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 c_0≥ 2^(-(log_2 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.pdf130.3 KiB · pdf
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16496300fd4562d1636c56f14c57fcb2d0be79a19b6357ec5dcdf1555ef1970f - Revised_publication_package.zip147.5 KiB · package
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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
Exact signed-tableau recovery under global depolarization by single-copy certified filtering: nearly linear original-copy complexity with subexponential classical processing, and a separate polynomial regime under the supplied-frame visibility promise.
Disclosures
AI tools assisted research, derivation, programming, literature discovery and checking, as disclosed in the manuscript. This is an author-published preprint; AI-assisted checking is not external human refereeing or formal proof-assistant certification. 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 paper has 11 pages. The editable-source archive contains 6 files. Compile manuscript/main.tex. Standard-library verify.py reconstructs exact finite stabilizer/filtering controls and compares with expected_checks.json.