Effective dissipation rate in a Liouvillean graph picture of high-temperature quantum hydrodynamics

White, Christopher D.

doi:10.48550/arxiv.2108.00019

Cited by 2 publications

(6 citation statements)

References 33 publications

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“…D.) Dot mark points where we measure the mana, every time step dt = 1/8. We see again a fast early rise and a long-time decay, matching the Haar prediction based on (8). At intermediate times the state mana undershoots the Haar prediction.…”

Section: Figsupporting

confidence: 76%

“…Looking at the energy for pairs of single qutrit stabilizers we can see what energy densities and therefore temperatures will be accessible to this choice of initial states. The energy densities for pairs of stabilizer states are grouped into the X eigenstates (1,11,12), the Z eigenstates (2, 9, 10), and other stabilizer states (3)(4)(5)(6)(7)(8). The energies with highest degeneracy are any of the non X or Z eigenstates, which have zero energy density when paired together, or a slightly positive or negative energy density when paired with one of the X or Z eigenstates.…”

Section: Acknowledgmentsmentioning

confidence: 99%

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

J.¹,

White²

2022

Preprint

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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+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 ifinite-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 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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Section: Figsupporting

confidence: 76%

Section: Acknowledgmentsmentioning

confidence: 99%

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

J.¹,

White²

2022

Preprint

Self Cite

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“…Recently, a number of methods have been proposed for sidestepping these issues [5][6][7][8][9][10][11]. All of these methods (with the exception of Ref.…”

Section: Introductionmentioning

confidence: 99%

“…All of these methods (with the exception of Ref. 7) rely on the intuition that much of the information content of a many-body density matrix -particularly correlation functions involving products of many-operators [9], or operators with large spatial support [5,8,10,11] -can be thrown away without greatly affecting the calculation of transport coefficients. This intuition has been articulated in various forms for decades in (for example) the formulation of the BBGKY hierarchy, and the approximations employed in the mode-coupling/memory-matrix formalism and fluctuating hydrodynamics approaches to many-body systems [12,13] .…”

Section: Introductionmentioning

confidence: 99%

“…The present paper aims to remedy this gap in the literature. Although our results are relevant to various recently proposed methods [5,8,10], our primary interest is in the dissipation assisted operator evolution ('DAOE') method [9]. For DAOE, the correlation functions are approximated by modifying unitary Heisenberg dynamics so that operators with support on, say, more than * sites are discarded or strongly dissipated.…”

Section: Introductionmentioning

confidence: 99%

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Operator backflow and the classical simulation of quantum transport

von Keyserlingk,

Pollmann,

Rakovszky

2021

Preprint

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Tensor product states have proved extremely powerful for simulating the area-law entangled states of many-body systems, such as the ground states of gapped Hamiltonians in one dimension. The applicability of such methods to the dynamics of many-body systems is less clear: the memory required grows exponentially in time in most cases, quickly becoming unmanageable. New methods reduce the memory required by selectively discarding/dissipating parts of the many-body wavefunction which are expected to have little effect on the hydrodynamic observables typically of interest: for example, some methods discard fine-grained correlations associated with n-point functions, with n exceeding some cutoff * . In this work, we present a theory for the sizes of 'backflow corrections', i.e., systematic errors due to discarding this fine-grained information. In particular, we focus on their effect on transport coefficients. Our results suggest that backflow corrections are exponentially suppressed in the size of the cutoff * . Moreover, the backflow errors themselves have a hydrodynamical expansion, which we elucidate. We test our predictions against numerical simulations run on random unitary circuits and ergodic spin-chains. These results lead to the conjecture that transport coefficients in ergodic diffusive systems can be captured to a given precision with an amount of memory scaling as exp î O(log( ) 2 ) ó , significantly better than the naive estimate of memory exp O(poly( −1 )) required by more brute-force methods.

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Effective dissipation rate in a Liouvillean graph picture of high-temperature quantum hydrodynamics

Cited by 2 publications

References 33 publications

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

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

Operator backflow and the classical simulation of quantum transport

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