Putting fermions onto a digital quantum computer

TL;DR

This paper reviews methods for encoding fermionic systems into qubits on digital quantum computers, addressing the misconception that higher-dimensional fermionic systems are inherently more complex to simulate.

Contribution

It provides a comprehensive overview of fermion-to-qubit encoding techniques and clarifies their applicability beyond one-dimensional systems.

Findings

Fermionic systems can be efficiently encoded into qubits.

Encoding methods are applicable to higher-dimensional systems.

Challenges in simulating fermions are less fundamental than previously thought.

Abstract

Quantum computers are expected to become a powerful tool for studying physical quantum systems. Consequently, a number of quantum algorithms for studying the physical properties of such systems have been developed. While qubit-based quantum computers are naturally suited to the study of spin-1/2 systems, systems containing other degrees of freedom must first be encoded into qubits. Transformations to and from fermionic degrees of freedom have long been an important tool in physics and, now the simulation of fermionic systems on quantum computers based on qubits provides yet another application. In this perspective, we review methods for encoding fermionic degrees of freedom into qubits and attempt to dispel the persistent notion that fermionic systems beyond one dimension are fundamentally more difficult to deal with.