Efficient Quantum Implementation of Dynamical Mean Field Theory for Correlated Materials

TL;DR

This paper introduces a quantum computing framework for dynamical mean field theory (DMFT) to efficiently study strongly correlated materials, demonstrating convergence and hardware viability on IBM quantum processors.

Contribution

It presents a novel quantum algorithm for DMFT that uses a low-rank Gaussian subspace and short-depth circuits, enabling practical computations on near-term quantum hardware.

Findings

Convergence of the DMFT algorithm using Gaussian subspace demonstrated in noise-free simulations.

Impurity Green's function successfully extracted on IBM quantum processors with 8 qubits.

Circuit compression shows potential for hardware-efficient quantum simulations in materials science.

Abstract

The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge in condensed matter physics and computational chemistry. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some of the correlated behavior using an impurity model, but it is limited by the need to calculate the impurity Green's function. This work proposes a framework for DMFT calculations on quantum computers, focusing on near-term applications. It leverages the structure of the impurity problem, combining a low-rank Gaussian subspace representation of the ground state and a compressed, short-depth quantum circuit that joins state preparation with time evolution to compute Green's functions. We demonstrate the convergence of the DMFT algorithm using the Gaussian subspace in a noise-free setting, and show the hardware viability of circuit compression by extracting the impurity Green's function on IBM quantum processors for a single impurity coupled to three bath orbitals (8 qubits, 1 ancilla). We discuss potential paths toward realizing this quantum computing use case in materials science.