A recent study has explored the dynamics of nonstabilizerness, a quantum resource complementary to entanglement, in many-body systems with symmetries. Researchers calculated the stabilizer Rényi entropy, a measure of nonstabilizerness, in one-dimensional random circuits with U(1) symmetry. This work sheds light on how symmetries influence the generation and evolution of this quantum resource, whose understanding is crucial for the development of quantum computing and the characterization of complex quantum states.

The disorder-averaged dynamics of these circuits were modeled using a four-replica tensor network. To evaluate this network directly in the thermodynamic limit, the team employed an S4-adapted infinite Time-Evolving Block Decimation (iTEBD) algorithm. Combining these results with a hydrodynamic argument, the authors identified a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value. Specifically, they observed that the stabilizer Rényi entropy gap closes with a 1/t scaling.

This same temporal scaling was verified in a non-integrable energy-conserving Ising chain, suggesting the robustness of this diffusive behavior. The methodological framework proposed in this study offers a hydrodynamic perspective on nonstabilizerness generation. Furthermore, it provides valuable tools and insights for the design of states that approximate Haar-random states in Hamiltonian dynamics, an important goal for quantum simulation and computation. This advance contributes to a deeper understanding of quantum resources and their manipulation in complex systems.