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

Understand

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.