Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model

TL;DR

This paper presents a quantum gate decomposition and a scalable architecture for simulating the Fermi-Hubbard model, enabling the study of strongly correlated materials with quantum computers.

Contribution

It introduces a novel, implementation-independent qubit layout and a gate decomposition method for simulating the Fermi-Hubbard model using a hybrid variational quantum-classical approach.

Findings

Gate decomposition for Fermi-Hubbard Hamiltonian demonstrated

Proposed layout supports simulation of general fermionic systems

Estimated scaling and error analysis for complex applications

Abstract

Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counter-intuitive macroscopic phenomena such as high-temperature superconductivity. In this paper, we provide a gate decomposition and an architecture for a quantum simulator used to simulate the Fermi-Hubbard model in a hybrid variational quantum-classical algorithm. We propose a simple planar implementation-independent layout of qubits that can also be used to simulate more general fermionic systems. By working through a concrete application, we show the gate decomposition used to simulate the Hamiltonian of a cluster of the Fermi-Hubbard model. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications.