  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.
