2012
Green, Todd; Uys, Hermann; Biercuk, Michael J
High-Order Noise Filtering in Nontrivial Quantum Logic Gates Journal Article
In: Physical Review Letters, vol. 109, no. 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
In: Nature, vol. 484, no. 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.
Blanvillain, S; Colless, JI; Reilly, DJ; Lu, H; Gossard, AC
Suppressing On-Chip EM Crosstalk for Spin Qubit Devices Journal Article
In: arXiv preprint arXiv:1205.4072, 2012.
@article{blanvillain2012suppressing,
title = {Suppressing On-Chip EM Crosstalk for Spin Qubit Devices},
author = {S Blanvillain and JI Colless and DJ Reilly and H Lu and AC Gossard},
year = {2012},
date = {2012-01-01},
journal = {arXiv preprint arXiv:1205.4072},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2011
Biercuk, Michael J; Reilly, David J
Solid-state spins survive Journal Article
In: Nature Nanotechnology, vol. 6, no. 1, pp. 9–11, 2011.
@article{biercuk2011solid,
title = {Solid-state spins survive},
author = {Michael J Biercuk and David J Reilly},
year = {2011},
date = {2011-01-01},
journal = {Nature Nanotechnology},
volume = {6},
number = {1},
pages = {9--11},
publisher = {Nature Publishing Group UK London},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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
In: Nature Communications, vol. 1, no. 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
In: New Journal of Physics, vol. 11, no. 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.