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arXiv · 2511.07769

Local spreading of stabilizer R\'enyi entropy in a brickwork random Clifford circuit

Somnath Maity·Ryusuke Hamazaki
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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 R\'enyi 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 non-ballistic 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 non-ballistic spreading within the light cone is found for another indicator of the magic, i.e., the robustness of magic.

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Somnath Maity, Ryusuke Hamazaki. 2025-11-11. Local spreading of stabilizer R\'enyi entropy in a brickwork random Clifford circuit. https://doi.org/10.1103/68g7-8pdc

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