This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring bit-level oscillation patterns during BP, our method identifies unreliable bits and generates multiple candidate vectors to selectively flip syndromes. Each modified syndrome is then decoded independently using short-depth BP, a process we refer to as BP-SF (syndrome flip). This design eliminates the need for costly Gaussian elimination used in the current BP-OSD approaches. Our implementation achieves logical error rates comparable to or better than BP-OSD while offering significantly lower latency due to its high degree of parallelism for a variety of bivariate bicycle codes. Evaluation on the$\llbracket 144,12,12 \rrbracket$bivariate bicycle code shows that the proposed decoder reduces average latency to approximately 70% of BP-OSD. When post-processing is parallelized the average latency is reduced by 55% compared to the single process implementation, with the maximum latency reaching as low as 18%. These advantages make it particularly well-suited for real-time and resource-constrained quantum error correction systems.
This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring bit-level oscillation patterns during BP, our method identifies unreliable bits and generates multiple candidate vectors to selectively flip syndromes. Each modified syndrome is then decoded independently using short-depth BP, a process we refer to as BP-SF (syndrome flip). This design eliminates the need for costly Gaussian elimination used in the current BP-OSD approaches. Our implementation achieves logical error rates comparable to or better than BP-OSD while offering significantly lower latency due to its high degree of parallelism for a variety of bivariate bicycle codes. Evaluation on the[[144,12,12]]bivariate bicycle code shows that the proposed decoder reduces average latency to approximately 70% of BP-OSD. When post-processing is parallelized the average latency is reduced by 55% compared to the single process implementation, with the maximum latency reaching as low as 18%. These advantages make it particularly well-suited for real-time and resource-constrained quantum error correction systems.
Quantum low-density parity-check (qLDPC) decoding requires reliable corrections and low latency over long syndrome histories. We extend BP-SF, an oscillation-guided belief-propagation (BP) decoder with independent syndrome-flip trials, by introducing windowed and streaming operations. Our CUDA implementation combines disordered-memory retries, sliding windows, correlation-aware graphs, and layered scheduling. Circuit-level simulations test fixed-basis memory and complete logical Pauli-frame recovery. On the [[144,12,12]] bivariate bicycle code at physical error rate p = 0.002, parallel BP-SF reduces 99.9th-percentile call latency by a factor of 13.15 relative to an eight-chain Relay-BP GPU baseline on 100,000 matched samples for which every tested method's initial BP stage fails within 80 iterations. Windowed BP-SF maintains a flat logical error rate and nearly constant per-round compute time through 512 rounds, reaching a 17.1-fold speedup over monolithic decoding. In 512-round full-frame streaming decoding with 2.97-ms syndrome arrivals, layered BP-SF on a transformed joint graph with 20 retries reduces 99.9th-percentile correction-release age from 166.29 to 36.25 ms relative to the joint graph with flooding updates and 100 retries. These results connect parallel BP post-processing to lower decoding costs and earlier correction release in streaming quantum memory.
We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy tradeoffs by tuning its parameters such as the beam width. We perform numerical simulations under circuit level noise for the [[144,12,12]] bivariate bicycle (BB) code at noise rate p=10−3 to estimate the logical error rate and the 99.9 percentile runtime and we compare with the BP-OSD decoder which has been the default quantum LDPC decoder for the past six years. A variant of our beam search decoder with a beam width of 64 achieves a 17× reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a 26.2× reduction in the 99.9 percentile runtime. We identify the beam search decoder with beam width of 32 as a promising candidate for trapped ion architectures because it achieves a 5.6× reduction in logical error rate with a 99.9 percentile runtime per syndrome extraction round below 1ms at p=5×10−4. Remarkably, this is achieved in software on a single core, without any parallelization or specialized hardware (FPGA, ASIC), suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits.
Due to the high error rate of qubits, detecting and correcting errors is essential for achieving fault-tolerant quantum computing (FTQC). Quantum low-density parity-check (QLDPC) codes are one of the most promising quantum error correction (QEC) methods due to their high encoding rates. BP (Belief Propagation)-based decoders are widely used and highly competitive for QLDPC codes because BP offers inherent parallelism and strong scalability. However, BP-based decoders still suffer from high decoding latency, a large portion of which is spent in the iterative BP stage. In this paper, we propose a lightweight preprocessing step that utilizes local patterns in the syndrome to detect likely trivial error events and provide them as hints to BP-based decoders. These hints accelerate BP convergence and thereby reduce the overall decoding time. The proposed preprocessing step offers a broadly compatible approach to reducing the latency of BP-based QLDPC decodes. On the bivariate bicycle code [[144,12,12]] at low physical error rates, our method achieves a 10× speedup in decoding time for BP-OSD, and more than 2× speedup for both BP-LSD and Relay-BP. Our method maintains the logical error rate when combined with BP-OSD and Relay-BP, while further achieving a significant reduction in logical error rate when combined with BP-LSD.
We propose a decoder for quantum low-density parity-check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy tradeoffs by tuning its parameters such as the beam width. We perform numerical simulations under circuit level noise for the [ [ 144 , 12 , 12 ] ] bivariate bicycle (BB) code at noise rate p = 10 − 3 to estimate the logical error rate and the 99.9 percentile runtime and we compare with the BP-OSD decoder which has been the default quantum LDPC decoder for the past six years. A variant of our beam search decoder with a beam width of 64 achieves a 17 × reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a 26.2 × reduction in the 99.9 percentile runtime. We identify the beam search decoder with beam width of 32 as a promising candidate for trapped ion architectures because it achieves a 5.6 × reduction in logical error rate with a 99.9 percentile runtime per syndrome extraction round below 1 ms at p = 5 × 10 − 4 . Remarkably, this is achieved in software on a single core, without any parallelization or specialized hardware (FPGA, ASIC), suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits.
Quantum low-density parity-check (QLDPC) codes are promising candidates for low-overhead fault-tolerant quantum computation, but their practical use requires fast, low-complexity, and reliable decoders. Belief propagation (BP) is attractive because of its local message-passing structure, yet standard flooding BP often suffers from convergence failures on QLDPC codes due to short cycles, degeneracy, and symmetric decoding trajectories. Learned sequential BP improves convergence by using a reinforcement-learning policy to choose variable-node update orders, but a single learned trajectory can still be sensitive to unfavorable local Pauli decisions. We propose a learned parallel bit-flipping sequential BP decoder with a new quaternary score combining syndrome gain, a quantized Pauli log-likelihood penalty, and Q-table lookahead at hypothetical post-flip states. Our decoder first runs learned sequential BP for a fixed number of iterations. If the syndrome is not satisfied, it constructs quaternary bit-flipping candidates, each corresponding to changing the current Pauli decision of one qubit. The selected candidates initialize independent learned sequential BP continuations from the same decoder state. Since these continuations are independent, they can be executed in parallel, so testing several candidates mainly increases parallel hardware resources rather than sequential decoding latency. Simulations on representative QLDPC codes over the depolarizing channel show that the proposed decoder improves the reliability of learned sequential BP while having a parallel low-latency structure.
Belief Propagation combined with Ordered Statistics Decoding (BP OSD) is an open-source decoding tool used widely within the community due to its versatility and ease of application to Quantum Low Density Parity Check (QLDPC) codes. However, the degeneracy of quantum codes has been observed to degrade the performance of BP OSD, particularly leading to error floors for low physical error rates. Here, we investigate the low-weight error configurations responsible for such failures in Bivariate Bicycle codes. We show that, at code capacity, BP OSD fails on errors whose weight is significantly smaller than d/2, arising from global symmetries of the decoding graph that prevent the convergence of parallel BP. Furthermore, our analysis reveals new pitfalls that can arise when analysing the performance of BP OSD in the rare events regime, such as loss of ergodicity in splitting methods and numerical instabilities in the decoder. We show how to mitigate these failure mechanisms by modifying the BP update rules and the decoder implementation, leading to substantial improvement in logical error rate.