Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation

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