Optimal fermionic swap networks for Hubbard models

TL;DR

This paper introduces an optimized fermionic swap network scheme for simulating Fermi-Hubbard models, reducing swap depth and interaction layers, with potential extensions to other lattice types.

Contribution

It presents a novel, efficient variation of the fermionic swap network scheme specifically tailored for 2D Fermi-Hubbard models, leveraging combinatorial graph theory.

Findings

Minimized swap depth for 2D Hubbard models

Reduced number of Hamiltonian interaction layers

Potential for extension to other lattice structures

Abstract

We propose an efficient variation of the fermionic swap network scheme used to efficiently simulate n-dimensional Fermi-Hubbard-model Hamiltonians encoded using the Jordan-Wigner transform. For the two-dimensional versions, we show that our choices minimize swap depth and number of Hamiltonian interaction layers. The proofs, along with the choice of swap network, rely on isoperimetric inequality results from the combinatorics literature, and are closely related to graph bandwidth problems. The machinery has the potential to be extended to maximize swap network efficiency for other types of lattices.