Quasilinear Equivalence Checking for Detector Error Models

• URL: http://arxiv.org/abs/2606.14677v1
• Date: Fri, 12 Jun 2026 17:42:16 GMT
• Title: Quasilinear Equivalence Checking for Detector Error Models
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A Detector Error Model (DEM) is a structured representation of error mechanisms in quantum circuits, which has gained popularity in quantum compilation pipelines for its ability to capture fault-tolerance at a circuit level. It lists error mechanisms as instructions targeting detectors and observables, specifying for each physical fault channel the probability that the fault fires, the detectors it triggers, and the observables it flips. In this paper, we develop an equational theory for DEMs, with its associated categorical semantics. We present a sound, terminating, confluent rewriting system for DEM terms, formulating it as a symmetric monoidal theory (a PROP) over the Giry monad. We prove that every DEM term has a unique normal form, which can be computed efficiently in quasilinear time $O(k|E|\log|E|)$, where $|E|$ is the number of instructions and $k$ bounds the size of a target set. This provides a complete set of invariants (via Tanner graphs) for structural DEM equivalence. We provide the first static decision procedure for DEM equivalence, with rigorous correctness guarantees. It is complete (decides full decoder-equivalence exactly) for non-adaptive quantum error correction (QEC) pipelines, and scales to a sound and applicable decision procedure for partially-adaptive circuits (lattice surgery, distributed QEC, ...) without suffering exponential overhead. We discuss its application to the verification and optimisation of quantum compilers.

Related papers

• Modeling Quantum Error Detection with Transition Matrices [0.3274502177751997]
  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.
  arXiv  Detail & Related papers  (2026-09-10T18:03:43Z)
• Equation Recast for Canonical Operator Learning Across Parametric PDEs [59.44573033543284]
  We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator.<n>In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries.
  arXiv  Detail & Related papers  (2026-09-02T13:15:50Z)
• Intrinsic Structure: Spectral Identifiability for Mechanistic Interpretability [51.56484100374058]
  We prove the first identifiability theorem for a mechanistic-interpretability primitive.<n>The spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.
  arXiv  Detail & Related papers  (2026-08-10T19:42:01Z)
• Theory of approximate quantum error correction and the error-set model [53.73800998389749]
  We develop a theory of approximate quantum error correction based on the error-set model.<n>Code correcting a given error set automatically protects against every channel whose Kraus operators lie in their linear span.<n>This linearity gives rise to code distance, the equivalence between erasures and general errors, and a theory ofally good codes.
  arXiv  Detail & Related papers  (2026-07-25T02:15:33Z)
• What Does a Discrete Diffusion Model Learn? [71.03603607324338]
  discrete diffusion model learns: a denoiser, a score ratio, or a bridge plug-in predictor.<n>We start with a rigorous derivation of the continuous-time Markov chain (CTMC) ELBO for any noising process.<n>Every identity is verified numerically, without approximation, on an exactly solvable model.
  arXiv  Detail & Related papers  (2026-07-06T17:56:11Z)
• Tailoring Strictly Proper Scoring Rules for Downstream Tasks: An Application to Causal Inference [48.78219918881965]
  We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric.<n>We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping.
  arXiv  Detail & Related papers  (2026-06-02T08:41:25Z)
• Understanding Quantum Instruments [0.304585143845864]
  Correctly modeling QIs is essential for applications using MCMs, such as adaptive circuits and quantum error correction.<n>This Note offers practical guidance on understanding and interpreting QI error models.
  arXiv  Detail & Related papers  (2026-04-20T22:06:54Z)
• Variational Rectification Inference for Learning with Noisy Labels [74.85528327499662]
  We propose variational rectification inference (VRI) to formulate the adaptive rectification for loss functions.<n>VRI is constructed as a hierarchical Bayes by treating the rectifying vector as a latent variable.<n>By introducing the variational term in VRI, the conditional posterior is estimated accurately and avoids collapsing to a Dirac delta function.
  arXiv  Detail & Related papers  (2026-03-18T01:25:08Z)
• Ising on the donut: Regimes of topological quantum error correction from statistical mechanics [0.0]
  Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates.<n>Here we exploit an exact mapping, from a toric code under bit-flip noise that is post-selected on being syndrome free to the exactly-solvable two-dimensional Ising model on a torus, to derive an analytic solution for the logical failure rate.
  arXiv  Detail & Related papers  (2025-12-11T08:06:23Z)
• 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)
• Universal quantum computation via scalable measurement-free error correction [45.29832252085144]
  We show that universal quantum computation can be made fault-tolerant in a scenario where the error-correction is implemented without mid-circuit measurements.<n>We introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $mathitCCZ$ gate.<n>In particular, our findings support that below-breakeven logical performance is achievable with a circuit-level error rate below $10-3$.
  arXiv  Detail & Related papers  (2024-12-19T18:55:44Z)
• A correspondence between quantum error correcting codes and quantum reference frames [0.0]
  In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information.<n>We elaborate this parallel in terms of quantum reference frames (QRFs), which are a universal toolkit for dealing with symmetries in quantum systems.<n>We show that there is a one-to-one correspondence between maximal correctable error sets and tensor factorizations splitting system from error-generated QRF degrees of freedom.
  arXiv  Detail & Related papers  (2024-12-19T18:52:38Z)
• Measurement-free fault-tolerant quantum error correction in near-term devices [0.0]
  We provide a novel scheme to perform QEC cycles without the need of measuring qubits. We benchmark logical failure rates of the scheme in comparison to a flag-qubit based EC cycle. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array.
  arXiv  Detail & Related papers  (2023-07-25T07:22:23Z)
• 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)

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.