All-optical quantum computing with GKP states — Rafael Alexander (Xanadu)

I will present some updates on Xanadu’s approach to photonic quantum computing. The architecture combines an all-optical method for generating Gottesman-Kitaev-Preskill bosonic qubits with a shallow network of static beamsplitters to create universal resources for fault-tolerant quantum computation. Computation, syndrome data extraction, and final measurement readouts are all achieved using homodyne detectors, which are fast, reliable, accurate, and operate at room temperature. The architecture is based on modular, easy-to-network integrated photonic chips.

Playing nonlocal games across a topological phase transition on a quantum computer — Dominic Williamson (IBM)

Many-body quantum games provide a natural perspective on phases of matter in quantum hardware, crisply relating the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In this paper we introduce a family of multiplayer quantum games for which topologically ordered phases of matter are a resource yielding quantum advantage. Unlike previous examples, quantum advantage persists away from the exactly solvable point and is robust to arbitrary local perturbations, irrespective of system size. We demonstrate this robustness experimentally on Quantinuum’s H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states that can be created with constant-depth circuits leveraging mid-circuit measurements and unitary feedback. We are thus able to tune through a topological phase transition – witnessed by the loss of robust quantum advantage – on currently available quantum hardware. This behavior is contrasted with an analogous family of deformed GHZ states, for which arbitrarily weak local perturbations destroy quantum advantage in the thermodynamic limit. Finally, we discuss a topological interpretation of the game, which leads to a natural generalization involving an arbitrary number of players.

Two topics for discussion: friendliness inequalities and a new family of Floquet codes — Eleanor Rieffel (NASA)

In the first part of the talk, I will discuss work, joint with Howard Wiseman and Eric Cavalcanti on Wigner’s friend scenarios, that leads to new inequalities with assumptions strictly weaker than those of Bell’s inequalities (arXiv:2209.08491). Our proposal for an ambitious but feasible experiment, which, if the results violate the inequalities as predicted by quantum theory, forces rejection of at least one of four metaphysical assumptions that are widely held by scientists. We provide a loose upper bound the resources needed to realize the experiment, which involves a human level artificial intelligence running on a large fault-tolerant quantum computer. This part of the talk will conclude the open question of what are compelling experiments to carry out in the intermediate term.

In the second part of the talk, I will discuss work, joint with Sohaib Alam, on Dynamical Logical Qubits in the Bacon-Shor Code (arXiv:2403.03291). We choose measurement schedules on a d x d square lattice that at each round is a subset of the Bacon-Shor code checks. These measurement schedule results in a Floquet code with several dynamical logical qubits. This work is part of a larger program in the field trying to understand when one can define Floquet codes, when it is useful to do so, and subtleties with regard to defining their distance.

The aim of the talk is to provide grounding for lively discussions of these topics at the workshop. I will conclude, as time permits, with very brief glimpses of a few other topics for discussion.

Building inherently robust qubits — Tom Stace (AQC/Queensland)

Transmons are now the standard pathway being pursued toward building superconducting quantum computers. However, these are many-body systems with a very large microscopic Hilbert space, in which non-standard encodings may be possible. In this talk, I will use the “dualmon” and the “Bloch-encoded transmon” to motivate the general question of how to access and use the underlying physical resources inherent in superconducting devices.

Quantum memory at nonzero temperature in a thermodynamically trivial system — Andrew Lucas (Boulder)

Passive error correction protects logical information forever (in the thermodynamic limit) by updating the system based only on instantaneous information and few-body interactions. A paradigmatic example is the classical two-dimensional Ising model: a Metropolis-style Gibbs sampler retains the sign of the initial magnetization (a logical bit) for thermodynamically long times in the low-temperature phase.  Known models of passive quantum error correction, such as the four-dimensional toric code, similarly exhibit thermodynamic phase transitions to a low-temperature phase wherein logical qubits are protected by thermally stable topological order. Here, in contrast, I describe constant-rate classical and quantum low-density parity check codes which have no thermodynamic phase transitions at nonzero temperature, but nonetheless exhibit ergodicity-breaking dynamical transitions: below a critical nonzero temperature, the mixing time of local Gibbs sampling diverges in the thermodynamic limit. This result suggests that NLTS can be a property of thermodynamically trivial phases of matter. Fault-tolerant passive “decoding” inspired by Gibbs sampling is amenable to measurement-free quantum error correction, and may be a desirable experimental alternative to conventional quantum error correction based on syndrome measurements and active feedback.

The limits of braiding with Majorana zero modes — Eric Mascot (Melbourne)

Majorana zero modes have been celebrated as a promising avenue for achieving topologically protected quantum computing. Recent experiments show strong evidence for the presence of Majorana zero modes. However, doubts persist regarding their practical viability. To address this, numerical simulations become essential for assessing their real-world potential. A novel method has simplified such simulations and drastically reduced the computational cost. We have conducted a comprehensive investigation on the impact of factors such as disorder, low-lying sub-gap states, and dissipation to elucidate the limitations of a topological quantum computer. In this talk, I will present the current progress of experiments and these simulations.

Color code decoder with improved scaling for correcting circuit-level noise — Seok-Hyung Lee (Sydney)

Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing because of their advantages, including high encoding rates and the capability to implement Clifford gates transversally. However, decoding these color codes, especially under circuit-level noise, presents a significant challenge due to their intrinsic structure and the complexity in extracting syndrome. In this talk, I introduce a color-code decoder that efficiently tackles these issues by combining two minimum-weight perfect matching (MWPM) decoders for each color, which can be generalized to handle circuit-level noise by employing detector error models. I provide comprehensive analyses of the decoder, covering its threshold and sub-threshold scaling, which show that the decoder outperforms existing matching-based decoders.

Machine Learning with Continuous Variable Quantum Kernels: A Toolkit — Laura Henderson (Queensland)

The popular qubit framework has dominated recent work on quantum ker- nel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for continuous variable (CV) quantum computing platforms. In this paper we represent CV quantum kernels as holomorphic functions and use this representation to provide several important theoretical insights. We derive a general closed form solution for all CV quantum kernels and show every such kernel can be expressed as the product of Gaussian and polynomial terms. Furthermore, we present quantification of a quantum-classical separation for all quantum kernels via a hierarchical notion of “stellar rank”. We then prove kernels of infinite stellar rank, such as those generated by GKP-state encod- ings, can be approximated arbitrarily well by kernels of finite stellar rank. Finally, we simulate learning with a single-mode displaced Fock state encoding and show that (i) accuracy on our specific task (an annular data set) increases with stellar rank, (ii) for underfit models, accuracy can be improved by in- creasing a bandwidth hyperparameter, and (iii) for noisy data that is overfit, decreasing the bandwidth will improve generalisation but does so at the cost of effective stellar rank and thus quantum advantage.

Fault-tolerant logical gates for neutral-atom surface codes — Kaavya Sahay (Yale)

Recent advances in noise channel engineering and experimental demonstrations using neutral-atom qubits have led to their emergence as an attractive option for fault-tolerant quantum computation (FTQC). In particular, the Yb atom can be engineered to experience as its dominant noise an error channel known as biased erasure. This noise model has higher error-correction thresholds than both biased Pauli noise and conventional unbiased erasures, and thus the use of biased-erasure qubits leads to relaxed hardware fidelity requirements for FTQC.

We investigate the fidelity of logical CNOT gates between two blocks of neutral atom-based surface code states under biased-erasure noise. We analyze the performance of two gate methods: (1) a fault-tolerant transversal CNOT, and (2) lattice surgery. While lattice surgery has been the established method for fixed qubits a transversal CNOT is believed to be more appropriate with reconfigurable atomic qubits. The strategy of performing a direct transversal CNOT gate between two surface codes was proposed two decades ago but extensive studies on optimal strategies for decoding and a comparison of its performance with the more widely studied lattice surgery technique has been thus far missing. Here, we fill this gap. We highlight key fundamental differences between the noise correlations that arise in the two strategies for gate operations, which require starkly different decoding strategies. We also provide full space-time overhead comparison between the two strategies, thus working towards the determination of an optimal path to FTQC with biased-erasure qubits.

Scalable noise characterisation of syndrome extraction circuits with averaged circuit eigenvalue sampling — Evan Hockings (Sydney)

Operating quantum error-correcting codes entails continuously performing syndrome extraction circuits, which are therefore key targets for noise characterisation. Averaged circuit eigenvalue sampling (ACES) is a general framework for the scalable noise characterisation of quantum circuits, capable of simultaneously estimating the Pauli error probabilities of all gates in a Clifford circuit. Our formulation of ACES naturally describes noise characterisation experiments for the syndrome extraction circuits of topological quantum codes. By rigorously characterising the performance of ACES experiments, we derive a figure of merit for their expected performance, allowing us to optimise ACES experimental designs and improve the precision to which we estimate noise given a fixed resource budget, including by improving the noise estimation procedure itself. We demonstrate the scalability and performance of our ACES protocol through circuit-level numerical simulations of the entire noise characterisation procedure for the syndrome extraction circuit of a distance-25 surface code with over 1000 qubits. Our results indicate that detailed noise characterisation methods are scalable to practically-relevant quantum devices.

Surface codes and modular chiplets in the presence of defects — Sophia Lin (Chicago)

Fabrication errors pose a significant challenge in scaling up solid-state quantum devices to the sizes required for fault-tolerant quantum applications. In this talk I will present the paper, “Codesign of quantum error-correcting codes and modular chiplets in the presence of defects”, which combines two approaches to mitigate the resource overhead caused by fabrication errors: (1) leveraging the flexibility of a modular architecture, (2) adapting the procedure of quantum error correction to account for fabrication defects. As an extension to this topic, I hope to start a discussion on how fabrication errors affect the performance and resource overhead of other codes.

Individually tunable tunnelling coefficients in optical lattices using local periodic driving — Georgia Nixon (Cambridge)

Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant lattice Hamiltonians eg. Hubbard or Heisenberg models. This has been useful when modelling condensed matter systems of the same uniform nature. However, the ability to encode and study Hamiltonians with arbitrary local parameters remains an outstanding goal that would enable optical lattice experiments to simulate an incredibly diverse range of problems and quantum phenomena well beyond solid-state settings.  Motivated by recent advances in quantum gas microscopes and optical tweezers, in this talk I will show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by utilising the Floquet physics of local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide various example configurations of this technique realising e.g. interesting topological models such as the extended Su Schrieffer Heeger model, and even black hole physics by realising a quantum simulator of Hawking radiation.  Extending to two dimensions, we demonstrate how this technique can be used to generate a 2D square network with fully controllable tunnelling magnitudes by driving two sub-lattices in a Lieb Lattice. This technique can also be used to engineer complex tunnelling amplitudes and therefore gauge invariant flux values around closed plaquettes.  We explore this in detail by driving a three-site plaquette, achieving full simultaneous control over both the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette.  We also demonstrate how to utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries.