Single-copy learning of noisy stabilizers by certified filtering
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Abstract
We give a single-copy recovery framework for an unknown qubit stabilizer state mixed with global white noise. For every fixed ε>0, 0<γ<1 and fixed confidence, the exact target can be recovered from O(n^(1+ε)) original copies when the retained signal has a known lower bound c₀≥2^(−(log₂ n)^γ). The total number of ideal quantum operations is polynomial, while classical processing takes 2^O(n/log log n) time. A random Clifford frame and a known partial-derivative measurement reduce discovery of one complete target Pauli to classical noisy-parity search. Fresh verification and a short certified seed then amplify the signal enough for known high-fidelity single-copy learning. This avoids recovering every graph row through a noisy solver. We also obtain polynomial classical time for every fixed positive signal under a supplied fractional diagonal-subspace promise, including dense CSS states and a CSS-defect class. The latter uses finite-field subspace recovery, with an explicit proof of the required fixed-weight extension. Supporting bounds distinguish partial code measurements from full-basis readout. The measurements, classical solvers and high-fidelity endpoint are established ingredients; the contribution is their operational combination and original-copy resource accounting.
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- Single_Copy_Learning_Noisy_Stabilizers_Certified_Filtering.pdf130.0 KiB · pdf
SHA-256
d74b44480cbc42db5ce7e9d194669dbb65687649045e0231df0c4b308f844bfc - Single_Copy_Certified_Filtering_Publication_Package_20261022.zip147.0 KiB · package
SHA-256
cecafa03f9ccc53234eb47da3a2f105164cc3337657a031b9468a1412f19bbd9
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Research details
- Subjects
- Mathematics · Quantum Information Theory
- Keywords
- stabilizer learning, single-copy measurements, global depolarization, certified filtering, learning parity with noise, CSS states
- Manuscript date
- 2026-10-22
- Reader reuse
- No additional permission granted
Scope
Independent globally depolarized qubit stabilizer inputs, supplied rational signal floor and ideal within-copy Clifford operations/readout. The general near-linear-original-copy theorem has fixed confidence and exponents, subexponential classical time and the specified subpolynomially vanishing signal floor. Polynomial classical time applies to the supplied-frame fractional diagonal-subspace promise at fixed positive signal and gap, including the stated CSS-defect class. This follows the author’s algorithm-specific noise-transition paper and changes its discovery mechanism.
Disclosures
AI tools assisted research, derivation, programming, literature discovery and checking, as disclosed in the manuscript. Established measurement primitives, classical solvers, high-fidelity learning, counting and polynomial-rank ingredients are credited. The contribution is the stated certified-filtering combination and original-copy resource accounting.
Reproduction
The six-member package contains the eleven-page paper, self-contained LaTeX source and bibliography, verify.py, expected_checks.json, README.txt and SHA256SUMS.txt. Run python verify.py with Python 3.10 or newer; no third-party packages are needed. Normal and optimized Python both retain the checks. Exact finite controls cover symplectic counts, support/difference laws, polynomial ranks, complex graph-state parity measurements, noise-grid estimates and signed projector identities. The finite diagnostics support the analytic all-dimensional proofs. Density-projector fixtures use real Paulis; separate graph-state controls include complex phases. Build instructions are in the README.