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

• URL: http://arxiv.org/abs/2511.07769v1
• Date: Wed, 12 Nov 2025 01:16:38 GMT
• Title: Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit
• Abstract summary: We investigate the spreading of Rényi entropy (SRE) in terms of single-qubit reduced density matrices.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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