Improved quantum error correction using soft information

Pattison, Christopher A.; Beverland, Michael E.; da Silva, Marcus P.; Delfosse, Nicolas

doi:10.48550/arxiv.2107.13589

Cited by 5 publications

(3 citation statements)

References 45 publications

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“…In such a scenario, the analog syndrome itself would be noisy, which needs to be incorporated in the syndrome-based iterative decoder. We expect the GKP-QLDPC concatenation scheme to work well even in such a noisy syndrome setting using outer code decoders that can utilize the soft syndrome information [59,60]. Furthermore, having considered an application-agnostic setting in this paper, we will also consider noise models spe-cialized towards fault-tolerant quantum computing or quantum communications (e.g., quantum repeaters [24]).…”

Section: Discussionmentioning

confidence: 99%

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Raveendran

Rengaswamy

Rozpędek

et al. 2022

Quantum

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Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder – a hardware-friendly min-sum algorithm (MSA) – utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.

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Section: Discussionmentioning

confidence: 99%

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Raveendran

Rengaswamy

Rozpędek

et al. 2022

Quantum

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“…Instead of quantizing this analog information to a binary outcome and losing crucial information, one can leverage the soft syndrome in the iterative decoder and modify the update rules accordingly. In the work by Pattinson et al [22], syndrome measurement outcomes beyond simple binary values were considered. The decoders used for surface codes, such as minimum weight perfect matching and union-find, were modified accordingly to obtain higher decoding thresholds.…”

Section: Introductionmentioning

confidence: 99%

Soft syndrome iterative decoding of quantum LDPC codes and hardware architectures

Raveendran,

Valls,

Pradhan

et al. 2023

EPJ Quantum Technol.

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In practical quantum error correction implementations, the measurement of syndrome information is an unreliable step—typically modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this “soft” or analog information to benefit iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation decoders are modified to utilize the soft syndrome to correct both data and syndrome errors simultaneously. We demonstrate the advantages of the proposed scheme not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families but also with faster convergence of iterative decoders. Additionally, we derive hardware (FPGA) architectures of these soft syndrome decoders and obtain similar performance in terms of error correction to the ideal models even with reduced precision in the soft information. The total latency of the hardware architectures is about 600 ns (for the QLDPC codes considered) in a 20 nm CMOS process FPGA device, and the area overhead is almost constant—less than 50% compared to min-sum decoders with noisy syndromes.

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“…Instead of quantizing this analog information to a binary outcome and losing crucial information, one can leverage the soft syndrome in the iterative decoder and modify the update rules accordingly. In a recent work by Pattinson et al [19], syndrome measurement outcomes beyond simple binary values were considered. The decoders used for surface codes, such as minimum weight perfect matching and union-find, were modified accordingly to obtain higher decoding thresholds.…”

Section: Introductionmentioning

confidence: 99%

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors

Raveendran¹,

Rengaswamy²,

Pradhan³

et al. 2022

Preprint

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Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation decoders are modified to utilize the syndrome-soft information to successfully correct both data and syndrome errors simultaneously, without repeated measurements. We demonstrate the advantages of extracting the soft information from the syndrome in our improved decoders, not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families, but also for faster convergence of iterative decoders. In particular, the new BP decoder with noisy syndrome performs as good as the standard BP decoder under ideal syndrome.

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Improved quantum error correction using soft information

Cited by 5 publications

References 45 publications

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Soft syndrome iterative decoding of quantum LDPC codes and hardware architectures

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors

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