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Single-copy learning of stabilizers with correlated diagonal noise

Scott Schubr

Luminary Oddities

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

Abstract

We study 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 additional nonmajority correlated mixtures. For a supplied gap μ_0≥2^(-(log_2 n)^γ), fixed γ<1, recovery uses O(n^(1+ε)) original copies at fixed confidence, polynomial ideal quantum work, and 2^(O(n/log log n)) classical time. The new step is a uniformly spread successful component in a learned, verified Pauli direction, giving contraction of surviving error odds without independent syndrome errors. We also give polynomial-time recovery when the background is an unknown target-containing stabilizer code projector and a relative diagonal-visibility promise holds. Dense CSS targets with sufficiently small background-code rank are included. Known noisy-parity solvers, polynomial subspace lifts and high-fidelity learning are explicit ingredients. A bounded-weight local-Pauli corollary supplies another polynomial regime.

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

Scope of the work

Single-copy stabilizer identification under a target-signed expectation gap for correlated diagonal noise, with near-linear copy/subexponential classical bounds and separate polynomial-time relative-visibility regimes.

Reproduction notes

10-page manuscript and 7 source-package members. Compile main.tex. Python 3.10+ and its standard library run python verify.py, also under -O; compare its parsed JSON with expected_checks.json for the finite stabilizer/filtering controls. These fixtures accompany the analytic learning bounds.

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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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Cite this edition

Scott Schubr. (2026). Single-copy learning of stabilizers with correlated diagonal noise (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/single-copy-learning-stabilizers-correlated-diagonal-noise/v/2

BibTeX
@techreport{luminary_single_copy_learning_stabilizers_correlated_diagonal_noise_v2,
  title = {Single-copy learning of stabilizers with correlated diagonal noise},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 2},
  url = {https://research.luminaryoddities.com/single-copy-learning-stabilizers-correlated-diagonal-noise/v/2}
}

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