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arXiv · 2201.12367

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

Troy J. Sewell·Christopher David White
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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.

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Troy J. Sewell, Christopher David White. 2022-01-28. Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation. https://doi.org/10.1103/physrevb.106.125130

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