Noise-induced errors in quantum information processing corrupt computation and cause useful algorithms to fail. Quantum ErrorCorrection (QEC) counteracts this by encoding a single logical qubit across many physical qubits and correcting errors through repeatedsyndrome measurements. The Minimum-Weight Perfect Matching (MWPM) decoder is the accuracy benchmark for surface-codedecoding, but its microsecond-scale latency can consume the entire QEC cycle time of superconducting processors, leaving almost nomargin for other control operations. Pre-decoded lookup tables reduce latency to the nanosecond scale, but their memory requirementsgrow exponentially with code size, limiting them to very small code distances. In this work, we demonstrate a single-level cache,implemented as a software prototype, that accelerates decoding by exploiting the repetitive nature of surface-code syndromes. Hitrates above 80% are achieved for code distances up to 9 at below-threshold noise rates, and effective decoding speedups of up to18.1 times over PyMatching’s standalone decoding time are observed at code distance ≥ 5. Cache lookup latency remains below 400nanoseconds in the worst case, with memory well below that of full lookup tables. We further develop a mathematical frameworkdefining the theoretical limits of any cache-based decoder.
Noise-induced errors in quantum information processing corrupt computation and cause useful algorithms to fail. Quantum ErrorCorrection (QEC) counteracts this by encoding a single logical qubit across many physical qubits and correcting errors through repeatedsyndrome measurements. The Minimum-Weight Perfect Matching (MWPM) decoder is the accuracy benchmark for surface-codedecoding, but its microsecond-scale latency can consume the entire QEC cycle time of superconducting processors, leaving almost nomargin for other control operations. Pre-decoded lookup tables reduce latency to the nanosecond scale, but their memory requirementsgrow exponentially with code size, limiting them to very small code distances. In this work, we demonstrate a single-level cache,implemented as a software prototype, that accelerates decoding by exploiting the repetitive nature of surface-code syndromes. Hitrates above 80% are achieved for code distances up to 9 at below-threshold noise rates, and effective decoding speedups of up to18.1 times over PyMatching’s standalone decoding time are observed at code distance ≥ 5. Cache lookup latency remains below 400nanoseconds in the worst case, with memory well below that of full lookup tables. We further develop a mathematical frameworkdefining the theoretical limits of any cache-based decoder.
Quantum computers can solve selected problems more efficiently than classical computers, but current devices are limited by high physical error rates. Quantum Error Correction (QEC) mitigates this by encoding many physical qubits into a logical qubit, with the surface code among the most widely studied approaches. Since syndrome measurements are produced continuously, the decoder must process them fast enough to avoid becoming a system bottleneck, making real-time decoding essential for fault-tolerant quantum computing. While most state-of-the-art real-time decoders rely on Minimum-Weight Perfect Matching (MWPM), we instead use a high-accuracy Graph Neural Network (GNN) that trades higher computational cost for lower logical error rates. To make this GNN practical for real-time decoding, we apply algorithm-hardware co-design. We reduce complexity through hardware-guided pruning and retraining, producing two hardware-friendly models that reduce parameter count by 3.1× and 6.5×. These target, respectively, an average decoding latency of one syndrome cycle and a worst-case latency within one syndrome cycle. We further reduce hardware cost using input-graph filtering and post-training quantization. Based on these optimized models, we propose an FPGA-based architecture for low-latency inference and real-time decoding. Evaluated on surface codes up to distance 7 under circuit-level noise at physical error rate p=10−3, our decoder outperforms MWPM in decoding accuracy for both average-latency and max-latency settings. It reduces logical error rate by 40% at 1μs average latency, and by 13% under a strict 1μs deadline.
Abstract Quantum error-correction decoders must convert noisy syndrome records into logical decisions while operating under strict latency and reliability constraints. Minimum-weight perfect matching (MWPM) remains a strong baseline for surface-code decoding because it is fast, interpretable, and exact for its graphlike optimization problem [1–8]. However, the graphlike independent-error approximation can become mismatched when syndrome records contain temporal drift, measurement corruption, crosstalk, bursts, or mixtures of mechanisms [9–18]. We introduce SAGE-QEC, a failure-aware selective decoder that retains nominal PyMatching as its default decision and learns when an observable syndrome structure warrants an alternative candidate. SAGE-QEC uses train-frozen structure thresholds, a candidate ranker, validation-only policy selection, and a paired blind evaluation. Across 45 simulator conditions, SAGE-QEC reduced the aggregate logical error rate from 27.1285% for PyMatching to 24.8320%, corresponding to an 8.47% relative reduction. The campaign used rotated surface-code memory circuits at distances 3, 5, and 7, nominal circuit parameters 0.002, 0.003, and 0.005, five seeds, and four test regimes withheld from training: Burst-3, Temporal Drift, Crosstalk, and Mixed Noise. The test set contained 81,000 paired shots. All twelve distance-by-regime aggregate comparisons favored SAGE-QEC in the executed campaign, with paired bootstrap intervals below zero for SAGE-QEC minus PyMatching. The result is evidence of a reproducible simulator-level improvement, not a claim of universal decoder superiority. SAGE-QEC currently uses logical-output proxy candidates rather than a complete physical correction search, and its intervention rate remains high under distribution shift. It has not yet been compared with a fully calibrated correlated-noise space-time PyMatching baseline or hardware calibration data. We therefore characterize SAGE-QEC as a strong qualification-stage prototype and release a complete audit protocol for the next industrial validation stage.
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 [1, 2, 3, 4] provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. Here, we present two below-threshold surface code memories on our newest generation of superconducting processors, Willow: a distance-7 code, and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of Λ=2.14±0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% ± 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit’s lifetime by a factor of 2.4±0.3 . Our system maintains below-threshold performance when decoding in real time, achieving an average decoder latency of 63 μs at distance-5 up to a million cycles, with a cycle time of 1.1 μs. We also run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3×109 cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.
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.
Quantum devices suffer from high error rates, which makes them ineffective for running practical applications. Quantum computers can be made fault tolerant using Quantum Error Correction (QEC), which protects quantum information by encoding logical qubits using data qubits and parity qubits. The data qubits collectively store the quantum information and the parity qubits are measured periodically to produce a syndrome, which is decoded by a classical decoder to identify the location and type of errors. To prevent errors from accumulating and causing a logical error, decoders must accurately identify errors in real-time, necessitating the use of hardware solutions because software decoders are slow. Ideally, a real-time decoder must match the performance of the Minimum-Weight Perfect Matching (MWPM) decoder. However, due to the complexity of the underlying Blossom algorithm, state-of-the-art real-time decoders either use lookup tables, which are not scalable, or use approximate decoding, which significantly increases logical error rates.