Local spin operators for fermion simulations

TL;DR

This paper explores a local spin operator approach for simulating fermionic systems on quantum computers, introducing auxiliary modes to efficiently handle non-consecutive couplings.

Contribution

It re-examines an auxiliary fermion construction that maps fermionic operators to local spin operators using auxiliary modes, improving simulation efficiency.

Findings

Auxiliary fermion construction enables local simulation of fermionic operators.

The method allows non-consecutive fermionic couplings with constant low-rank tensor products.

Connections to topological models are established.

Abstract

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on spins. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here we re-examine an auxiliary fermion construction which maps fermionic operators to local operators on spins. The local simulation is performed by relaxing the requirement that the number of spins should match the number of fermionic modes. Instead, auxiliary modes are introduced to enable non-consecutive fermionic couplings to be simulated with constant low-rank tensor products on spins. We connect the auxiliary fermion construction to other topological models and give examples of the construction.