Diffusive Dynamics of Nonstabilizerness

• URL: http://arxiv.org/abs/2606.13606v1
• Date: Thu, 11 Jun 2026 17:22:50 GMT
• Title: Diffusive Dynamics of Nonstabilizerness
• Abstract summary: We compute the stabilizer Rényi entropy, a measure of nonstabilizerness, in $mathrmU(1)$-symmetric one-dimensional random circuits.<n>Together with a hydrodynamic argument, our results identify a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value.
• Score: 9.107796201474187
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Symmetries shape the quantum-information dynamics of many-body systems, but their effect on nonstabilizerness, the resource complementary to entanglement, is less understood. We compute the stabilizer Rényi entropy, a measure of nonstabilizerness, in $\mathrm{U}(1)$-symmetric one-dimensional random circuits. The disorder-averaged dynamics is captured by a four-replica tensor network, which we evaluate by $S_4$-adapted infinite time-evolving block decimation (iTEBD) directly in the thermodynamic limit. Together with a hydrodynamic argument, our results identify a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value, with the stabilizer Rényi entropy gap closing as $1/t$. The same scaling is verified in an energy-conserving nonintegrable Ising chain. More broadly, our framework provides a hydrodynamic perspective on nonstabilizerness generation and offers insight into the design of approximate Haar-random states in Hamiltonian dynamics.

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