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Research Article · Preprint Mathematics

Single-copy learning of stabilizers with correlated diagonal noise

Scott Schubr

Luminary Oddities LLC

  • Mathematics
  • Quantum Information Theory
Primary subject
Mathematics
Subject subfields
Quantum Information Theory
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
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Overview

Abstract

This paper studies exact identification of an unknown qubit stabilizer from a state diagonal in its stabilizer eigenbasis. A positive lower bound on every target-signed stabilizer expectation unifies global white noise, strict-majority diagonal mixtures and further correlated mixtures. For a supplied floor μ₀ ≥ 2^{−(log₂ n)^γ}, with fixed γ < 1, fixed-confidence recovery uses O(n^{1+ε}) original copies, polynomial ideal quantum work and 2^{O(n/log log n)} classical time. A uniformly spread successful component in a learned, verified Pauli direction contracts surviving error odds without independent syndrome errors. An unknown target-containing stabilizer-code background admits polynomial recovery under a relative diagonal-visibility promise. Dense CSS targets with sufficiently small background-code rank and a bounded-weight local-Pauli regime are included. Known noisy-parity solvers, polynomial subspace lifts and high-fidelity learning are explicit ingredients. General polynomial-time recovery and arbitrary coherent noise remain unresolved.

Keywords stabilizer learning · correlated diagonal noise · quantum state learning · noisy parity · positive spectrum

Scope of the work

Recovery assumes diagonal iid input, the stated positive-spectrum floor, ideal operations and readout, and the specified copy model. Polynomial code-background recovery retains its signal and relative-visibility promises. This extends the certified-filtering predecessor rather than replacing its edition history. The finite checker does not execute the quantum learner or a noisy-parity solver.

Reproduction notes

The seven-member package includes the 10-page manuscript, complete LaTeX source and bibliography, a standard-library checker, expected JSON results, reader instructions, citation metadata and checksums. With Python 3.10 or later, run verify.py in normal and optimized modes and compare the parsed output with expected_checks.json. Build main.tex with Tectonic or two pdflatex runs. Finite rational checks supplement the analytic argument and cited learning theorems.

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Author disclosures

AI systems assisted research exploration, literature discovery, drafting and internal checking. The author retains responsibility for the manuscript. Internal AI-assisted and computational checks are distinct from external human peer review.

References and related publications

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A stable scholarly record

Cite this edition

Scott Schubr. (2026). Single-copy learning of stabilizers with correlated diagonal noise (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/single-copy-learning-stabilizers-correlated-diagonal-noise/v/1

BibTeX
@techreport{luminary_single_copy_learning_stabilizers_correlated_diagonal_noise_v1,
  title = {Single-copy learning of stabilizers with correlated diagonal noise},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 1},
  url = {https://research.luminaryoddities.com/single-copy-learning-stabilizers-correlated-diagonal-noise/v/1}
}

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