Anticoncentration and nonstabilizerness spreading under ergodic quantum dynamics

TL;DR

This paper investigates how quantum resources like anticoncentration and nonstabilizerness spread in ergodic quantum systems, revealing differences between Floquet and Hamiltonian dynamics in their timescales for resource saturation.

Contribution

It provides a comparative analysis of magic resource spreading in ergodic Floquet and Hamiltonian systems, highlighting the impact of conservation laws on these dynamics.

Findings

Floquet systems reach resource saturation at logarithmic timescales.

Hamiltonian systems require linear timescales for resource saturation.

Conservation laws constrain the growth of quantum magic resources.

Abstract

Quantum state complexity metrics, such as anticoncentration and nonstabilizerness, or ``magic'', offer key insights into many-body physics, information scrambling, and quantum computing. Anticoncentration and equilibration of magic resources under dynamics of random quantum circuits occur at times scaling logarithmically with system size, a prediction that is believed to extend to more general ergodic dynamics. This work challenges this idea by examining the anticoncentration and magic spreading in one-dimensional ergodic Floquet models and Hamiltonian systems. Using participation and stabilizer entropies to probe these resources, we reveal significant differences between the two settings. Floquet systems align with random circuit predictions, exhibiting anticoncentration and magic saturation at time scales logarithmic in system size. In contrast, Hamiltonian dynamics deviate from the random circuit predictions and require times scaling approximately linearly with system size to achieve saturation of participation and stabilizer entropies, which remain smaller than that of the typical quantum states even in the long-time limit. Our findings establish the phenomenology of participation and stabilizer entropy growth in ergodic many-body systems and emphasize the role of conservation laws in constraining anticoncentration and magic dynamics.