A Query-based Quantum Eigensolver

Abstract

Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the quantum phase estimation(QPE) method and the variational quantum eigensolver for quantum computers. In this work, we present an alternative type of quantum method that uses fixed-point quantum search to solve Type II eigenvalue problems. It serves as an important complement to the QPE method, which is a Type I eigensolver. We find that the effectiveness of our method depends crucially on the appropriate choice of the initial state to guarantee a sufficiently large overlap with the unknown target eigenstate. We also show that the quantum oracle of our query-based method can be efficiently constructed for efficiently-simulated Hamiltonians, which is crucial for analyzing the total gate complexity. In addition, compared with the QPE method, our query-based method achieves a quadratic speedup in solving Type II problems.

References in corpus (2)

• Simulated Quantum Computation of Molecular Energies
• Fixed-point quantum search with an optimal number of queries

Cited by in corpus (7)

• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems
• Assessment of the variational quantum eigensolver: application to the Heisenberg model
• Circuit Design for Clique Problem and Its Implementation on Quantum Computer
• Hybrid algorithms to solve linear systems of equations with limited qubit resources
• Fixed-point quantum continuous search algorithm with optimal query complexity
• Robust Quantum Circuit for Clique Problem with Intermediate Qudits
• Quantum algorithm for solving generalized eigenvalue problems with application to the Schrödinger equation