Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensions
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Abstract
We strengthen proper agnostic learning of stabilizer states for arbitrary mixed inputs in every odd-prime dimension. Given stabilizer overlap F ≥ τ, the learner returns a pure stabilizer of overlap at least F − ε, with confidence 1 − δ, using exp(O(log²(2/τ))) poly(n,p,ε⁻¹,log(2/δ)) resources with absolute exponential constants and fixed polynomial degree. An even quotient-convolution argument strengthens mixed-input escape to (p−1)Fʳ/(4p), where r=6 for p≡3 mod4 and r=4 for p≡1 mod4. Spectral concentration and observed eigenoutcomes remove local-dimension losses from the exponent. This is a strengthened edition of the same work, using established measurement and bootstrapping methods.
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Research details
- Subjects
- Mathematics · Quantum Information Theory
- Keywords
- stabilizer states, agnostic learning, quantum learning, mixed states, odd-prime dimensions
- Manuscript date
- 2026-10-19
- Reader reuse
- No additional permission granted
Scope
Arbitrary mixed inputs in odd-prime dimension, in an exact Clifford and coherent-measurement model. The stated copy counts and resource bounds are sufficient. The qutrit case is included in this consolidated paper.
Disclosures
Known weighted/skewed measurements, convolution tools and stabilizer bootstrapping are credited. Exact Clifford and coherent eigenspace operations are assumed; no noisy or compiled finite-gate theorem is proved. AI assistance was used in derivation, programming, literature discovery and proof checking. Personal explanations and internal review records are excluded from the public package.
Reproduction
Updated October 19, 2026 edition. The clean 13-file package contains the complete manuscript and LaTeX source, full proof supplement, seven verification programs, reproduction instructions and checksum manifest. Ordinary and optimized replays and 88 robustness cases passed. Finite diagnostics do not implement the complete quantum learner or prove arbitrary-n correctness.