Comparative study of decoding the surface code using simulated annealing under depolarizing noise

• URL: http://arxiv.org/abs/2311.07973v2
• Date: Tue, 21 Nov 2023 05:25:55 GMT
• Title: Comparative study of decoding the surface code using simulated annealing under depolarizing noise
• Authors: Yusaku Takeuchi, Yugo Takada, Tatsuya Sakashita, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii
• Abstract summary: We find that the proposed Ising-based decoding approaches provide higher accuracy compared to the minimum-weight perfect matching (MWPM) algorithm for depolarizing noise. Our results are important for devising efficient and fast decoders feasible with quantum computer control devices.
• Score: 0.6449786007855248
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explored decoding methods for the surface code under depolarizing noise by mapping the problem into the Ising model optimization. We consider two kinds of mapping with and without a soft constraint and also various optimization solvers, including simulated annealing implemented on a CPU, "Fujitsu Digital Annealer" (DA), a hardware architecture specialized for the Ising problems, and CPLEX, an exact integer programming solver. We find that the proposed Ising-based decoding approaches provide higher accuracy compared to the minimum-weight perfect matching (MWPM) algorithm for depolarizing noise and comparable to minimum distance decoding using CPLEX. While decoding time is longer than MWPM when we compare it with a single core CPU, our method is amenable to parallelization and easy to implement on dedicated hardware, suggesting potential future speedups. Regarding the mapping methods to the Ising model with and without a soft constraint, the SA decoder yielded higher accuracy without a soft constraint. In contrast, the DA decoder shows less difference between the two mapping methods, which indicates that DA can find a better solution with smaller number of iterations even under the soft constraint. Our results are important for devising efficient and fast decoders feasible with quantum computer control devices.

Related papers

• Even More Efficient Soft-Output Decoding with Extra-Cluster Growth and Early Stopping [2.370310454459195]
  We introduce two types of novel soft-outputs: the bounded cluster gap and the extra-cluster gap.<n>The latter, the extra-cluster gap, quantifies decoder reliability by performing a small, additional growth of the clusters obtained by the decoder.<n>These techniques offer lower computational complexity and higher hardware compatibility.
  arXiv  Detail & Related papers  (2026-02-03T10:00:40Z)
• Hierarchical quantum decoders [3.312392076411996]
  We propose a family of tunable quantum decoders with a trade-off between speed and accuracy.<n>This work bridges the gap between fast decodings and rigorous optimal decoding.
  arXiv  Detail & Related papers  (2026-01-29T13:42:58Z)
• SAQ: Stabilizer-Aware Quantum Error Correction Decoder [8.458339111154585]
  Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff.<n>Recent neural decoders reduce complexity but lack the accuracy needed to compete with computationally expensive classical methods.<n>We introduce SAQ-Decoder, a framework combining transformer-based learning with constraint post-processing.
  arXiv  Detail & Related papers  (2025-12-09T18:51:35Z)
• Fast correlated decoding of transversal logical algorithms [67.01652927671279]
  Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead.<n>Recent advances have shown that by jointly decoding logical qubits in algorithms composed of logical gates, the number of syndrome extraction rounds can be reduced.<n>Here, we reform the problem of decoding circuits by directly decoding relevant logical operator products as they propagate through the circuit.
  arXiv  Detail & Related papers  (2025-05-19T18:00:00Z)
• Joint Transmit and Pinching Beamforming for Pinching Antenna Systems (PASS): Optimization-Based or Learning-Based? [89.05848771674773]
  A novel antenna system ()-enabled downlink multi-user multiple-input single-output (MISO) framework is proposed. It consists of multiple waveguides, which equip numerous low-cost antennas, named (PAs) The positions of PAs can be reconfigured to both spanning large-scale path and space.
  arXiv  Detail & Related papers  (2025-02-12T18:54:10Z)
• Threshold Selection for Iterative Decoding of $(v,w)$-regular Binary Codes [84.0257274213152]
  Iterative bit flipping decoders are an efficient choice for sparse $(v,w)$-regular codes. We propose concrete criteria for threshold determination, backed by a closed form model.
  arXiv  Detail & Related papers  (2025-01-23T17:38:22Z)
• Progressive Mixed-Precision Decoding for Efficient LLM Inference [49.05448842542558]
  We introduce Progressive Mixed-Precision Decoding (PMPD) to address the memory-boundedness of decoding. PMPD achieves 1.4$-$12.2$times$ speedup in matrix-vector multiplications over fp16 models. Our approach delivers a throughput gain of 3.8$-$8.0$times$ over fp16 models and up to 1.54$times$ over uniform quantization approaches.
  arXiv  Detail & Related papers  (2024-10-17T11:46:33Z)
• Progressive-Proximity Bit-Flipping for Decoding Surface Codes [8.971989179518214]
  Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation. Existing decoders often fall short of meeting requirements such as having low computational complexity. We propose a novel bit-flipping (BF) decoder tailored for toric and surface codes.
  arXiv  Detail & Related papers  (2024-02-24T22:38:05Z)
• Fast, Scalable, Warm-Start Semidefinite Programming with Spectral Bundling and Sketching [53.91395791840179]
  We present Unified Spectral Bundling with Sketching (USBS), a provably correct, fast and scalable algorithm for solving massive SDPs. USBS provides a 500x speed-up over the state-of-the-art scalable SDP solver on an instance with over 2 billion decision variables.
  arXiv  Detail & Related papers  (2023-12-19T02:27:22Z)
• Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes [3.4602940992970908]
  We introduce a new post-processing algorithm with a hardware-friendly orientation, providing error correction performance competitive to the state-of-the-art techniques. We show that latency values close to one microsecond can be obtained on the FPGA board, and provide evidence that much lower latency values can be obtained for ASIC implementations.
  arXiv  Detail & Related papers  (2023-10-23T14:51:22Z)
• Quality-Aware Translation Models: Efficient Generation and Quality Estimation in a Single Model [77.19693792957614]
  We propose to make neural machine translation (NMT) models quality-aware by training them to estimate the quality of their own output. We obtain quality gains similar or even superior to quality reranking approaches, but with the efficiency of single pass decoding.
  arXiv  Detail & Related papers  (2023-10-10T15:33:51Z)
• Machine Learning-Aided Efficient Decoding of Reed-Muller Subcodes [59.55193427277134]
  Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels. RM codes only admit limited sets of rates. Efficient decoders are available for RM codes at finite lengths.
  arXiv  Detail & Related papers  (2023-01-16T04:11:14Z)
• A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer [0.5658123802733283]
  We propose an efficient and scalable decoder for quantum error correction using Fujitsu Digital Annealer (DA) In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code to see its performance and scalability. It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation.
  arXiv  Detail & Related papers  (2022-03-29T07:48:51Z)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)
• Fast Convergence Algorithm for Analog Federated Learning [30.399830943617772]
  We propose an AirComp-based FedSplit algorithm for efficient analog federated learning over wireless channels. We prove that the proposed algorithm linearly converges to the optimal solutions under the assumption that the objective function is strongly convex and smooth. Our algorithm is theoretically and experimentally verified to be much more robust to the ill-conditioned problems with faster convergence compared with other benchmark FL algorithms.
  arXiv  Detail & Related papers  (2020-10-30T10:59:49Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Communication-Efficient Gradient Coding for Straggler Mitigation in Distributed Learning [17.454251607446555]
  Distributed implementations of gradient-based methods, wherein a server distributes gradient computations across worker machines, need to overcome two limitations. Ye and Abbe [ICML 2018] proposed a coding-theoretic paradigm to characterize a fundamental trade-off between computation load per worker, communication overhead per worker, and straggler tolerance. We develop a communication-efficient gradient coding framework to overcome these drawbacks.
  arXiv  Detail & Related papers  (2020-05-14T17:57:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.