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

TL;DR

This paper investigates the non-Clifford resource requirements for simulating quantum hydrodynamics on quantum computers, using mana as a diagnostic, revealing how initial states influence the resource demands.

Contribution

It introduces a mana-based analysis of quantum hydrodynamics simulation, highlighting the role of initial states and subsystem entropy in non-Clifford resource needs.

Findings

Mana approaches zero for infinite-temperature states

Mana remains nonzero for high-energy states

Finite-time mana correlates with subsystem entropy

Abstract

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 of quantum hydrodynamics in 1+1d tractable, but they do not naturally generalize to 2+1d 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.