Structural encoding with classical codes for computational-basis bit-flip correction in the early fault-tolerant regime

• URL: http://arxiv.org/abs/2510.10888v1
• Date: Mon, 13 Oct 2025 01:36:06 GMT
• Title: Structural encoding with classical codes for computational-basis bit-flip correction in the early fault-tolerant regime
• Authors: IlKwon Sohn, Changyeol Lee, Wooyeong Song, Kwangil Bae, Wonhyuk Lee,
• Abstract summary: We propose a novel framework that integrates quantum computation with the functionality of classical error correction.<n>In this approach, quantum computation is performed within the codeword subspace defined by a classical error correction code.
• Score: 0.6524460254566904
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the functionality of classical error correction. In this approach, quantum computation is performed within the codeword subspace defined by a classical error correction code. The correction of various types of errors that manifest as bit flips is carried out based on the final measurement outcomes. The approach leverages the asymmetric structure of many key algorithms, where problem-defining diagonal operators (e.g., oracles) are paired with fixed non-diagonal operators (e.g., diffusion operators). The proposed encoding maps computational basis states to classical codewords. This approach commutes with diagonal operators, obviating their overhead and confining the main computational cost to simpler non-diagonal components. Noisy simulations corroborate this analysis, demonstrating that the proposed scheme serves as a viable protocol-level layer for enhancing performance in the early fault-tolerant regime.

Related papers

• The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositions [45.88028371034407]
  Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations.<n>Despite proven universal approximation properties, deep operator networks (DeepONets) often exhibit limited accuracy and generalization in practice.<n>This work analyzes performance limitations of the classical DeepONet architecture.
  arXiv  Detail & Related papers  (2026-02-25T13:38:08Z)
• Fault-tolerant quantum computation with constant overhead for general noise [8.49301882142233]
  We show that fault-tolerant quantum computation can be achieved with constant qubit overhead under general noise models.<n>We develop a fault-tolerant error correction scheme and a method for implementing logic gates under general circuit noise.
  arXiv  Detail & Related papers  (2025-12-02T13:41:25Z)
• Correcting quantum errors using a classical code and one additional qubit [0.0]
  We introduce Hadamard-based Virtual Error Correction (H-VEC), a protocol that empowers any classical bit-flip code to correct arbitrary Pauli noise.<n>H-VEC virtually filters the error channel, projecting the noise into pure Y-type errors that are subsequently corrected using the classical code's native decoding algorithm.
  arXiv  Detail & Related papers  (2025-10-06T16:52:05Z)
• Distributed Quantum Error Correction with Permutation-Invariant Approximate Codes [0.7161783472741748]
  We introduce a distributed quantum error correction framework based on approximate codes to address this challenge.<n>We derive a lower bound and present corresponding simulations which indicate that this nontraditional approach can provide marked advantage.<n>Results highlight the potential of approximate distributed error correction strategies for scalable, modular, fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2025-09-29T17:28:39Z)
• 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)
• 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)
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice [41.94295877935867]
  Topological quantum error correction is a milestone in the scaling roadmap of quantum computers.<n>The square-lattice surface code has become the workhorse to address this challenge.<n>In some platforms, however, the connectivities are kept even lower in order to minimise gate errors.
  arXiv  Detail & Related papers  (2024-02-03T15:28:27Z)
• Fault-tolerant quantum architectures based on erasure qubits [49.227671756557946]
  We exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into erasures at known locations. We propose and optimize QEC schemes based on erasure qubits and the recently-introduced Floquet codes. Our results demonstrate that, despite being slightly more complex, QEC schemes based on erasure qubits can significantly outperform standard approaches.
  arXiv  Detail & Related papers  (2023-12-21T17:40:18Z)
• Union-find quantum decoding without union-find [4.24243593213882]
  We show that the behaviour of the decoder at scale underutilises the data structure. Improvements and simplifications can be made to architectural designs to reduce resource overhead in practice. This yields a linear-time worst-case complexity for the decoder at scale, even with a naive implementation omitting popular optimisations.
  arXiv  Detail & Related papers  (2023-06-16T10:54:59Z)
• 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)
• Robust nonadiabatic geometric quantum computation by dynamical correction [0.0]
  We propose a robust scheme for nonadiabatic geometric quantum computation (NGQC) combining with the dynamical correction technique. We numerically show that our scheme can greatly improve the gate robustness in previous protocols. Our scheme provides a promising alternation for the future scalable fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2022-08-02T14:09:48Z)
• Random Alloy Codes and the Fundamental Limits of Coded Distributed Tensors [1.8130068086063333]
  Stragglers and other failures can severely impact the overall completion time. Recent works in coded computing provide a novel strategy to mitigate stragglers with coded tasks. We show that this strict definition does not directly optimize the probability of failure.
  arXiv  Detail & Related papers  (2022-02-07T19:20:00Z)
• Activation Relaxation: A Local Dynamical Approximation to Backpropagation in the Brain [62.997667081978825]
  Activation Relaxation (AR) is motivated by constructing the backpropagation gradient as the equilibrium point of a dynamical system. Our algorithm converges rapidly and robustly to the correct backpropagation gradients, requires only a single type of computational unit, and can operate on arbitrary computation graphs.
  arXiv  Detail & Related papers  (2020-09-11T11:56:34Z)

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.