arXiv subjects

David Byfield

Publications and source records attributed to David Byfield.

3 recordsLinked to original sources

arXiv2025

Directional Codes: a new family of quantum LDPC codes on hexagonal- and square-grid connectivity hardware

Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and feasible scalability. However, it is often restricted to two-dimensional nearest-neighbour connectivity, and therefore the variety of quantum low-density parity-check (qLDPC) codes that can be implemented on it without sacrificing QEC performance is believed to be greatly restricted. In this paper we construct a new family of qLDPC codes, which we call ``directional codes'', that outperforms the rotated toric code (RTC) while satisfying the connectivity requirements of the widely adopted square-grid, and some even the sparser hexagonal-grid, on a torus. The key idea is to utilise the iSWAP gate -- a native gate demonstrated on superconducting qubits -- to construct circuits that measure the stabilisers of these qLDPC codes without the need for additional connections. We numerically evaluate the performance of directional codes, encoding four, six, twelve and eighteen logical qubits, using a common superconducting-inspired circuit-level Pauli noise model. We also compare them to the RTC and to the bivariate bicycle (BB) codes, currently the two most popular quantum LDPC code families. As a concrete example, when evaluated with the Tesseract decoder with short beam setting, the best directional code family investigated achieves the same logical error rate as the RTC at physical error rate $p=10^{-3}$ but requires only a quarter to a third of the number of physical qubits. Our discovery opens a novel direction in QEC code design, suggesting that complex high-connectivity hardware may not be necessary for low-overhead fault-tolerant quantum computation.

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arXiv2024

Reducing the error rate of a superconducting logical qubit using analog readout information

Quantum error correction enables the preservation of logical qubits with a lower logical error rate than the physical error rate, with performance depending on the decoding method. Traditional error decoding approaches, relying on the binarization (`hardening') of readout data, often ignore valuable information embedded in the analog (`soft') readout signal. We present experimental results showcasing the advantages of incorporating soft information into the decoding process of a distance-three ($d=3$) bit-flip surface code with transmons. To this end, we use the $3\times3$ data-qubit array to encode each of the $16$ computational states that make up the logical state $\ket{0_{\mathrm{L}}}$, and protect them against bit-flip errors by performing repeated $Z$-basis stabilizer measurements. To infer the logical fidelity for the $\ket{0_{\mathrm{L}}}$ state, we average across the $16$ computational states and employ two decoding strategies: minimum weight perfect matching and a recurrent neural network. Our results show a reduction of up to $6.8\%$ in the extracted logical error rate with the use of soft information. Decoding with soft information is widely applicable, independent of the physical qubit platform, and could reduce the readout duration, further minimizing logical error rates.

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arXiv2023

Neural network decoder for near-term surface-code experiments

Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the physical error rates, making them highly adaptable. In this study, we investigate the performance of such a decoder using both simulated and experimental data obtained from a transmon-qubit processor, focusing on small-distance surface codes. We first show that the neural network typically outperforms the matching decoder due to better handling errors leading to multiple correlated syndrome defects, such as $Y$ errors. When applied to the experimental data of [Google Quantum AI, Nature 614, 676 (2023)], the neural network decoder achieves logical error rates approximately $25\%$ lower than minimum-weight perfect matching, approaching the performance of a maximum-likelihood decoder. To demonstrate the flexibility of this decoder, we incorporate the soft information available in the analog readout of transmon qubits and evaluate the performance of this decoder in simulation using a symmetric Gaussian-noise model. Considering the soft information leads to an approximately $10\%$ lower logical error rate, depending on the probability of a measurement error. The good logical performance, flexibility, and computational efficiency make neural network decoders well-suited for near-term demonstrations of quantum memories.

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