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- W3048017836 abstract "We propose a quantum-classical hybrid algorithm of the power method, here dubbed as the quantum power method, to evaluate H^n|ψ⟩ with quantum computers, where n is a non-negative integer, H^ is a time-independent Hamiltonian of interest, and |ψ⟩ is a quantum state. We show that the number of gates required for approximating H^n scales linearly in the power and the number of qubits, making it a promising application for near-term quantum computers. Using numerical simulation, we show that the power method can control systematic errors in approximating the Hamiltonian power H^n for n as large as 100. As an application, we combine our method with a multireference Krylov-subspace-diagonalization scheme to show how one can improve the estimation of ground-state energies and the ground-state fidelities found using a variational-quantum-eigensolver scheme. Finally, we outline other applications of the quantum power method, including several moment-based methods. We numerically demonstrate the connected-moment expansion for the imaginary-time evolution and compare the results with the multireference Krylov-subspace diagonalization.16 MoreReceived 11 August 2020Revised 19 November 2020Accepted 7 January 2021DOI:https://doi.org/10.1103/PRXQuantum.2.010333Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum gatesQuantum simulationQuantum Information" @default.
- W3048017836 created "2020-08-13" @default.
- W3048017836 creator A5048160827 @default.
- W3048017836 creator A5068173013 @default.
- W3048017836 date "2021-02-26" @default.
- W3048017836 modified "2023-10-17" @default.
- W3048017836 title "Quantum Power Method by a Superposition of Time-Evolved States" @default.
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