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Single-copy learning of stabilizers with correlated diagonal noise

Scott Schubr

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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.

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Available editions

  1. Edition 2 · 2026-10-27 · public
  2. Edition 1 · 2026-10-24 · public

Research details

Subjects
Mathematics · Quantum Information Theory
Keywords
stabilizer learning, correlated diagonal noise, quantum state learning, noisy parity, positive spectrum
Manuscript date
2026-10-23
Reader reuse
No additional permission granted

Scope

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 verifies the stated auxiliary calculations.

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.

Reproduction

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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