Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer

TL;DR

This paper demonstrates the measurement of the Loschmidt amplitude for the Fermi-Hubbard model on a current ion-trap quantum computer, analyzing noise effects and error mitigation to explore finite-energy properties.

Contribution

It presents the first experimental implementation of a hybrid quantum-classical algorithm to measure Loschmidt amplitudes for the Fermi-Hubbard model on a trapped-ion device, including noise analysis and resource estimation.

Findings

Successfully measured Loschmidt amplitude on a 16-site Fermi-Hubbard model

Analyzed noise impact and implemented error mitigation techniques

Provided resource estimates for scaling the algorithm

Abstract

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $\langle \psi| e^{-i \hat H t}|\psi \rangle$ from initial states $|\psi\rangle$ and a time evolution under the Hamiltonian $\hat H$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.