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

• DOI: 10.1103/prxquantum.5.030323
• Publication Date: 2024-08-05T14:22:43Z
• Authors: 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
• Keywords: 0301 basic medicine; QA76.75-76.765; Quantum Physics; 03 medical and health sciences; Physics; QC1-999; FOS: Physical sciences; Computer software; Quantum Physics (quant-ph)

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mo fence="false" stretchy="false">⟨</a:mo><a:mi>ψ</a:mi><a:mrow><a:mo stretchy="false">|</a:mo></a:mrow><a:msup><a:mi>e</a:mi><a:mrow><a:mo>−</a:mo><a:mi>i</a:mi><a:mrow><a:mover><a:mi>H</a:mi><a:mo stretchy="false">^</a:mo></a:mover></a:mrow><a:mi>t</a:mi></a:mrow></a:msup><a:mrow><a:mo stretchy="false">|</a:mo></a:mrow><a:mi>ψ</a:mi><a:mo stretchy="false">⟩</a:mo></a:math> initial states <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" overflow="scroll"><k:mrow><k:mo stretchy="false">|</k:mo></k:mrow><k:mi>ψ</k:mi><k:mo stretchy="false">⟩</k:mo></k:math> and time evolution under Hamiltonian <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" overflow="scroll"><q:mrow><q:mover><q:mi>H</q:mi><q:mo stretchy="false">^</q:mo></q:mover></q:mrow></q:math> up short times <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" overflow="scroll"><u:mi>t</u:mi></u:math>. In this work, we study operation algorithm on present-day computer. Specifically, measure for Fermi-Hubbard model <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" overflow="scroll"><x:mn>16</x:mn></x:math>-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 error model, numerically analyze influence full by measuring expectation values local observables at finite energies. Finally, estimate resources needed scaling algorithm. Published American Physical Society 2024