Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly interacting quantum systems. Recent matrix product operator methods [1,2] have made simulations of quantum hydrodynamics in $1+1\mathrm{D}$ tractable, but they do not naturally generalize to $2+1\mathrm{D}$ or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using mana, a resource theory of non-Clifford operations. For infinite-temperature starting states, we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.

• Received 14 February 2022
• Revised 24 May 2022
• Accepted 27 May 2022

DOI:https://doi.org/10.1103/PhysRevB.106.125130