PRX Quantum (Aug 2024)

Measuring the Loschmidt Amplitude for Finite-Energy Properties of the Fermi-Hubbard Model on an Ion-Trap Quantum Computer

  • Kévin Hémery,
  • Khaldoon Ghanem,
  • Eleanor Crane,
  • Sara L. Campbell,
  • Joan M. Dreiling,
  • Caroline Figgatt,
  • Cameron Foltz,
  • John P. Gaebler,
  • Jacob Johansen,
  • Michael Mills,
  • Steven A. Moses,
  • Juan M. Pino,
  • Anthony Ransford,
  • Mary Rowe,
  • Peter Siegfried,
  • Russell P. Stutz,
  • Henrik Dreyer,
  • Alexander Schuckert,
  • Ramil Nigmatullin

DOI
https://doi.org/10.1103/PRXQuantum.5.030323
Journal volume & issue
Vol. 5, no. 3
p. 030323

Abstract

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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 ⟨ψ|e^{−iH[over ^]t}|ψ⟩ from initial states |ψ⟩ and a time evolution under the Hamiltonian H[over ^] 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.