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.

1 aSewell, Troy, J.1 aWhite, Christopher, David uhttps://arxiv.org/abs/2201.1236701258nas a2200157 4500008004100000245004100041210004100082260001400123300001100137490000800148520084100156100003000997700001701027700001901044856003701063 2021 eng d00aConformal field theories are magical0 aConformal field theories are magical c2/25/2021 a0751450 v1033 a"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.

1 aWhite, Christopher, David1 aCao, ChunJun1 aSwingle, Brian uhttps://arxiv.org/abs/2007.0130301733nas a2200133 4500008004100000245014300041210006900184260001400253520122700267100001601494700003001510700002201540856003701562 2021 eng d00aLocalization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain0 aLocalization crossover and subdiffusive transport in a classical c9/22/20213 aWe consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model's non-interacting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes, and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath, and provides a classical analogue for the many-body localization transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

1 aKlocke, Kai1 aWhite, Christopher, David1 aBuchhold, Michael uhttps://arxiv.org/abs/2109.10926