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  • Open Access

Geometric and resource-theoretic characterization of nonstabilizerness in quantum algorithms

Tom Krueger*

Wolfgang Mauerer†

  • *Contact author: tom.krueger@othr.de
  • †Contact author: wolfgang.mauerer@othr.de
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Phys. Rev. A 114, 022421 – Published 11 August, 2026

DOI: https://doi.org/10.1103/1f5p-rhy4

Abstract

While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a still incomplete understanding of the sources of quantum computational power. Advancing toward systematic quantum advantage calls for a better understanding of the efficient use of nonclassical resources like nonstabilizer states. We present an approach to track nonclassical contributions in the form of nonstabilizerness across various algorithms by pairing resource theory of nonstabilizer entropies with the geometry of quantum state evolution, and introduce permutation agnostic distance measures that reveal and quantify nonstabilizer effects previously hidden by a subset of Clifford operations. We find different efficiency in the use of nonstabilizerness for structured and unstructured variational approaches and show that greater freedom for classical optimization in quantum-classical methods increases unnecessary nonstabilizer consumption. Our results open alternative means of analyzing the efficient utilization of quantum resources and contribute toward the targeted construction of algorithmic quantum advantage.

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Phys. Rev. A 114, 022421– Published 11 August, 2026
  • Received 13 October 2025
  • Accepted 7 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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