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

• DOI: 10.48550/arxiv.2309.10552
• Publication Date: 2023-01-01
• Authors: Kévin Hémery; Khaldoon Ghanem; Eleanor Crane; Sara Campbell; Joan Dreiling; Caroline Figgatt; Cameron Foltz; John Gaebler; Jacob Johansen; Michael Mills; Steven A. Moses; Juan Miguel Rey Pino; Anthony Ransford; M. W. Rowe; Peter Siegfried; Russell Stutz; Henrik Dreyer; Alexander Schuckert; Ramil Nigmatullin
• Keywords: Hamiltonian (control theory)

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