Quantum Power Method by a Superposition of Time-Evolved States

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