Decoding of Quantum Data-Syndrome Codes via Belief Propagation

Kuo, Kao-Yueh; Chern, I-Chun; Lai, Ching-Yi

doi:10.1109/isit45174.2021.9518018

Cited by 11 publications

(4 citation statements)

References 35 publications

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“…MWPM has been extended to handle measurement and gate errors in FTQC [7]- [10]. BP can be extended to correct data and measurement errors simultaneously [36]. It is interesting to consider gate errors in BP as well.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Comparison of 2D topological codes and their decoding performances

Kuo¹,

Lai²

2022

Preprint

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Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An N -qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity O(poly(N )) if it is of CSS-type. Recently it is shown that various quantum codes, including non-CSS codes, can be decoded by an adapted belief propagation with memory effects (denoted MBP) with complexity almost linear in N . In this paper, we show that various twodimensional topological codes, CSS or non-CSS, regardless of the layout, can be decoded by MBP, including color codes and twisted XZZX codes. We will comprehensively compare these codes in terms of code efficiency and decoding performance, assuming perfect error syndromes.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Comparison of 2D topological codes and their decoding performances

Kuo¹,

Lai²

2022

Preprint

Self Cite

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“…Note that we are not using an explicit syndrome code for protecting the syndrome bits as in [19,28], instead relying on the message passing algorithm to infer what the syndromes should be. Using this modified MSA decoder, we hope to avoid the overhead of repeated measurements as we can identify the measurement errors in the instances where this decoder converges.…”

Section: Updating the Halting Conditionmentioning

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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“…Note that we are not using an explicit syndrome code for protecting the syndrome bits as in [16], [25], instead relying on the message passing algorithm to infer what the syndromes should be. Using this modified MSA decoder, we can avoid the overhead of repeated measurements as we can identify the measurement errors in the instances where this decoder converges.…”

Section: Soft Syndrome Decodermentioning

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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Decoding of Quantum Data-Syndrome Codes via Belief Propagation

Cited by 11 publications

References 35 publications

Comparison of 2D topological codes and their decoding performances

Comparison of 2D topological codes and their decoding performances

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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