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  • Open Access

Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit

Somnath Maity1,* and Ryusuke Hamazaki1,2

  • *Contact author: somnath.maity@riken.jp
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Phys. Rev. Research 8, 013324 – Published 25 March, 2026

DOI: https://doi.org/10.1103/68g7-8pdc

Abstract

Nonstabilizerness, or magic, constitutes a fundamental resource for quantum computation and a crucial ingredient for quantum advantage. Recent progress has substantially advanced the characterization of magic in many-body quantum systems, with stabilizer Rényi entropy (SRE) emerging as a computable and experimentally accessible measure. In this work, we investigate the spreading of SRE in terms of single-qubit reduced density matrices, where an initial product state that contains magic in a local region evolves under brickwork random Clifford circuits. For the case with Haar-random local Clifford gates, we find that the spreading profile exhibits a diffusive structure within a ballistic light cone when viewed through a normalized version of single-qubit SRE, despite the absence of explicit conserved charges. We further examine the robustness of this nonballistic behavior of the normalized single-qubit SRE spreading by extending the analysis to a restricted Clifford circuit, where we unveil a superdiffusive spreading. Finally, we discuss that a similar nonballistic spreading within the light cone is also observed for another indicator of the magic, i.e., the robustness of magic.

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Phys. Rev. Research 8, 013324– Published 25 March, 2026
  • Received 14 November 2025
  • Accepted 25 February 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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