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

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