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arXiv:2111.00044 · Physical Review A

Classically efficient quantum scalable Fermi-Hubbard benchmark

Bryan Gard, Adam M. Meier

Published Apr 8, 2022• 6 citations
arXivHTMLPDF

Abstract

In order to quantify the relative performance of different test-bed quantum computing devices, it is useful to benchmark them using a common protocol. While some benchmarks rely on the performance of random circuits and are generic in nature, here we instead propose and implement a practical, application-based benchmark. In particular, our protocol calculates the energy of the ground state in the single-particle subspace of a one-dimensional (1D) Fermi Hubbard model, a problem which is efficient to solve classically. We provide a quantum ansatz for the problem that is provably able to probe the full single-particle subspace for a general-length 1D chain and scales efficiently in number of gates and measurements. Finally, we demonstrate and analyze the benchmark performance on superconducting and ion-trap test-bed hardware from three hardware vendors and with up to 24 qubits.

DOI
10.1103/physreva.105.042602

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In order to quantify the relative performance of different test-bed quantum computing devices, it is useful to benchmark them using a common protocol. While some benchmarks rely on the performance of random circuits and are generic in nature, here we instead propose and implement a practical, application-based benchmark. In particular, our protocol calculates the energy of the ground state in the single-particle subspace of a one-dimensional (1D) Fermi Hubbard model, a problem which is efficient to solve classically. We provide a quantum ansatz for the problem that is provably able to probe the full single-particle subspace for a general-length 1D chain and scales efficiently in number of gates and measurements. Finally, we demonstrate and analyze the benchmark performance on superconducting and ion-trap test-bed hardware from three hardware vendors and with up to 24 qubits.
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We developed a practical quantum advantage benchmarking framework that connects the accumulation of entropy in a quantum processing unit and the degradation of the solution to a target optimization problem. The benchmark is based on approximating from below the Gibbs states boundary in the energy-entropy space for the application of interest. We believe the proposed benchmarking technique creates a powerful bridge between hardware benchmarking and application benchmarking, while remaining hardware-agnostic. It can be extended to fault-tolerant scenarios and relies on computationally tractable numerics. We demonstrate its applicability on the problem of finding the ground state of the two-dimensional Fermi-Hubbard.
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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 − i H ^ t | ψ ⟩ from initial states | ψ ⟩ and a time evolution under the Hamiltonian 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. Published by the American Physical Society 2024