Affine-Profile Stabilizer Thresholds for Magic in Codeword-Stabilized Quantum Codes
Abstract
Codeword-stabilized quantum codes give a unified graph-state description of stabilizer and nonadditive quantum error-correcting codes. Although each individual CWS word state is stabilizer, coherent superpositions of different word states can be nonstabilizer. We develop a CWS-adapted magic-witness framework that isolates this codeword coherence and converts it into certified lower bounds on robustness of magic. The main result is an exact reduction of the stabilizer threshold of a natural CWS coherence witness to a finite-geometric problem over the classical CWS word set. For general weighted superpositions, the threshold is computed by enumerating affine intersections and affine-quadratic phases. For equal-weight superpositions, the phase optimization collapses, and the threshold is determined entirely by how many CWS words can lie in affine flats of each dimension. Thus a quantum optimization over stabilizer states becomes a classical affine-incidence problem. This reduction yields a fixed-parameter algorithm, an analytic lower bound for an infinite union-stabilizer family, and exact rational certificates for several standard nonadditive CWS examples. The framework also clarifies why exact enumeration fails for large structured families and identifies the remaining task as an affine-intersection problem. The result provides a geometric mechanism by which nonlinear CWS word sets generate certifiable magic.
Related
- Quantifying Nonstabilizerness of Codeword-Stabilized Codes
- Quantum Codeword Sensing
- Stabilizer-based quantum simulation of fermion dynamics with local qubit encodings
- Quantum codes are quantized codes: Stabilizer codes from quantization over finite fields
- Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation
BibTeX
@misc{hsu2026affineprofile,
title = {{Affine-Profile Stabilizer Thresholds for Magic in Codeword-Stabilized Quantum Codes}},
author = {Li-Yi Hsu and En-Jui Kuo},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.25414},
eprint = {2608.25414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25414},
}
RIS
TY - UNPB
TI - Affine-Profile Stabilizer Thresholds for Magic in Codeword-Stabilized Quantum Codes
AU - Li-Yi Hsu
AU - En-Jui Kuo
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.25414
UR - https://arxiv.org/abs/2608.25414
AB - Codeword-stabilized quantum codes give a unified graph-state description of stabilizer and nonadditive quantum error-correcting codes. Although each individual CWS word state is stabilizer, coherent superpositions of different word states can be nonstabilizer. We develop a CWS-adapted magic-witness framework that isolates this codeword coherence and converts it into certified lower bounds on robustness of magic. The main result is an exact reduction of the stabilizer threshold of a natural CWS coherence witness to a finite-geometric problem over the classical CWS word set. For general weighted superpositions, the threshold is computed by enumerating affine intersections and affine-quadratic phases. For equal-weight superpositions, the phase optimization collapses, and the threshold is determined entirely by how many CWS words can lie in affine flats of each dimension. Thus a quantum optimization over stabilizer states becomes a classical affine-incidence problem. This reduction yields a fixed-parameter algorithm, an analytic lower bound for an infinite union-stabilizer family, and exact rational certificates for several standard nonadditive CWS examples. The framework also clarifies why exact enumeration fails for large structured families and identifies the remaining task as an affine-intersection problem. The result provides a geometric mechanism by which nonlinear CWS word sets generate certifiable magic.
ER -