Cancellation of Correlated Readout Errors in Measurement-Based Quantum Wires: Exact Channels, Finite-Memory Crossover, and Length-Reversal Boundaries
Year: 2026
Type: preprint
Abstract: This record contains the revision 9 preprint and its verification and figure-reproduction materials. We determine when correlated readout-label errors cancel in a fixed measurement-based quantum wire and how finite correlation and independent noise determine its optimal length. Quantum operations and X measurements are ideal. A stationary binary Markov component with marginal 0 < p < 1/2 and persistence 0 ≤ c ≤ 1, combined with independent flips of probability 0 ≤ r < 1/2, yields an exact output Pauli channel through two-dimensional transfer matrices. The channel acts on arbitrary inputs, including reference-entangled inputs, and its entanglement infidelity equals its half-diamond distance from the identity. Common-mode errors cancel at lengths divisible by four when c = 1 and r = 0. Every fixed c < 1 instead gives a completely depolarizing long-wire limit; two residue-class crossover functions resolve the singular limit. Fidelity decreases within each even residue class, so its maximum over all positive even lengths is attained at two or four steps. Exact boundaries select the maximizer, and an effective depolarizing penalty quantifies the overhead tolerance of the four-step advantage. Contents. The ZIP includes the latest 19-page manuscript PDF, its authoritative LaTeX source, the three manuscript figures, the unchanged ESM_1.zip containing Python verification and figure-generation code, numerical data, saved execution records and provenance, plus licensing information, a BibTeX citation, and SHA-256 checksums. Scientific files are unchanged from the supplied revision 9 materials. The packaging did not rerun calculations or recompile the manuscript. The earlier reference-only PDF and submission-preparation working records are excluded. Licenses. MIT applies to Python source code, including code inside ESM_1.zip. CC BY 4.0 applies to the manuscript, LaTeX source, figures, numerical data, documentation, and other non-code research materials. These licenses apply to the respective material categories; see the README and license files for scope. Funding. No funding or grants were received for this study. Competing interests. The author has no relevant financial or non-financial interests to disclose. AI-assisted preparation. ChatGPT (OpenAI) was used to assist with mathematical analysis, code development, figure preparation, English-language editing, LaTeX submission preparation, and organization of supplementary files. The author carefully reviewed the mathematical reasoning, code, figures, and manuscript text, and takes full responsibility for the scientific content and the final manuscript.
Author: Tsuzurugi, Jun
Institution: Okayama University of Science
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225739983
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