Quantum Power Method by a Superposition of Time-Evolved States
Kazuhiro Seki, Seiji Yunoki · PRX Quantum · 2021
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as the quantum power method, to evaluate Ĥn |ψ with quantum computers, where n is a non-negative integer, Ĥ is a time-independent Hamiltonian of interest, and |ψ is a quantum state.We show that the number of gates required for approximating Ĥn 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 Ĥn 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 connectedmoment expansion for the imaginary-time evolution and compare the results with the multireference Krylov-subspace diagonalization.