This project received an MICDE Catalyst Grant in summer 2018.

## Overview

The research team will design quantum embedding algorithms that can be early adopters of quantum computers on development of advanced materials for possible applications in modern batteries, next-generation oxide electronics, or high-temperature superconducting power cables.

The main long-term goal of this research direction is to explore the use of quantum computers as quantum impurity solvers in quantum embedding methods, and to explore the application of the resulting methods to the simulation of strongly correlated solids and molecules. The main short-term goal of the proposal is the exploration of theory and production of preliminary data that shows that the long-term goals are achievable, such that a proposal can be funded by federal agencies or private industry partners.

The brute force simulation of strongly correlated solids is not feasible and, barring new theory developments, will not become feasible due to an exponential barrier. Useful practical methods therefore have to approximate the quantum problem, and one of the most promising ways of doing so consists in splitting the quantum problem into a ‘large but easy’ part, which can be solved approximately, and a ‘small but difficult’ part, which needs to be treated more carefully. In the quantum context, methods of this type are called embedding methods, and the ‘small but difficult’ part is represented by a so-called quantum impurity problem.

Reliable methods exist for treating the ‘large but easy’ problem. The subtle and difficult quantum mechanical effects are hidden in the quantum impurity problem, and in the embedding construction that connects the impurity to the ‘easy’ problem. So far, this quantum problem was always solved on classical computers, where it scales exponentially in the number of degrees of freedom. However, since this is a small quantum problem, it is ideally suited to be solved by quantum computers which, for this problem, are now about to catch up with their capabilities to classical computers and promise to overcome the exponential barriers intrinsic to classical computers. The time is therefore ripe for testing the capabilities of quantum computers for applications to quantum impurity problems.

## Principal Investigators

Emanuel Gull, Associate Professor of Physics, College of Literature, Science and the Arts, U-M

Dominika Zgid, Associate Professor of Chemistry and Physics, College of Literature, Science, and the Arts, U-M