Diffusive Dynamics of Nonstabilizerness

Zhenyu Xiao; Shinsei Ryu

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arXiv · 2606.13606

Diffusive Dynamics of Nonstabilizerness

Zhenyu Xiao·Shinsei Ryu

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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 R\'enyi 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 R\'enyi 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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Zhenyu Xiao, Shinsei Ryu. 2026-06-11. Diffusive Dynamics of Nonstabilizerness. https://arxiv.org/abs/2606.13606

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