Dynamical mean field theory with quantum computing

TL;DR

This paper explores how quantum computing can enhance dynamical mean field theory by overcoming classical impurity solver limitations, using both long-term fully quantum and short-term hybrid algorithms.

Contribution

It introduces quantum computing tools and methods to improve impurity solvers in dynamical mean field theory, addressing classical computational bottlenecks.

Findings

Quantum algorithms can simulate impurity dynamics more efficiently.

Hybrid quantum-classical algorithms offer practical near-term solutions.

Potential to extend parameter regimes accessible to simulations.

Abstract

Near-term quantum processors are limited in terms of the number of qubits and gates they can afford. They nevertheless give unprecedented access to programmable quantum systems that can efficiently, although imperfectly, simulate quantum time evolutions. Dynamical mean field theory, on the other hand, maps strongly-correlated lattice models like the Hubbard model onto simpler, yet still many-body models called impurity models. Its computational bottleneck boils down to investigating the dynamics of the impurity upon addition or removal of one particle. This task is notoriously difficult for classical algorithms, which has warranted the development of specific classical algorithms called "impurity solvers" that work well in some regimes, but still struggle to reach some parameter regimes. In these lecture notes, we introduce the tools and methods of quantum computing that could be used to overcome the limitations of these classical impurity solvers, either in the long term -- with fully quantum algorithms, or in the short term -- with hybrid quantum-classical algorithms.