Edition 2
Scott Schubr
- Primary subject
- Mathematics
- Subject subfields
- Quantum Information Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
We study exact identification of an unknown qubit stabilizer from a state diagonal in its stabilizer eigenbasis. A positive lower bound on every target-signed stabilizer expectation unifies global white noise, strict-majority diagonal mixtures, and additional nonmajority correlated mixtures. For a supplied gap μ_0≥2^(-(log_2 n)^γ), fixed γ<1, recovery uses O(n^(1+ε)) original copies at fixed confidence, polynomial ideal quantum work, and 2^(O(n/log log n)) classical time. The new step is a uniformly spread successful component in a learned, verified Pauli direction, giving contraction of surviving error odds without independent syndrome errors. We also give polynomial-time recovery when the background is an unknown target-containing stabilizer code projector and a relative diagonal-visibility promise holds. Dense CSS targets with sufficiently small background-code rank are included. Known noisy-parity solvers, polynomial subspace lifts and high-fidelity learning are explicit ingredients. A bounded-weight local-Pauli corollary supplies another polynomial regime.
Edition 3
Scott Schubr
- Primary subject
- Mathematics
- Subject subfields
- Quantum Information Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
We strengthen proper agnostic learning of stabilizer states for arbitrary mixed inputs in every odd-prime local dimension. Given an overlap promise F≥τ, the learner returns a pure stabilizer of overlap at least F-ε, with confidence 1-δ, using exp(O(log^2(2/τ))) poly(n,p,ε^(-1),log(2/δ)) resources with absolute exponent constants and fixed polynomial degree. The previous dimension-dependent exponent is removed by testing Weyl spectral concentration and selecting an observed eigenvalue. An even quotient-convolution argument also improves escape to (p-1)F^r/(4p), where r=6 for p≡3(mod 4) and r=4 for p≡1(mod 4), using the same known measurements. Explicit rational counters cover all rejection attempts and final validation. The model still uses exact Clifford operations and coherent eigenspace measurements. We attribute the measurement primitives, uncertainty ingredients and bootstrapping framework to prior work; the strengthening concerns their uniform quantitative combination.
Edition 2
Scott Schubr
- Primary subject
- Mathematics
- Subject subfields
- Quantum Information Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
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, the expected time to record the optimizing stabilizer is linear in the number n of qudits when c^2>p/(p+1), quadratic at equality, and exponential when c^2<p/(p+1). We obtain the exact supercritical speed, subcritical exponential prefactors, and the complete 1/n critical-window mean profile. 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.
Edition 2
Scott Schubr
- Primary subject
- Mathematics
- Subject subfields
- Quantum Information Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
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.