The Minimum-Weight Perfect Matching (MWPM) decoder is widely used in Quantum Error Correction (QEC) decoding. Despite its high accuracy, existing implementations of the MWPM decoder cannot catch up with quantum hardware, e.g., 1 million measurements per second for superconducting qubits. They suffer from a backlog of measurements that grows exponentially and as a result, cannot realize the power of quantum computation. We design and implement a fast MWPM decoder, called Parity Blossom, which reaches a time complexity almost proportional to the number of defect measurements. We further design and implement a parallel version of Parity Blossom called Fusion Blossom. Given a practical circuit-level noise of 0.1%, Fusion Blossom can decode a million measurement rounds per second up to a code distance of 33. Fusion Blossom also supports stream decoding mode that reaches a 0.7 ms decoding latency at code distance 21 regardless of the measurement rounds.
The Minimum-Weight Perfect Matching (MWPM) decoder is widely used in Quantum Error Correction (QEC) decoding. Despite its high accuracy, existing implementations of the MWPM decoder cannot catch up with quantum hardware, e.g., 1 million measurements per second for superconducting qubits. They suffer from a backlog of measurements that grows exponentially and as a result, cannot realize the power of quantum computation. We design and implement a fast MWPM decoder, called Parity Blossom, which reaches a time complexity almost proportional to the number of defect measurements. We further design and implement a parallel version of Parity Blossom called Fusion Blossom. Given a practical circuit-level noise of 0.1%, Fusion Blossom can decode a million measurement rounds per second up to a code distance of 33. Fusion Blossom also supports stream decoding mode that reaches a 0.7 ms decoding latency at code distance 21 regardless of the measurement rounds.
Minimum-Weight Perfect Matching (MWPM) decoding is important to quantum error correction decoding because of its accuracy. However, many believe that it is difficult, if possible at all, to achieve the microsecond latency requirement posed by superconducting qubits. This work presents the first publicly known MWPM decoder, called Micro Blossom, that achieves sub-microsecond decoding latency. Micro Blossom employs a heterogeneous architecture that carefully partitions a state-of-the-art MWPM decoder between software and a programmable accelerator with parallel processing units, one of each vertex/edge of the decoding graph. On a surface code with code distance d and a circuit-level noise model with physical error rate p, Micro Blossom's accelerator employs O(d3) parallel processing units to reduce the worst-case latency from O(d12) to O(d9) and reduce the average latency from O(pd3+1) to O(p2 d2+1) when p «1.
Sparse-Blossom Decoding in o(1) Time
Matching-based decoding is widely used in quantum error correction, and accelerating it is key to enabling fast and scalable fault-tolerant quantum computation. Minimum-weight perfect matching (MWPM) decoding provides rigorous guarantees for error suppression, while sparse blossom enables its practical implementation at modest problem sizes. However, the runtime of existing sparse-blossom implementations unavoidably increases with problem size, motivating a rigorous parallelization framework that guarantees correctness and a runtime shorter than the syndrome-extraction timescale. Here, we present such a framework and prove that the resulting parallel sparse-blossom algorithm produces the same correction as the original, non-parallel sparse blossom. For the rotated surface code with code distance d and physical error rates below a finite threshold, we prove that the average parallel runtime of decoding for O(d) rounds of syndrome extraction is upper bounded by a quasi-polylogarithmic function of d. For a d-round decoding window, this implies that the average parallel runtime per round is o(1). We also perform numerical simulation to identify conditions under which the parallel runtime per round decreases with increasing code distance. These results suggest that increasing code distance need not lead to longer parallel decoding times, providing a foundation for scalable parallel matching-based decoding.
In this work, we introduce a fast implementation of the minimum-weight perfect matching (MWPM) decoder, the most widely used decoder for several important families of quantum error correcting codes, including surface codes. Our algorithm, which we call sparse blossom, is a variant of the blossom algorithm which directly solves the decoding problem relevant to quantum error correction. Sparse blossom avoids the need for all-to-all Dijkstra searches, common amongst MWPM decoder implementations. For 0.1% circuit-level depolarising noise, sparse blossom processes syndrome data in both X and Z bases of distance-17 surface code circuits in less than one microsecond per round of syndrome extraction on a single core, which matches the rate at which syndrome data is generated by superconducting quantum computers. Our implementation is open-source, and has been released in version 2 of the PyMatching library.
Fault-tolerant quantum computing relies on Quantum Error Correction (QEC), which encodes logical qubits into data and parity qubits. Error decoding is the process of translating the measured parity bits into types and locations of errors. To prevent a backlog of errors, error decoding must be performed in real-time (i.e., within 1μs on superconducting machines). Minimum Weight Perfect Matching (MWPM) is an accurate decoding algorithm for surface code, and recent research has demonstrated real-time implementations of MWPM (RT-MWPM) for a distance of up to 9. Unfortunately, beyond d=9, the number of flipped parity bits in the syndrome, referred to as the Hamming weight of the syndrome, exceeds the capabilities of existing RT-MWPM decoders. In this work, our goal is to enable larger distance RT-MWPM decoders by using adaptive predecoding that converts high Hamming weight syndromes into low Hamming weight syndromes, which are accurately decoded by the RT-MWPM decoder.
Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R) $regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving O(k) complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at d≤5 under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.
Fault-tolerant quantum computing requires classical decoders that keep pace with the underlying hardware, translating syndrome measurements into corrections fast enough to avoid an exponential backlog. To meet this real-time constraint, pre-decoders have emerged as part of a hierarchical decoding approach to resolve simple, local errors before passing a sparser residual syndrome to a strong decoder. While pre-decoding should, in theory, speed up the strong decoder, in practice, the speedup is only marginal, since existing strong decoders are designed to decode dense syndromes and cannot exploit the sparsity provided by pre-decoders. To address this, we present Zero-G, a strong decoder designed for use alongside pre-decoders. As a stochastic approximate minimum-weight perfect matching (MWPM) decoder, Zero-G exploits sparse residual syndromes, dynamically trading latency for accuracy rather than relying on an all-or-nothing runtime-accuracy trade-off. By decoupling hardware control from the decoding core itself, we enable heterogeneous deployment across both FPGAs and CPUs without maintaining separate implementations. Zero-G achieves a 10× latency improvement over existing strong decoders at matching accuracy, with worst-case sub-350ns decoding at code distances up to d=15, while scaling to 640 logical qubits on a single 128-core CPU and 32 logical qubits on a single AMD Versal V80 FPGA.