Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction

• URL: http://arxiv.org/abs/2412.21118v1
• Date: Mon, 30 Dec 2024 17:45:08 GMT
• Title: Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction
• Authors: Ching-Feng Kung, Kao-Yueh Kuo, Ching-Yi Lai,
• Abstract summary: We introduce the concept of approximate degenerate decoding and integrate it with ordered statistics decoding (OSD) We present an ADOSD algorithm that significantly improves OSD efficiency in the code capacity noise model.
• Score: 5.625796693054094
• License:
• Abstract: Efficient decoding of quantum codes is crucial for achieving high-performance quantum error correction. In this paper, we introduce the concept of approximate degenerate decoding and integrate it with ordered statistics decoding (OSD). Previously, we proposed a reliability metric that leverages both hard and soft decisions from the output of belief propagation (BP), which is particularly useful for identifying highly reliable subsets of variables. Using the approach of reliable subset reduction, we reduce the effective problem size. Additionally, we identify a degeneracy condition that allows high-order OSD to be simplified to order-0 OSD. By integrating these techniques, we present an ADOSD algorithm that significantly improves OSD efficiency in the code capacity noise model. We demonstrate the effectiveness of our BP+ADOSD approach through extensive simulations on a varity of quantum codes, including generalized hypergraph-product codes, topological codes, lift-connected surface codes, and bivariate bicycle codes. The results indicate that the BP+ADOSD decoder outperforms existing methods, achieving higher error thresholds and enhanced performance at low error rates. Additionally, we validate the efficiency of our approach in terms of computational time, demonstrating that ADOSD requires, on average, the same amount of time as two to three BP iterations on surface codes at a depolarizing error rate of around $1\%$. All the proposed algorithms are compared using single-threaded CPU implementations.

Related papers

• 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)
• Optimizing hypergraph product codes with random walks, simulated annealing and reinforcement learning [4.642647756403864]
  Hypergraph products are quantum low-density parity-check (LDPC) codes constructed from two classical LDPC codes. In this work, we focus on optimizing performance against the quantum erasure channel. A key advantage of this channel is the existence of an efficient maximum-likelihood decoder.
  arXiv  Detail & Related papers  (2025-01-16T16:01:02Z)
• Quantum-enhanced belief propagation for LDPC decoding [0.0]
  We introduce the quantum-enhanced belief propagation algorithm, which acts as a pre-processing step to belief propagation. We study the possibility of having shared variational parameters between syndromes and, in this case, code lengths.
  arXiv  Detail & Related papers  (2024-12-11T18:14:18Z)
• 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)
• An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise [0.562479170374811]
  We introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes. We show that the BP+OTF decoder achieves logical error suppression within an order of magnitude of state-of-the-art inversion-based decoders.
  arXiv  Detail & Related papers  (2024-09-02T19:50:57Z)
• Near-optimal decoding algorithm for color codes using Population Annealing [44.99833362998488]
  We implement a decoder that finds the recovery operation with the highest success probability. We study the decoder performance on a 4.8.8 color code lattice under different noise models.
  arXiv  Detail & Related papers  (2024-05-06T18:17:42Z)
• Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes [6.175503577352742]
  We propose a differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural network (GNN) layers.
  arXiv  Detail & Related papers  (2023-10-26T19:56:25Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices [60.02503434201552]
  We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
  arXiv  Detail & Related papers  (2022-12-20T13:41:27Z)
• 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)
• AQD: Towards Accurate Fully-Quantized Object Detection [94.06347866374927]
  We propose an Accurate Quantized object Detection solution, termed AQD, to get rid of floating-point computation. Our AQD achieves comparable or even better performance compared with the full-precision counterpart under extremely low-bit schemes.
  arXiv  Detail & Related papers  (2020-07-14T09:07:29Z)

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.