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IEEE International Conference on Quantum Computing and Engineering (QCE)

A Scalable Real-Time Decoder for Quantum Error Correction Based on Hyperdimensional Computing

Rob A. Damsteegt, Masoud Babaie, Sebastian Feld, Fabio Sebastiano

Published Aug 30, 2025• 0 citations
Publisher

Abstract

Quantum computers require large-scale error correction codes to circumvent the limited fidelity of physical qubits. However, current error decoders are either not scalable to practical code sizes or cannot meet the strict real-time decoding requirements. This work presents a novel decoder for stabilizer error correction codes that exploits hyperdimensional computing to offer an efficient hardware implementation for large-scale codes, thus achieving low latency and high throughput. Next to a universal approach for generating the necessary hypervectors, an efficient method specific to surface codes is devised. In this very first implementation, the proposed decoder outclasses popular graph-based decoders for small surface codes with depolarizing noise and efficiently scales to large codes, thus representing both a suitable solution for near-term real-time error correction and a promising alternative for future large-scale codes.

DOI
10.1109/qce65121.2025.00120

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Quantum computers require large-scale error correction codes to circumvent the limited fidelity of physical qubits. However, current error decoders are either not scalable to practical code sizes or cannot meet the strict real-time decoding requirements. This work presents a novel decoder for stabilizer error correction codes that exploits hyperdimensional computing to offer an efficient hardware implementation for large-scale codes, thus achieving low latency and high throughput. Next to a universal approach for generating the necessary hypervectors, an efficient method specific to surface codes is devised. In this very first implementation, the proposed decoder outclasses popular graph-based decoders for small surface codes with depolarizing noise and efficiently scales to large codes, thus representing both a suitable solution for near-term real-time error correction and a promising alternative for future large-scale codes.
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 operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from the depolarizing error model. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O( μ sec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the classical electronic back-end. Decoders employing neural networks (NN) are well-suited for this task but their hardware implementation has not been presented yet. This work presents a space exploration of fully-connected feed-forward NN decoders for small distance surface codes. The goal is to optimize the neural network for high decoding performance, while keeping a minimalistic hardware implementation. This is needed to meet the tight delay constraints of real-time surface code decoding. We demonstrate that hardware based NN-decoders can achieve high decoding performance comparable to other state-of-the-art decoding algorithms whilst being well below the tight delay requirements (440 ns) of current solid-state qubit technologies for both ASIC designs (<30 ns) and FPGA implementations (<90 ns). These results indicate that NN-decoders are viable candidates for further exploration of an integrated hardware implementation in future large-scale quantum computers.
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the [144,12,12][144, 12, 12][144,12,12] Gross code, the decoder achieves logical error rates up to ∼17\sim 17∼17x below existing decoders - reaching logical error rates ∼10−10\sim 10^{-10}∼10−10 at physical error p=0.1%p=0.1\%p=0.1% - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.
Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many challenges to implement a high-performance real-time decoding system. Many decoding algorithms have been proposed and optimized in the past few decades, of which neural network (NNs) based solutions have drawn an increasing amount of attention due to their high efficiency. Unfortunately, previous works on neural decoders are still at an early stage and have only relatively simple architectures, which makes them unsuitable for practical QEC. In this work, we propose a scalable, fast, and programmable neural decoding system to meet the requirements of FTQEC for rotated surface codes (RSC). Firstly, we propose a hardware-efficient NN decoding algorithm with relatively low complexity and high accuracy. Secondly, we develop a customized hardware decoder with architectural optimizations to reduce latency. Thirdly, our proposed programmable architecture boosts the scalability and flexibility of the decoder by maximizing parallelism. Fourthly, we build an FPGA-based decoding system with integrated control hardware for evaluation. Our L=5L=5L=5 (LLL is the code distance) decoder achieves an extremely low decoding latency of 197 ns, and the L=7L=7L=7 configuration also requires only 1.136 μμμs, both taking 2L2L2L rounds of syndrome measurements. The accuracy results of our system are close to minimum weight perfect matching (MWPM). Furthermore, our programmable architecture reduces hardware resource consumption by up to 3.0×3.0\times3.0× with only a small latency loss. We validated our approach in real-world scenarios by conducting a proof-of-concept benchmark with practical noise models, including one derived from experimental data gathered from physical hardware.
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and corrected by a classical decoder. To prevent error accumulation, decoding must be performed with both high throughput and low latency to keep pace with the QEC cycle and enable real-time feedback for universal logical operations. Here we report a hardware-integrated control architecture featuring an FPGA-based neural-network (NN) decoder and experimentally demonstrate real-time surface-code (distance-3) QEC on a superconducting quantum processor. The system achieves a deterministic closed-loop latency of 550 ns, including 124 ns for NN decoding, enabling feedback corrections within a 1.25 us QEC cycle. We show that real-time decoding and feedback correction achieve logical performance comparable to offline decoding while maintaining robustness against varying error conditions. We further demonstrate mid-circuit feedback correction in non-Clifford logical circuits, where Pauli-frame updating alone becomes insufficient. Our results establish a low-latency hardware architecture for embedded QEC control and provide a pathway towards scalable fault-tolerant quantum computing systems.
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We introduce GraphQEC, a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity. GraphQEC demonstrates unprecedented accuracy and efficiency across all tested code families, including surface codes, color codes, and quantum low-density parity-check (QLDPC) codes. For instance, on a distance-12 QLDPC code, GraphQEC achieves a logical error rate of 9.55×10−59.55 \times 10^{-5}9.55×10−5, an 18-fold improvement over the previous best specialized decoder's 1.74×10−31.74 \times 10^{-3}1.74×10−3 under p=0.005p=0.005p=0.005 physical error rates, while maintaining 157μ157μ157μs/cycle decoding speed. Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.