Bounding Fidelity of Non-Stabilizer States from Local Pauli Measurements
Abstract
Nonstabilizerness, commonly referred to as magic, is essential for universal quantum computation. Yet, for pure n-qubit states this property is directly linked to the hardness of direct fidelity estimation. We propose a scheme to bound the fidelity on non-stabilizer states by choosing operators with low measurement overhead and using parallel local Pauli measurements to estimate compatible observables. We selectively measure operators that share a permutational symmetry without imposing any assumption on the physical system. This selection reduces the optimization to a linear program with only O(n) variables for bounding fidelity. Our methods can be extended to bound nonlinear quantities like the purity via convex quadratic programs. For hypergraph states that can exhibit extensive nonstabilizerness, we demonstrate for up to n=500 qubits that our framework substantially reduces the measurement overhead under both local and global depolarizing noise. These results show that symmetry induced by measurement selection reduces both measurement and computational costs, enabling scalable characterization of magic resources in quantum computing and quantum networks.
Related
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BibTeX
@misc{li2026bounding,
title = {{Bounding Fidelity of Non-Stabilizer States from Local Pauli Measurements}},
author = {Yi Li and Otfried Gühne and Qiongyi He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41808},
eprint = {2610.41808},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41808},
}
RIS
TY - UNPB
TI - Bounding Fidelity of Non-Stabilizer States from Local Pauli Measurements
AU - Yi Li
AU - Otfried Gühne
AU - Qiongyi He
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41808
UR - https://arxiv.org/abs/2610.41808
AB - Nonstabilizerness, commonly referred to as magic, is essential for universal quantum computation. Yet, for pure n-qubit states this property is directly linked to the hardness of direct fidelity estimation. We propose a scheme to bound the fidelity on non-stabilizer states by choosing operators with low measurement overhead and using parallel local Pauli measurements to estimate compatible observables. We selectively measure operators that share a permutational symmetry without imposing any assumption on the physical system. This selection reduces the optimization to a linear program with only O(n) variables for bounding fidelity. Our methods can be extended to bound nonlinear quantities like the purity via convex quadratic programs. For hypergraph states that can exhibit extensive nonstabilizerness, we demonstrate for up to n=500 qubits that our framework substantially reduces the measurement overhead under both local and global depolarizing noise. These results show that symmetry induced by measurement selection reduces both measurement and computational costs, enabling scalable characterization of magic resources in quantum computing and quantum networks.
ER -