Using Quantum Computers for Quantum Simulation

TL;DR

This paper surveys the development of quantum simulation using quantum computers, highlighting its importance for modeling complex quantum systems in physics and chemistry, and its potential as an early practical application of quantum computing.

Contribution

It provides a comprehensive overview of both theoretical and experimental progress in quantum simulation, from early concepts to current research efforts.

Findings

Quantum simulation can model complex quantum systems beyond classical capabilities.

Fewer than a hundred qubits may suffice for useful quantum simulations.

Active research is advancing both theory and experiments in quantum simulation.

Abstract

Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.