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  1. Spectral Crowding and Compression Limits for Arithmetic Covariance OperatorsScott SchubrEdition 2 · 2026-11-02 Public
  2. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 2 · 2026-11-02 Public
  3. Stable star marginals and strict edge correlations for random forestsScott SchubrEdition 3 · 2026-11-02 Public
  4. Sharp output ranges and bias frontiers for stabilizer purity estimationScott SchubrEdition 2 · 2026-11-02 Public
  5. Covariance confidence bounds and parity certificates for stable count lawsScott SchubrEdition 3 · 2026-11-02 Public
  6. Log-concave polynomial prefix sums: algebraic certificates and a sharp zero sectorScott SchubrEdition 3 · 2026-11-02 Public
  7. Audibility of all odd blind modes in rapidly twisted polar-strip tubesScott SchubrEdition 3 · 2026-11-02 Public
  8. Sharp collision criteria for frozen color histogramsScott SchubrEdition 3 · 2026-11-02 Public
  9. Sharp noise transitions for an adaptive single-copy stabilizer-learning processScott SchubrEdition 3 · 2026-11-02 Public
  10. Leading bias and positive correction of heat-kernel Sinkhorn metricsScott SchubrEdition 3 · 2026-11-02 Public
  11. Chollet's inequality for positive semidefinite matrices of rank at most fourScott SchubrEdition 4 · 2026-11-02 Public
  12. Bose gases in weakly twisted annular-sector waveguidesScott SchubrEdition 3 · 2026-11-02 Public
  13. Optimal concavity powers for lattice counts on smooth toric Fano threefoldsScott SchubrEdition 3 · 2026-11-02 Public
  14. A square-integral threshold for subadditivity on shrinking corridorsScott SchubrEdition 5 · 2026-11-02 Public
  15. Small-ball estimates for Hölder centers of the Kloosterman processScott SchubrEdition 3 · 2026-11-02 Public
  16. Finite-projection holomorphic stabilization of contractible affine manifoldsScott SchubrEdition 4 · 2026-11-02 Public
  17. Power Concavity of Low-Dimensional Unimodular Fiber CountsScott SchubrEdition 5 · 2026-11-02 Public
  18. Positive Eigenfunctions Above the First Eigenvalue of the Affine 2-LaplacianScott SchubrEdition 4 · 2026-11-02 Public
  19. Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory BoundsScott SchubrEdition 3 · 2026-11-02 Public
  20. Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensionsScott SchubrEdition 4 · 2026-11-02 Public
  21. Resolving Goldreich's Open Problem 4.1: Linear Lower Bounds for Cubic Graph Isomorphism TestingScott SchubrEdition 7 · 2026-11-02 Public
  22. Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codesScott SchubrEdition 3 · 2026-11-01 Public
  23. Single-time boundary heat-flux rigidity for smooth domainsScott SchubrEdition 4 · 2026-11-01 Public
  24. RH: Complete Signed Certificates and Canonical Null SynthesisScott SchubrEdition 12 · 2026-11-01 Public
PublicEdition 3

Sharp noise transitions for an adaptive single-copy stabilizer-learning process

Scott Schubr ORCID

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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, starting with all n diagonal stabilizers missing, the expected time to record the optimizing stabilizer is linear in n when c²>p/(p+1), quadratic at equality, and exponential when c²<p/(p+1). We obtain the exact supercritical speed, subcritical exponential prefactors, and a critical-window mean profile uniform over all initial missing ranks, with an O(n) remainder and the exact leading recording penalty. 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.

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