced, leading to the selection of Walsh functions as an effective functional basis for both programing and controller hardware implementation. This approach leverages the simplicity of real-time Walsh-function generation in classical digital hardware, and the fact that a wide variety of physical layer controls, such as dynamic error suppression, are known to fall within the Walsh family. We experimentally implement a real-time field-programmable-gate-array-based Walsh controller producing Walsh timing signals and Walsh-synthesized analog waveforms appropriate for critical tasks in error-resistant quantum control and noise characterization. These demonstrations represent the first step towards a unified framework for the realization of physical layer controls compatible with large-scale quantum-information processing.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The rapid progress seen in the development of quantum-coherent devices for information processing has motivated serious consideration of quantum computer architecture and organization. One topic which remains open for investigation and optimization relates to the design of the classical-quantum interface, where control operations on individual qubits are applied according to higher-level algorithms; accommodating competing demands on performance and scalability remains a major outstanding challenge. In this work, we present a resource-efficient, scalable framework for the implementation of embedded physical layer classical controllers for quantum-information systems. Design drivers and key functionalities are introduced, leading to the selection of Walsh functions as an effective functional basis for both programing and controller hardware implementation. This approach leverages the simplicity of real-time Walsh-function generation in classical digital hardware, and the fact that a wide variety of physical layer controls, such as dynamic error suppression, are known to fall within the Walsh family. We experimentally implement a real-time field-programmable-gate-array-based Walsh controller producing Walsh timing signals and Walsh-synthesized analog waveforms appropriate for critical tasks in error-resistant quantum control and noise characterization. These demonstrations represent the first step towards a unified framework for the realization of physical layer controls compatible with large-scale quantum-information processing. |
2015 |
Ball, Harrison; Biercuk, Michael J Walsh-synthesized noise filters for quantum logic Journal Article EPJ Quantum Technology, 2 (1), pp. 11, 2015. @article{Ball.2015, title = {Walsh-synthesized noise filters for quantum logic}, author = {Harrison Ball and Michael J Biercuk}, url = {https://epjquantumtechnology.springeropen.com/articles/10.1140/epjqt/s40507-015-0022-4}, doi = {10.1140/epjqt/s40507-015-0022-4}, year = {2015}, date = {2015-01-01}, journal = {EPJ Quantum Technology}, volume = {2}, number = {1}, pages = {11}, abstract = {We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance. |
Fogarty, M A; Veldhorst, M; Harper, R; Yang, C H; Bartlett, S D; Flammia, S T; Dzurak, A S Nonexponential fidelity decay in randomized benchmarking with low-frequency noise Journal Article Physical Review A, 92 (2), pp. 022326, 2015, ISSN: 1050-2947. @article{Fogarty.2015, title = {Nonexponential fidelity decay in randomized benchmarking with low-frequency noise}, author = {M A Fogarty and M Veldhorst and R Harper and C H Yang and S D Bartlett and S T Flammia and A S Dzurak}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.022326}, doi = {10.1103/physreva.92.022326}, issn = {1050-2947}, year = {2015}, date = {2015-01-01}, journal = {Physical Review A}, volume = {92}, number = {2}, pages = {022326}, abstract = {We show that nonexponential fidelity decays in randomized benchmarking experiments on quantum-dot qubits are consistent with numerical simulations that incorporate low-frequency noise and correspond to a control fidelity that varies slowly with time. By expanding standard randomized benchmarking analysis to this experimental regime, we find that such nonexponential decays are better modeled by multiple exponential decay rates, leading to an instantaneous control fidelity for isotopically purified silicon metal-oxide-semiconductor quantum-dot qubits which is 98.9% when the low-frequency noise causes large detuning but can be as high as 99.9% when the qubit is driven on resonance and system calibrations are favorable. These advances in qubit characterization and validation methods underpin the considerable prospects for silicon as a qubit platform for fault-tolerant quantum computation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We show that nonexponential fidelity decays in randomized benchmarking experiments on quantum-dot qubits are consistent with numerical simulations that incorporate low-frequency noise and correspond to a control fidelity that varies slowly with time. By expanding standard randomized benchmarking analysis to this experimental regime, we find that such nonexponential decays are better modeled by multiple exponential decay rates, leading to an instantaneous control fidelity for isotopically purified silicon metal-oxide-semiconductor quantum-dot qubits which is 98.9% when the low-frequency noise causes large detuning but can be as high as 99.9% when the qubit is driven on resonance and system calibrations are favorable. These advances in qubit characterization and validation methods underpin the considerable prospects for silicon as a qubit platform for fault-tolerant quantum computation. |
2014 |
Green, Todd J; Biercuk, Michael J Phase-Modulated Decoupling and Error Suppression in Qubit-Oscillator Systems Journal Article Physical Review Letters, 114 (12), pp. 120502, 2014, ISSN: 0031-9007. @article{Green.2015, title = {Phase-Modulated Decoupling and Error Suppression in Qubit-Oscillator Systems}, author = {Todd J Green and Michael J Biercuk}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.120502}, doi = {10.1103/physrevlett.114.120502}, issn = {0031-9007}, year = {2014}, date = {2014-01-01}, journal = {Physical Review Letters}, volume = {114}, number = {12}, pages = {120502}, abstract = {We present a scheme designed to suppress the dominant source of infidelity in entangling gates between quantum systems coupled through intermediate bosonic oscillator modes. Such systems are particularly susceptible to residual qubit-oscillator entanglement at the conclusion of a gate period that reduces the fidelity of the target entangling operation. We demonstrate how the exclusive use of discrete shifts in the phase of the field moderating the qubit-oscillator interaction is sufficient to both ensure multiple oscillator modes are decoupled and to suppress the effects of fluctuations in the driving field. This approach is amenable to a wide variety of technical implementations including geometric phase gates in superconducting qubits and the Molmer-Sorensen gate for trapped ions. We present detailed example protocols tailored to trapped-ion experiments and demonstrate that our approach has the potential to enable multiqubit gate implementation with a significant reduction in technical complexity relative to previously demonstrated protocols.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a scheme designed to suppress the dominant source of infidelity in entangling gates between quantum systems coupled through intermediate bosonic oscillator modes. Such systems are particularly susceptible to residual qubit-oscillator entanglement at the conclusion of a gate period that reduces the fidelity of the target entangling operation. We demonstrate how the exclusive use of discrete shifts in the phase of the field moderating the qubit-oscillator interaction is sufficient to both ensure multiple oscillator modes are decoupled and to suppress the effects of fluctuations in the driving field. This approach is amenable to a wide variety of technical implementations including geometric phase gates in superconducting qubits and the Molmer-Sorensen gate for trapped ions. We present detailed example protocols tailored to trapped-ion experiments and demonstrate that our approach has the potential to enable multiqubit gate implementation with a significant reduction in technical complexity relative to previously demonstrated protocols. |
Hayes, David; Flammia, Steven T; Biercuk, Michael J Programmable quantum simulation by dynamic Hamiltonian engineering Journal Article New Journal of Physics, 16 (8), pp. 083027, 2014, ISSN: 1367-2630. @article{Hayes.2014, title = {Programmable quantum simulation by dynamic Hamiltonian engineering}, author = {David Hayes and Steven T Flammia and Michael J Biercuk}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/16/8/083027}, doi = {10.1088/1367-2630/16/8/083027}, issn = {1367-2630}, year = {2014}, date = {2014-01-01}, journal = {New Journal of Physics}, volume = {16}, number = {8}, pages = {083027}, abstract = {Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions and relativistic quantum mechanics. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin- XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries. We show that determining the appropriate 'program' of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions and relativistic quantum mechanics. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin- XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries. We show that determining the appropriate 'program' of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information. |
Lee, Michael W; Jarratt, Marie Claire; Marciniak, Christian; Biercuk, Michael J Frequency stabilization of a 369 nm diode laser by nonlinear spectroscopy of Ytterbium ions in a discharge Journal Article Optics Express, 22 (6), pp. 7210, 2014. @article{Lee.20149r9, title = {Frequency stabilization of a 369 nm diode laser by nonlinear spectroscopy of Ytterbium ions in a discharge}, author = {Michael W Lee and Marie Claire Jarratt and Christian Marciniak and Michael J Biercuk}, url = {http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-7210}, doi = {10.1364/oe.22.007210}, year = {2014}, date = {2014-01-01}, journal = {Optics Express}, volume = {22}, number = {6}, pages = {7210}, abstract = {We demonstrate stabilization of an ultraviolet diode laser via Doppler-free spectroscopy of Ytterbium ions in a discharge. Our technique employs polarization spectroscopy, which produces a natural dispersive lineshape whose zero-crossing is largely immune to environmental drifts, making this signal an ideal absolute frequency reference for Yb+ ion trapping experiments. We stabilize an external-cavity diode laser near 369 nm for cooling Yb+ ions, using amplitude modulated polarization spectroscopy and a commercial PID feedback system. We achieve stable, low-drift locking with a standard deviation of measured laser frequency ∼ 400 kHz over 10 minutes, limited by the instantaneous linewidth of the diode laser. These results and the simplicity of our optical setup makes our approach attractive for stabilization of laser sources in atomic physics applications.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We demonstrate stabilization of an ultraviolet diode laser via Doppler-free spectroscopy of Ytterbium ions in a discharge. Our technique employs polarization spectroscopy, which produces a natural dispersive lineshape whose zero-crossing is largely immune to environmental drifts, making this signal an ideal absolute frequency reference for Yb+ ion trapping experiments. We stabilize an external-cavity diode laser near 369 nm for cooling Yb+ ions, using amplitude modulated polarization spectroscopy and a commercial PID feedback system. We achieve stable, low-drift locking with a standard deviation of measured laser frequency ∼ 400 kHz over 10 minutes, limited by the instantaneous linewidth of the diode laser. These results and the simplicity of our optical setup makes our approach attractive for stabilization of laser sources in atomic physics applications. |
Soare, A; Ball, H; Hayes, D; Sastrawan, J; Jarratt, M C; McLoughlin, J J; Zhen, X; Green, T J; Biercuk, M J Experimental noise filtering by quantum control Journal Article Nature Physics, 10 (11), pp. 825–829, 2014, ISSN: 1745-2473. @article{Soare.2014, title = {Experimental noise filtering by quantum control}, author = {A Soare and H Ball and D Hayes and J Sastrawan and M C Jarratt and J J McLoughlin and X Zhen and T J Green and M J Biercuk}, url = {http://www.nature.com/nphys/journal/v10/n11/full/nphys3115.html}, doi = {10.1038/nphys3115}, issn = {1745-2473}, year = {2014}, date = {2014-01-01}, journal = {Nature Physics}, volume = {10}, number = {11}, pages = {825--829}, abstract = {Quantum technologies are extremely sensitive to environmental disturbance. Control techniques inspired by classical systems engineering allow selective filtering of the noise spectrum, suppressing time-varying noise over defined frequency bands. Extrinsic interference is routinely faced in systems engineering, and a common solution is to rely on a broad class of filtering techniques to afford stability to intrinsically unstable systems or isolate particular signals from a noisy background. Experimentalists leading the development of a new generation of quantum-enabled technologies similarly encounter time-varying noise in realistic laboratory settings. They face substantial challenges in either suppressing such noise for high-fidelity quantum operations1 or controllably exploiting it in quantum-enhanced sensing2,3,4 or system identification tasks 5,6, due to a lack of efficient, validated approaches to understanding and predicting quantum dynamics in the presence of realistic time-varying noise. In this work we use the theory of quantum control engineering7,8 and experiments with trapped 171Yb+ ions to study the dynamics of controlled quantum systems. Our results provide the first experimental validation of generalized filter-transfer functions casting arbitrary quantum control operations on qubits as noise spectral filters9,10. We demonstrate the utility of these constructs for directly predicting the evolution of a quantum state in a realistic noisy environment as well as for developing novel robust control and sensing protocols. These experiments provide a significant advance in our understanding of the physics underlying controlled quantum dynamics, and unlock new capabilities for the emerging field of quantum systems engineering.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum technologies are extremely sensitive to environmental disturbance. Control techniques inspired by classical systems engineering allow selective filtering of the noise spectrum, suppressing time-varying noise over defined frequency bands. Extrinsic interference is routinely faced in systems engineering, and a common solution is to rely on a broad class of filtering techniques to afford stability to intrinsically unstable systems or isolate particular signals from a noisy background. Experimentalists leading the development of a new generation of quantum-enabled technologies similarly encounter time-varying noise in realistic laboratory settings. They face substantial challenges in either suppressing such noise for high-fidelity quantum operations1 or controllably exploiting it in quantum-enhanced sensing2,3,4 or system identification tasks 5,6, due to a lack of efficient, validated approaches to understanding and predicting quantum dynamics in the presence of realistic time-varying noise. In this work we use the theory of quantum control engineering7,8 and experiments with trapped 171Yb+ ions to study the dynamics of controlled quantum systems. Our results provide the first experimental validation of generalized filter-transfer functions casting arbitrary quantum control operations on qubits as noise spectral filters9,10. We demonstrate the utility of these constructs for directly predicting the evolution of a quantum state in a realistic noisy environment as well as for developing novel robust control and sensing protocols. These experiments provide a significant advance in our understanding of the physics underlying controlled quantum dynamics, and unlock new capabilities for the emerging field of quantum systems engineering. |
Soare, A; Ball, H; Hayes, D; Zhen, X; Jarratt, M C; Sastrawan, J; Uys, H; Biercuk, M J Experimental bath engineering for quantitative studies of quantum control Journal Article Physical Review A, 89 (4), pp. 042329, 2014, ISSN: 1050-2947. @article{Soare.2014de3, title = {Experimental bath engineering for quantitative studies of quantum control}, author = {A Soare and H Ball and D Hayes and X Zhen and M C Jarratt and J Sastrawan and H Uys and M J Biercuk}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.042329}, doi = {10.1103/physreva.89.042329}, issn = {1050-2947}, year = {2014}, date = {2014-01-01}, journal = {Physical Review A}, volume = {89}, number = {4}, pages = {042329}, abstract = {We develop and demonstrate a technique to engineer universal unitary baths in quantum systems. Using the correspondence between unitary decoherence due to ambient environmental noise and errors in a control system for quantum bits, we show how a wide variety of relevant classical error models may be realized through in-phase or in-quadrature modulation on a vector signal generator producing a resonant carrier signal. We demonstrate our approach through high-bandwidth modulation of the 12.6-GHz carrier appropriate for trapped Yb171+ ions. Experiments demonstrate the reduction of coherent lifetime in the system in the presence of both engineered dephasing noise during free evolution and engineered amplitude noise during driven operations. In both cases, the observed reduction of coherent lifetimes matches well with quantitative models described herein. These techniques form the basis of a toolkit for quantitative tests of quantum control protocols, helping experimentalists characterize the performance of their quantum coherent systems.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We develop and demonstrate a technique to engineer universal unitary baths in quantum systems. Using the correspondence between unitary decoherence due to ambient environmental noise and errors in a control system for quantum bits, we show how a wide variety of relevant classical error models may be realized through in-phase or in-quadrature modulation on a vector signal generator producing a resonant carrier signal. We demonstrate our approach through high-bandwidth modulation of the 12.6-GHz carrier appropriate for trapped Yb171+ ions. Experiments demonstrate the reduction of coherent lifetime in the system in the presence of both engineered dephasing noise during free evolution and engineered amplitude noise during driven operations. In both cases, the observed reduction of coherent lifetimes matches well with quantitative models described herein. These techniques form the basis of a toolkit for quantitative tests of quantum control protocols, helping experimentalists characterize the performance of their quantum coherent systems. |
Kabytayev, Chingiz; Green, Todd J; Khodjasteh, Kaveh; Biercuk, Michael J; Viola, Lorenza; Brown, Kenneth R Robustness of composite pulses to time-dependent control noise Journal Article Physical Review A, 90 (1), pp. 012316, 2014, ISSN: 1050-2947. @article{Kabytayev.2014, title = {Robustness of composite pulses to time-dependent control noise}, author = {Chingiz Kabytayev and Todd J Green and Kaveh Khodjasteh and Michael J Biercuk and Lorenza Viola and Kenneth R Brown}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.012316}, doi = {10.1103/physreva.90.012316}, issn = {1050-2947}, year = {2014}, date = {2014-01-01}, journal = {Physical Review A}, volume = {90}, number = {1}, pages = {012316}, abstract = {We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as ∼10% of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic 1/f noise spectra with a roll-off to 1/f2, providing independent validation of our theoretical insights.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as ∼10% of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic 1/f noise spectra with a roll-off to 1/f2, providing independent validation of our theoretical insights. |
2013 |
Green, Todd J; Sastrawan, Jarrah; Uys, Hermann; Biercuk, Michael J Arbitrary quantum control of qubits in the presence of universal noise Journal Article New Journal of Physics, 15 (9), pp. 095004, 2013, ISSN: 1367-2630. @article{Green.2013, title = {Arbitrary quantum control of qubits in the presence of universal noise}, author = {Todd J Green and Jarrah Sastrawan and Hermann Uys and Michael J Biercuk}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/15/9/095004/meta}, doi = {10.1088/1367-2630/15/9/095004}, issn = {1367-2630}, year = {2013}, date = {2013-01-01}, journal = {New Journal of Physics}, volume = {15}, number = {9}, pages = {095004}, abstract = {We address the problem of deriving analytic expressions for calculating universal decoherence-induced errors in qubits undergoing arbitrary, unitary, time-dependent quantum control protocols. We show that the fidelity of a control operation may be expressed in terms of experimentally relevant spectral characteristics of the noise and of the control, over all Cartesian directions. We formulate control matrices in the time domain to capture the effects of piecewise-constant control, and convert them to generalized Fourier-domain filter functions. These generalized filter functions may be derived for complex temporally modulated control protocols, accounting for susceptibility to rotations of the qubit state vector in three dimensions. Taken together, we show that this framework provides a computationally efficient means to calculate the effects of universal noise on arbitrary quantum control protocols, producing results comparable with those obtained via time-consuming simulations of Bloch vector evolution. As a concrete example, we apply our method to treating the problem of dynamical decoupling incorporating realistic control pulses of arbitrary duration or form, including the replacement of simple π-pulses with complex dynamically corrected gates.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We address the problem of deriving analytic expressions for calculating universal decoherence-induced errors in qubits undergoing arbitrary, unitary, time-dependent quantum control protocols. We show that the fidelity of a control operation may be expressed in terms of experimentally relevant spectral characteristics of the noise and of the control, over all Cartesian directions. We formulate control matrices in the time domain to capture the effects of piecewise-constant control, and convert them to generalized Fourier-domain filter functions. These generalized filter functions may be derived for complex temporally modulated control protocols, accounting for susceptibility to rotations of the qubit state vector in three dimensions. Taken together, we show that this framework provides a computationally efficient means to calculate the effects of universal noise on arbitrary quantum control protocols, producing results comparable with those obtained via time-consuming simulations of Bloch vector evolution. As a concrete example, we apply our method to treating the problem of dynamical decoupling incorporating realistic control pulses of arbitrary duration or form, including the replacement of simple π-pulses with complex dynamically corrected gates. |
Medford, J; Beil, J; Taylor, J M; Bartlett, S D; Doherty, A C; Rashba, E I; DiVincenzo, D P; Lu, H; Gossard, A C; Marcus, C M Self-consistent measurement and state tomography of an exchange-only spin qubit Journal Article Nature Nanotechnology, 8 (9), pp. 654–659, 2013, ISSN: 1748-3387. @article{Medford.2013, title = {Self-consistent measurement and state tomography of an exchange-only spin qubit}, author = {J Medford and J Beil and J M Taylor and S D Bartlett and A C Doherty and E I Rashba and D P DiVincenzo and H Lu and A C Gossard and C M Marcus}, url = {http://www.nature.com/nnano/journal/v8/n9/full/nnano.2013.168.html}, doi = {10.1038/nnano.2013.168}, issn = {1748-3387}, year = {2013}, date = {2013-01-01}, journal = {Nature Nanotechnology}, volume = {8}, number = {9}, pages = {654--659}, abstract = {Quantum-dot spin qubits characteristically use oscillating magnetic or electric fields, or quasi-static Zeeman field gradients, to realize full qubit control. For the case of three confined electrons, exchange interaction between two pairs allows qubit rotation around two axes, hence full control, using only electrostatic gates. Here, we report initialization, full control, and single-shot readout of a three-electron exchange-driven spin qubit. Control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in less than 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements and non-orthogonal control axes. Full control by electric gates can be accomplished in exchange-driven spin qubits.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum-dot spin qubits characteristically use oscillating magnetic or electric fields, or quasi-static Zeeman field gradients, to realize full qubit control. For the case of three confined electrons, exchange interaction between two pairs allows qubit rotation around two axes, hence full control, using only electrostatic gates. Here, we report initialization, full control, and single-shot readout of a three-electron exchange-driven spin qubit. Control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in less than 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements and non-orthogonal control axes. Full control by electric gates can be accomplished in exchange-driven spin qubits. |
2012 |
Green, Todd; Uys, Hermann; Biercuk, Michael J High-Order Noise Filtering in Nontrivial Quantum Logic Gates Journal Article Physical Review Letters, 109 (2), pp. 020501, 2012, ISSN: 0031-9007. @article{Green.2012, title = {High-Order Noise Filtering in Nontrivial Quantum Logic Gates}, author = {Todd Green and Hermann Uys and Michael J Biercuk}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.020501}, doi = {10.1103/physrevlett.109.020501}, issn = {0031-9007}, year = {2012}, date = {2012-01-01}, journal = {Physical Review Letters}, volume = {109}, number = {2}, pages = {020501}, abstract = {Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics. |
Britton, Joseph W; Sawyer, Brian C; Keith, Adam C; Wang, Joseph C -C; Freericks, James K; Uys, Hermann; Biercuk, Michael J; Bollinger, John J Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins Journal Article Nature, 484 (7395), pp. 489–492, 2012, ISSN: 0028-0836. @article{Britton.2012, title = {Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins}, author = {Joseph W Britton and Brian C Sawyer and Adam C Keith and Joseph C -C Wang and James K Freericks and Hermann Uys and Michael J Biercuk and John J Bollinger}, url = {http://www.nature.com/doifinder/10.1038/nature10981}, doi = {10.1038/nature10981}, issn = {0028-0836}, year = {2012}, date = {2012-01-01}, journal = {Nature}, volume = {484}, number = {7395}, pages = {489--492}, abstract = {A trapped-ion quantum simulator is used to demonstrate tunable long-range spin-spin couplings in two dimensions, relevant to studies of quantum magnetism at a scale that is intractable for classical computers. Quantum simulations could be used to study currently intractable many-body problems, such as quantum magnetism. However, technical challenges have so far limited simulations to a few tens of qubits, which is not enough to be computationally relevant. Here, Britton et al. demonstrate that a naturally occurring two-dimensional triangular crystal lattice of a few hundred beryllium ions held in an electromagnetic Penning trap can be used to simulate tunable antiferromagnetic interactions. This approach should bring the power of quantum simulation to a range of interesting problems in quantum magnetism. The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity1,2. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles3. Feynman predicted that a quantum simulator—a special-purpose ‘analogue’ processor built using quantum bits (qubits)—would be inherently suited to solving such problems4,5. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach6,7,8,9,10,11,12,13,14, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin–spin interaction, Ji,j , on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction , where 0 ≤ a ≤ 3 and di,j is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb–like (a = 1), monopole–dipole (a = 2) and dipole–dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A trapped-ion quantum simulator is used to demonstrate tunable long-range spin-spin couplings in two dimensions, relevant to studies of quantum magnetism at a scale that is intractable for classical computers. Quantum simulations could be used to study currently intractable many-body problems, such as quantum magnetism. However, technical challenges have so far limited simulations to a few tens of qubits, which is not enough to be computationally relevant. Here, Britton et al. demonstrate that a naturally occurring two-dimensional triangular crystal lattice of a few hundred beryllium ions held in an electromagnetic Penning trap can be used to simulate tunable antiferromagnetic interactions. This approach should bring the power of quantum simulation to a range of interesting problems in quantum magnetism. The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity1,2. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles3. Feynman predicted that a quantum simulator—a special-purpose ‘analogue’ processor built using quantum bits (qubits)—would be inherently suited to solving such problems4,5. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach6,7,8,9,10,11,12,13,14, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin–spin interaction, Ji,j , on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction , where 0 ≤ a ≤ 3 and di,j is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb–like (a = 1), monopole–dipole (a = 2) and dipole–dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism. |
2010 |
Cramer, Marcus; Plenio, Martin B; Flammia, Steven T; Somma, Rolando; Gross, David; Bartlett, Stephen D; Landon-Cardinal, Olivier; Poulin, David; Liu, Yi-Kai Efficient quantum state tomography Journal Article Nature Communications, 1 (1), pp. 149, 2010. @article{Cramer.2010, title = {Efficient quantum state tomography}, author = {Marcus Cramer and Martin B Plenio and Steven T Flammia and Rolando Somma and David Gross and Stephen D Bartlett and Olivier Landon-Cardinal and David Poulin and Yi-Kai Liu}, url = {http://www.nature.com/ncomms/journal/v1/n9/abs/ncomms1147.html}, doi = {10.1038/ncomms1147}, year = {2010}, date = {2010-01-01}, journal = {Nature Communications}, volume = {1}, number = {1}, pages = {149}, abstract = {Quantum state tomography—deducing quantum states from measured data—is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes unfeasible because the number of measurements and the amount of computation required to process them grows exponentially in the system size. Here, we present two tomography schemes that scale much more favourably than direct tomography with system size. One of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing. Both rely only on a linear number of experimental operations and post-processing that is polynomial in the system size. These schemes can be applied to a wide range of quantum states, in particular those that are well approximated by matrix product states. The accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. Direct quantum state tomography—deducing the state of a system from measurements—is mostly unfeasible due to the exponential scaling of measurement number with system size. The authors present two new schemes, which scale linearly in this respect, and can be applied to a wide range of quantum states.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum state tomography—deducing quantum states from measured data—is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes unfeasible because the number of measurements and the amount of computation required to process them grows exponentially in the system size. Here, we present two tomography schemes that scale much more favourably than direct tomography with system size. One of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing. Both rely only on a linear number of experimental operations and post-processing that is polynomial in the system size. These schemes can be applied to a wide range of quantum states, in particular those that are well approximated by matrix product states. The accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. Direct quantum state tomography—deducing the state of a system from measurements—is mostly unfeasible due to the exponential scaling of measurement number with system size. The authors present two new schemes, which scale linearly in this respect, and can be applied to a wide range of quantum states. |
2009 |
Higgins, B L; Berry, D W; Bartlett, S D; Mitchell, M W; Wiseman, H M; Pryde, G J Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements Journal Article New Journal of Physics, 11 (7), pp. 073023, 2009, ISSN: 1367-2630. @article{Higgins.2009, title = {Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements}, author = {B L Higgins and D W Berry and S D Bartlett and M W Mitchell and H M Wiseman and G J Pryde}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/11/7/073023/meta;jsessionid=79AF7BFCB08ABBF6DA39FC4692A59A59.c4.iopscience.cld.iop.org}, doi = {10.1088/1367-2630/11/7/073023}, issn = {1367-2630}, year = {2009}, date = {2009-01-01}, journal = {New Journal of Physics}, volume = {11}, number = {7}, pages = {073023}, abstract = {We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our scheme resolves the phase ambiguity that exists when multiple passes through a phase shift, or NOON states, are used to obtain improved phase resolution. Like a recently introduced adaptive technique (Higgins et al 2007 Nature 450 393), our experiment uses multiple applications of the phase shift on single photons. By not requiring adaptive measurements, but rather using a predetermined measurement sequence, the present scheme is both conceptually simpler and significantly easier to implement. Additionally, we demonstrate a simplified adaptive scheme that also surpasses the standard quantum limit for single passes.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our scheme resolves the phase ambiguity that exists when multiple passes through a phase shift, or NOON states, are used to obtain improved phase resolution. Like a recently introduced adaptive technique (Higgins et al 2007 Nature 450 393), our experiment uses multiple applications of the phase shift on single photons. By not requiring adaptive measurements, but rather using a predetermined measurement sequence, the present scheme is both conceptually simpler and significantly easier to implement. Additionally, we demonstrate a simplified adaptive scheme that also surpasses the standard quantum limit for single passes. |