Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics
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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. No MeSH data available. Related in: MedlinePlus |
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Mentions: This and similar models are extremely challenging to study numerically due to the exponential growth of the Hilbert space with system size. One thus often resorts to mean field approximations which typically consider only a single lattice site and replace interactions with its neighbourhood by a mean field Λ. This turns a linear quantum problem in an exponentially large Hilbert space into a much smaller but non-linear problem where Λ needs to be determined self-consistently. Such mean field approximations become increasingly accurate with the number of nearest neighbours. A classic example of this approach is the Weiss theory of ferromagnetism21. For mean field theory to be applicable to strongly correlated Fermi systems in thermal equilibrium, the mean field Λσ(t) has to be dynamical to account for correlations between interactions with the environment that are separated by t in time, as schematically shown in Fig. 1a,b. |
View Article: PubMed Central - PubMed
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.
No MeSH data available.