Research Article · Preprint Mathematics
Sharp noise transitions for an adaptive single-copy stabilizer-learning process
- Primary subject
- Mathematics
- Subject subfields
- Quantum Information Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
Abstract
We determine the noise-dependent behavior of the adaptive single-copy stabilizer-learning update of Bittel, Eisert, Gong, Mele and Schatzki on globally depolarized stabilizer states. For every fixed prime local dimension p, the number of diagonal stabilizers still missing follows an exact birth–death chain. Writing c for the retained pure-state weight, the expected time to record the optimizing stabilizer is linear in the number n of qudits when c^2>p/(p+1), quadratic at equality, and exponential when c^2<p/(p+1). We obtain the exact supercritical speed, subcritical exponential prefactors, and the complete 1/n critical-window mean profile. An exact regeneration identity distinguishes first exposure of the computational-basis target from its actual recording. A finite-time bound shows that below threshold the unchanged algorithm has exponentially small success probability in any polynomial round budget, even on this simple noise family. The obstruction concerns this update and candidate generation rule.
Keywords stabilizer learning · adaptive measurements · global depolarizing noise · birth–death chains · critical windows · quantum learning
Scope of the work
Exact noise-dependent rank and candidate-recording laws for the specified unchanged adaptive single-copy stabilizer-learning process, including the sharp linear/quadratic/exponential transition, critical window and finite-time exponential barrier.
Reproduction notes
The paper has 11 pages. The editable-source archive contains 6 files. Compile manuscript/main.tex. Run verify.py with assertions enabled to check exact finite transition and recording controls against expected_checks.json.
The manuscript
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Author disclosures
AI tools assisted derivation, programming, literature discovery and proof checking, as disclosed in the manuscript. This is an author-published preprint. AI-assisted internal checking is not external human refereeing or formal proof-assistant verification. The paper credits the adaptive algorithm of Bittel et al. and distinguishes its analysis from prior multi-copy learning results.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Sharp noise transitions for an adaptive single-copy stabilizer-learning process (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/sharp-noise-transitions-adaptive-single-copy-stabilizer-learning/v/2
BibTeX
@techreport{luminary_sharp_noise_transitions_adaptive_single_copy_stabilizer_learning_v2,
title = {Sharp noise transitions for an adaptive single-copy stabilizer-learning process},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/sharp-noise-transitions-adaptive-single-copy-stabilizer-learning/v/2}
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