Gaussian Process States: A data-driven representation of quantum many-body physics

TY - JOUR

T1 - Gaussian Process States: A data-driven representation of quantum many-body physics

AU - Booth, George

AU - Glielmo, Aldo

AU - Rath, Yannic

AU - Csanyi, Gabor

AU - De Vita, Alessandro

PY - 2020/12

Y1 - 2020/12

N2 - We present a novel, non-parametric form for compactly representing entangled many-body quan- tum states, which we call a ‘Gaussian Process State’. In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way the non-local physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a ‘universal approximator’ for quantum states, able to capture any entangled many-body state with increasing data set size. We develop two numerical approaches which can learn this form directly: a fragmentation approach, and direct variational optimization, and apply these schemes to the Fermionic Hubbard model. We find competitive or su- perior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.

AB - We present a novel, non-parametric form for compactly representing entangled many-body quan- tum states, which we call a ‘Gaussian Process State’. In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way the non-local physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a ‘universal approximator’ for quantum states, able to capture any entangled many-body state with increasing data set size. We develop two numerical approaches which can learn this form directly: a fragmentation approach, and direct variational optimization, and apply these schemes to the Fermionic Hubbard model. We find competitive or su- perior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.

U2 - 10.1103/PhysRevX.10.041026

DO - 10.1103/PhysRevX.10.041026

M3 - Article

SN - 2160-3308

VL - 10

SP - 041026-1-041026-16

JO - Physical Review X

JF - Physical Review X

IS - 4

M1 - 041026

ER -