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Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…
Quantum error correction is necessary to protect logical quantum states and operations. However, no meaningful data protection can be made when the syndrome extraction is erroneous due to faulty measurement gates. Quantum data-syndrome (DS)…
We propose a Semantic Ordered Statistics Decoder (sem-OSD), a soft decoder for short linear block codes carrying byte-streamed sources such as natural-language text. Sem-OSD injects a byte-level language-model (LM) prior into ordered…
Quantum error correction (QEC) is essential for operating quantum computers in the presence of noise. Here, we accurately decode arbitrary Calderbank-Shor-Steane (CSS) codes via the maximum satisfiability (MaxSAT) problem. We show how to…
Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph.…
Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid…
Modern spacecraft communication systems rely on concatenated error correction schemes, typically combining convolutional and Reed-Solomon (RS) codes. This paper presents a decoder-side method that uses a machine learning model to estimate…
Artificial Neural Networks (ANNs) are a promising approach to the decoding problem of Quantum Error Correction (QEC), but have observed consistent difficulty when generalising performance to larger QEC codes. Recent scalability-focused…
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a…
We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the…
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…
To make practical quantum algorithms work, large-scale quantum processors protected by error-correcting codes are required to resist noise and ensure reliable computational outcomes. However, a major challenge arises from defects in…
Quantum stabilizer codes constructed from sparse matrices have good performance and can be efficiently decoded by belief propagation (BP). A conventional BP decoding algorithm treats binary stabilizer codes as additive codes over GF(4).…
We introduce a new heuristic decoder, Relay-BP, targeting real-time quantum circuit decoding for large-scale quantum computers. Relay-BP achieves high accuracy across circuit-noise decoding problems: significantly outperforming BP+OSD+CS-10…
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…