Modeling Quantum Error Detection with Transition Matrices

• URL: http://arxiv.org/abs/2609.12073v1
• Date: Thu, 10 Sep 2026 18:03:43 GMT
• Title: Modeling Quantum Error Detection with Transition Matrices
• Abstract summary: We construct an explicit transition matrix that exactly describes code-adapted basis-population dynamics of stabilizer codes under circuit-level Pauli noise.<n>For quantum error detection, we incorporate post-selection by aggregating rejected outcomes into an absorbing state.<n>We evaluate the framework on the $[[4,2,2]]$ and $[5,1,3]]$ codes under depolarizing gate noise and readout errors.
• Score: 0.3274502177751997
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct an explicit transition matrix that exactly describes code-adapted basis-population dynamics of stabilizer codes under circuit-level stochastic Pauli noise. The matrix is expressed in a code-adapted basis that captures probability flow between logical-basis labels and syndrome sectors. For quantum error detection (QED), we incorporate post-selection by aggregating rejected outcomes into an absorbing state, so that a single transition matrix represents a full clock cycle of gates, syndrome extraction, and post-selection. Additionally, we characterize when protocol symmetries permit exact lumping to simpler, more interpretable models. The transition matrix framework enables direct application of classical stochastic-matrix techniques to analyze multi-cycle QED protocols. First, we identify a leading-order obstruction to a stationary logical-only accepted-map description, and quantify the accepted leakage injection from QED-check imperfections that causes it. Second, we express leading-order QED efficiency as a function of check frequency in terms of physically meaningful parameters, and prove that less frequent checks improve efficiency to leading order. We evaluate the framework on the $[[4,2,2]]$ and $[[5,1,3]]$ codes under depolarizing gate noise and readout errors: transition-matrix predictions agree with million-shot Stim Monte Carlo at the scale of the reported confidence intervals, and matrix-computed results illustrate the first-cycle transient and interval-dependent efficiency. More broadly, the transition-matrix formalism provides both an analytical foundation for QED analysis and an interpretable tool for understanding code behavior under realistic noise.

Related papers

• Explicit block-encodings for biharmonic boundary-value problems [1.5922179327791923]
  We develop quantum linear-system algorithms for periodic, simply supported, and Dirichlet--Neumann boundary conditions.<n>For Dirichlet--Neumann problems, we introduce a second-order boundary-corrected finite-difference discretization.<n>We also formulate a coupled-Laplace system with additional boundary unknowns.
  arXiv  Detail & Related papers  (2026-07-24T15:20:32Z)
• Machine-learned syndrome post-selection for reliable quantum error correction [0.3181700357675698]
  Quantum error correction can be enhanced by post-selecting out runs that are likely to produce a logical failure.<n>We introduce a practical, decoder-agnostic post-selection method that learns directly from syndrome data.
  arXiv  Detail & Related papers  (2026-07-21T20:39:56Z)
• Quasilinear Equivalence Checking for Detector Error Models [0.0]
  A Detector Error Model (DEM) is a structured representation of error mechanisms in quantum circuits.<n>We develop an equational theory for DEMs, with its associated categorical semantics.<n>We provide the first static decision procedure for DEM equivalence, with rigorous correctness guarantees.
  arXiv  Detail & Related papers  (2026-06-12T17:42:16Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Weights to Code: Extracting Interpretable Algorithms from the Discrete Transformer [65.38883376379812]
  We propose the Discrete Transformer, an architecture engineered to bridge the gap between continuous representations and discrete symbolic logic.<n> Empirically, the Discrete Transformer not only achieves performance comparable to RNN-based baselines but crucially extends interpretability to continuous variable domains.
  arXiv  Detail & Related papers  (2026-01-09T12:49:41Z)
• Unsupervised Conformal Inference: Bootstrapping and Alignment to Control LLM Uncertainty [49.19257648205146]
  We propose an unsupervised conformal inference framework for generation.<n>Our gates achieve close-to-nominal coverage and provide tighter, more stable thresholds than split UCP.<n>The result is a label-free, API-compatible gate for test-time filtering.
  arXiv  Detail & Related papers  (2025-09-26T23:40:47Z)
• Characterizing Coherent Errors using Matrix-Element Amplification [0.27907340310431333]
  Matrix-Element Amplification using Dynamical Decoupling (MEADD)<n>We experimentally demonstrate that MEADD surpasses the accuracy and precision of existing characterization protocols for estimating systematic errors in single- and two-qubit gates.<n>We also use it to characterize coherent crosstalk in the processor which was previously too small to detect reliably.
  arXiv  Detail & Related papers  (2024-04-19T00:05:10Z)
• Randomized semi-quantum matrix processing [0.0]
  We present a hybrid quantum-classical framework for simulating generic matrix functions. The method is based on randomization over the Chebyshev approximation of the target function. We prove advantages on average depths, including quadratic speed-ups on costly parameters.
  arXiv  Detail & Related papers  (2023-07-21T18:00:28Z)
• Witnessing entanglement in trapped-ion quantum error correction under realistic noise [41.94295877935867]
  Quantum Error Correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks.
  arXiv  Detail & Related papers  (2022-12-14T20:00:36Z)
• Provably End-to-end Label-Noise Learning without Anchor Points [118.97592870124937]
  We propose an end-to-end framework for solving label-noise learning without anchor points. Our proposed framework can identify the transition matrix if the clean class-posterior probabilities are sufficiently scattered.
  arXiv  Detail & Related papers  (2021-02-04T03:59:37Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Matrix Smoothing: A Regularization for DNN with Transition Matrix under Noisy Labels [54.585681272543056]
  Training deep neural networks (DNNs) in the presence of noisy labels is an important and challenging task. Recent probabilistic methods directly apply transition matrix to DNN, neglect DNN's susceptibility to overfitting. We propose a novel method, in which a smoothed transition matrix is used for updating DNN, to restrict the overfitting.
  arXiv  Detail & Related papers  (2020-03-26T13:49:37Z)

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.