Adaptive syndrome measurements for Shor-style error correction

• URL: http://arxiv.org/abs/2208.05601v4
• Date: Fri, 28 Jul 2023 17:46:21 GMT
• Title: Adaptive syndrome measurements for Shor-style error correction
• Abstract summary: We improve the Shor fault-tolerant error correction scheme using an adaptive syndrome measurement technique. Our protocols satisfy the strong and the weak FTEC conditions.
• Score: 0.7734726150561088
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Shor fault-tolerant error correction (FTEC) scheme uses transversal gates and ancilla qubits prepared in the cat state in syndrome extraction circuits to prevent propagation of errors caused by gate faults. For a stabilizer code of distance $d$ that can correct up to $t=\lfloor(d-1)/2\rfloor$ errors, the traditional Shor scheme handles ancilla preparation and measurement faults by performing syndrome measurements until the syndromes are repeated $t+1$ times in a row; in the worst-case scenario, $(t+1)^2$ rounds of measurements are required. In this work, we improve the Shor FTEC scheme using an adaptive syndrome measurement technique. The syndrome for error correction is determined based on information from the differences of syndromes obtained from consecutive rounds. Our protocols that satisfy the strong and the weak FTEC conditions require no more than $(t+3)^2/4-1$ rounds and $(t+3)^2/4-2$ rounds, respectively, and are applicable to any stabilizer code. Our simulations of FTEC protocols with the adaptive schemes on hexagonal color codes of small distances verify that our protocols preserve the code distance, can increase the pseudothreshold, and can decrease the average number of rounds compared to the traditional Shor scheme. We also find that for the code of distance $d$, our FTEC protocols with the adaptive schemes require no more than $d$ rounds on average.

Related papers

• SS-ESOAP: Self-Scaled Adaptive Preconditioning for Physics-Informed Learning [70.71795707610961]
  method augments SOAP-style preconditioning with a scalar secant-energy correction adapted to Kronecker geometry.<n>Method attains the lowest final residual on six of eight PDE benchmarks.<n>Three-seed $L2$ and $H1$ errors on four representative PDEs support the link between lower residuals and improved solution accuracy.
  arXiv  Detail & Related papers  (2026-08-29T21:34:47Z)
• When to Skip Syndrome Extraction in Surface-GKP Codes [0.1909808926064466]
  We propose a concrete adaptive skipping scheme for the surface-GKP code.<n>We show that the scheme can reduce the number of surface-code stabilizer measurements while maintaining logical error rates comparable to or lower than those of the full-measurement baseline.
  arXiv  Detail & Related papers  (2026-06-23T12:01:14Z)
• Bandit Convex Optimization with Gradient Prediction Adaptivity [56.816177049016794]
  We investigate whether optimistic gradient predictions can improve worst-case regret guarantees in a prediction-adaptive manner.<n>The key idea is a novel variance-reduced gradient estimator whose variance scales with the prediction error rather than the gradient norm.<n>We establish an information-theoretic lower bound that scales as $(sqrtmathbbE[S_T])$, providing a fundamental characterization of the best achievable prediction-adaptive regret.
  arXiv  Detail & Related papers  (2026-05-21T08:57:38Z)
• Correction and Corruption: A Two-Rate View of Error Flow in LLM Protocols [51.56484100374058]
  We propose a paired-outcome measurement interface for auditing a single protocol step on exact-match tasks.<n>For each instance, the interface records a baseline correctness bit and a post-step correctness bit.<n>These rates predict accuracy changes and define a reusable empirical interface testable across seeds, mixtures, and pipelines.
  arXiv  Detail & Related papers  (2026-04-20T13:25:40Z)
• Adaptive Loss-tolerant Syndrome Measurements [1.7403133838762448]
  We extend the study of adaptive Shor-style measurement sequences to the mixed error model.<n>We discuss how to adaptively convert correctable erasures into located errors.<n>We then generalize both the weak and strong FTEC conditions.
  arXiv  Detail & Related papers  (2026-03-18T17:50:31Z)
• Fault-Tolerant Quantum Error Correction: Implementing Hamming-Based Codes with Advanced Syndrome Extraction Techniques [0.0]
  We show that intelligent ancilla management improves error suppression by up to 2.4$times$ compared to standard approaches.<n>Our implementations achieve logical error rates as low as $5.1 times 10-5$ under realistic noise conditions.<n>These results provide immediately deployable tools for near-term quantum devices.
  arXiv  Detail & Related papers  (2026-01-10T00:10:52Z)
• Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers [90.50039419576807]
  Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling.<n>To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary $0,1$ during training.<n>This choice carries a cost: it introduces textitfalse negatives (rejecting correct answers, FNs) and textitfalse positives (accepting incorrect ones, FPs)
  arXiv  Detail & Related papers  (2025-10-01T13:56:44Z)
• Demonstrating dynamic surface codes [138.1740645504286]
  We experimentally demonstrate three time-dynamic implementations of the surface code. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
  arXiv  Detail & Related papers  (2024-12-18T21:56:50Z)
• Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise [0.0]
  We present a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. We construct a correction protocol that confines errors into short-ranged pairs in the steady-state. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition.
  arXiv  Detail & Related papers  (2024-04-25T18:21:48Z)
• Bit-flipping Decoder Failure Rate Estimation for (v,w)-regular Codes [84.0257274213152]
  We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder. We validate our results, providing comparisons of the modeled and simulated weight of the syndrome, incorrectly-guessed error bit distribution at the end of the first iteration, and two-itcrypteration Decoding Failure Rates (DFR)
  arXiv  Detail & Related papers  (2024-01-30T11:40:24Z)
• Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons [59.63080344946083]
  We show that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit. We demonstrate mid-circuit detection of erasure errors while introducing $ 0.1%$ dephasing error per check. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.
  arXiv  Detail & Related papers  (2023-07-17T18:00:01Z)
• Conflict-driven Structural Learning Towards Higher Coverage Rate in ATPG [7.750468474116735]
  This paper proposes a conflict-driven structural learning (C) ATPG algorithm. It is shown that compared with the SAT-based ATPG, the proposed CDSL can on average decrease $25.6%$ aborted faults with $94.51%$ less run time.
  arXiv  Detail & Related papers  (2023-03-04T01:50:08Z)
• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction [1.6114012813668934]
  We propose fault-tolerant quantum error correction schemes based on the concatenation of small error detection codes with the three-dimensional cluster state. We find a set of codes for which such a conversion is possible, and study their performance against the standard circuit-level depolarizing model. Our best performing scheme, which is based on a concatenation with a classical code, improves the threshold by $16.5%$ and decreases the spacetime overhead by $32%$.
  arXiv  Detail & Related papers  (2022-09-20T00:08:28Z)
• Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics [0.0]
  We propose two schemes to obtain Gottesman-Kitaev-Preskill (GKP) error syndromes by means of linear optical operations, homodyne measurements and GKP ancillae. For a concatenation of GKP codes with a stabilizer code only $2n$ measurements are needed in order to obtain the complete syndrome information.
  arXiv  Detail & Related papers  (2021-10-11T14:35:07Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Fault-tolerant parity readout on a shuttling-based trapped-ion quantum computer [64.47265213752996]
  We experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)%. The scheme is an essential building block in a broad class of stabilizer quantum error correction protocols.
  arXiv  Detail & Related papers  (2021-07-13T20:08:04Z)
• Tail-to-Tail Non-Autoregressive Sequence Prediction for Chinese Grammatical Error Correction [49.25830718574892]
  We present a new framework named Tail-to-Tail (textbfTtT) non-autoregressive sequence prediction. Considering that most tokens are correct and can be conveyed directly from source to target, and the error positions can be estimated and corrected. Experimental results on standard datasets, especially on the variable-length datasets, demonstrate the effectiveness of TtT in terms of sentence-level Accuracy, Precision, Recall, and F1-Measure.
  arXiv  Detail & Related papers  (2021-06-03T05:56:57Z)
• Low overhead fault-tolerant quantum error correction with the surface-GKP code [60.44022726730614]
  We propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. We show that a low logical failure rate $p_L 10-7$ can be achieved with moderate hardware requirements.
  arXiv  Detail & Related papers  (2021-03-11T23:07:52Z)
• Between Shor and Steane: A unifying construction for measuring error syndromes [0.913755431537592]
  We find a unifying construction that generates a family of ancilla blocks that interpolate between Shor and Steane. This family increases the complexity of ancilla construction in exchange for reducing the rounds of measurement required to fault-tolerantly measure the error. Our method can be applied to any Calderbank-Shor-Steane codes and presents a new direction for optimizing fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2020-12-31T02:30:25Z)
• Short Shor-style syndrome sequences [0.0]
  We give both code-specific and general methods, using a variety of techniques and in a variety of settings. We design new quantum error-correcting codes specifically for efficient error correction, allowing single-shot error correction. For codes with multiple logical qubits, we give methods for combining error correction with partial logical measurements.
  arXiv  Detail & Related papers  (2020-08-12T01:01:27Z)

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.