An exact Error Threshold of Surface Code under Correlated Nearest-Neighbor Errors: A Statistical Mechanical Analysis

• URL: http://arxiv.org/abs/2510.24181v1
• Date: Tue, 28 Oct 2025 08:35:07 GMT
• Title: An exact Error Threshold of Surface Code under Correlated Nearest-Neighbor Errors: A Statistical Mechanical Analysis
• Authors: SiYing Wang, ZhiXin Xia, Yue Yan, Xiang-Bin Wang,
• Abstract summary: Current exact surface code threshold analyses are based on the assumption of independent and identically distributed (i.i.d.) errors.<n>Here, we establish an error-edge map, which allows for the mapping of quantum error correction to a square-octagonal random bond Ising model.<n>We then present the exact threshold under a realistic noise model that combines independent single-qubit errors with correlated errors between nearest-neighbor data qubits.
• Score: 1.8787735186976828
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold analyses are based on the assumption of independent and identically distributed (i.i.d.) errors. Though there are numerical studieds for threshold with correlated error, they are only the lower bond ranther than exact value, this offers potential for higher error thresholds.Here, we establish an error-edge map, which allows for the mapping of quantum error correction to a square-octagonal random bond Ising model. We then present the exact threshold under a realistic noise model that combines independent single-qubit errors with correlated errors between nearest-neighbor data qubits. Our method is applicable for any ratio of nearest-neighbor correlated errors to i.i.d. errors. We investigate the error correction threshold of surface codes and we present analytical constraints giving exact value of error threshold. This means that our error threshold is both upper bound and achievable and hence on the one hand the existing numerical threshold values can all be improved to our threshold value, on the other hand, our threshold value is highest achievable value in principle.

Related papers

• Linear Regression under Missing or Corrupted Coordinates [58.9213131489513]
  We study how data may be corrupted or erased by an adversary under a coordinate-wise budget.<n>In the incomplete data setting, an adversary may inspect the dataset and delete entries in up to an $eta$-fraction of samples per coordinate.<n>In the corrupted data setting, the adversary instead replaces values arbitrarily, and the corruption locations are unknown to the learner.
  arXiv  Detail & Related papers  (2025-09-23T17:01:43Z)
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds [0.7328300048311823]
  Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility.<n>We focus on several distinct types of correlated errors that could potentially arise from next-nearest-neighbor (NNN) coupling in quantum systems.<n>We find that errors correlated along straight lines possess a type of crucial symmetry, resulting in higher thresholds compared to other types of correlated errors.
  arXiv  Detail & Related papers  (2025-06-18T14:28:12Z)
• Classification Error Bound for Low Bayes Error Conditions in Machine Learning [50.25063912757367]
  We study the relationship between the error mismatch and the Kullback-Leibler divergence in machine learning.<n>Motivated by recent observations of low model-based classification errors in many machine learning tasks, we propose a linear approximation of the classification error bound for low Bayes error conditions.
  arXiv  Detail & Related papers  (2025-01-27T11:57:21Z)
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology [0.0]
  We consider the surface code under errors featuring both coherent and incoherent components.<n>We show that for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance.
  arXiv  Detail & Related papers  (2024-12-30T16:14:55Z)
• Processing and Decoding Rydberg Decay Error with MBQC [5.154331853803125]
  We present a novel approach to manage Rydberg decay errors in measurement-based quantum computation.<n>We leverage the inherent structure of topological cluster states and final leakage detection information to locate propagated errors from Rydberg decay error.<n>Results show a comparable performance within a modest R_e, which reveals possible application of our method in near-term platform.
  arXiv  Detail & Related papers  (2024-11-07T12:49:55Z)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition [0.0]
  robustness of quantum memory against physical noises is measured by two methods.<n> exact and approximate quantum error correction (QEC) conditions for error recoverability.<n> decoder-dependent error threshold which assesses if the logical error rate diminishes with system size.
  arXiv  Detail & Related papers  (2023-12-28T12:37:49Z)
• Proximity-Informed Calibration for Deep Neural Networks [49.330703634912915]
  ProCal is a plug-and-play algorithm with a theoretical guarantee to adjust sample confidence based on proximity. We show that ProCal is effective in addressing proximity bias and improving calibration on balanced, long-tail, and distribution-shift settings.
  arXiv  Detail & Related papers  (2023-06-07T16:40:51Z)
• Detecting Errors in a Numerical Response via any Regression Model [21.651775224356214]
  Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values. We introduce veracity scores that distinguish between genuine errors and natural data fluctuations. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors.
  arXiv  Detail & Related papers  (2023-05-26T02:15:26Z)
• Coherent errors and readout errors in the surface code [0.0]
  We consider the combined effect of readout errors and coherent errors on the surface code. We find a threshold for this combination of errors, with an error rate close to the threshold of the corresponding incoherent error channel.
  arXiv  Detail & Related papers  (2023-03-08T15:50:44Z)
• 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)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions [62.997667081978825]
  We present a study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level.
  arXiv  Detail & Related papers  (2020-12-21T14:20:40Z)
• Fault-tolerant measurement-free quantum error correction with multi-qubit gates [9.099365414925845]
  Measurement-free quantum error correction (MFQEC) offers an alternative to standard measurement-based QEC. We revisit the question of fault tolerance (FT) for a measurement-free variant of the Steane code. We construct a revised MFQEC circuit that is resistant to all single-qubit errors, but which nonetheless cannot tolerate certain correlated errors.
  arXiv  Detail & Related papers  (2020-07-19T22:32:38Z)

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.