Abstract
We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case.
Highlights
Generation scalable quantum devices[1,2] promise a step change in our ability to do computations
The scheme avoids the sign problem in classical quantum Monte Carlo methods and works for all interaction strengths, unlike classical methods based on perturbation theory
Note that non-local spatial fluctuations can be included in dynamical mean-field theory (DMFT) by going beyond the single-site approximation and considering a cluster of isolated sites[22,23], but this is beyond the scope of this work
Summary
Generation scalable quantum devices[1,2] promise a step change in our ability to do computations. We suggest a hybrid quantum-classical scheme to simulate non-equilibrium dynamics of the Hubbard model in a Bethe lattice directly in the thermodynamic limit. Instead of the traditional all-classical method, the proposed scheme uses a digital quantum simulator to efficiently solve the DMFT impurity problem, the parameters of which are iterated to self-consistency via a classically computed feedback loop.
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