Single-copy learning of noisy stabilizers by certified filtering
Scott Schubr, October 22, 2026

Contents
Single_Copy_Learning_Noisy_Stabilizers_Certified_Filtering.pdf: complete paper.
manuscript/main.tex: self-contained LaTeX source and bibliography.
verify.py and expected_checks.json: exact finite mathematical controls.
SHA256SUMS.txt: SHA-256 identities of the five substantive files.

Scope
The general theorem gives near-linear original-copy complexity with subexponential classical processing, under exact global depolarization and ideal within-copy operations. A separate supplied-frame/basis-gap regime has polynomial classical processing at fixed positive signal and gap. Read the paper for all quantifiers and assumptions.

Reproduction
With Python 3.10 or newer, no third-party packages are needed:
  python verify.py
The program reads adjacent expected_checks.json, checks exact identities and prints the expected JSON. It writes no files. Optimization does not disable its checks.
Controls cover small symplectic spaces, support/difference laws, polynomial ranks, complex graph-state parity measurements, noise-grid estimates and signed projector identities. They are finite controls for the stated cases. Density-projector fixtures use real Paulis; complex phases are covered by separate graph-state controls.

To rebuild with Tectonic, create a separate output directory and run:
  tectonic --outdir build manuscript/main.tex
Alternatively compile the source with a standard LaTeX installation supporting the packages listed there. Bibliography is embedded. PDF metadata may vary between builds.

Relationship and attribution
This is a follow-up to Sharp noise transitions for adaptive single-copy stabilizer learning (author-published edition 1), cited in the paper. Known measurements, classical learning algorithms and rank/counting ingredients are attributed in the manuscript. The new contribution is the stated certified-filtering resource synthesis and its structured regime. The manuscript includes an AI-assistance disclosure.
