Quantum Power Method by a Superposition of Time-Evolved States

• URL: http://arxiv.org/abs/2008.03661v3
• Date: Fri, 5 Mar 2021 07:01:36 GMT
• Title: Quantum Power Method by a Superposition of Time-Evolved States
• Authors: Kazuhiro Seki, Seiji Yunoki
• Abstract summary: We show that the number of gates required for approximating $hatcal Hn$ scales linearly in the power and the number of qubits. Using numerical simulation, we show that the power method can control systematic errors in approximating the Hamiltonian power $hatcal Hn$ for $n$ as large as 100.
• Score: 0.9137554315375919
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |\psi\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a time-independent Hamiltonian of interest, and $|\psi \rangle$ is a quantum state. We show that the number of gates required for approximating $\hat{\cal H}^n$ 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 ${\hat{\cal H}^n}$ 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.

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