Diffusive Dynamics of Nonstabilizerness (opens in new tab)

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 bl...