HUBO formulations for solving the eigenvalue problem

Abstract

Solving the eigenvalue problem is particularly important in almost all fields of science and engineering. With the development of quantum computers, multiple algorithms have been proposed for this purpose. However, such methods are usually only applicable to matrices of specific types, such as unitary or Hermitian matrices. The quantum annealer of the D-Wave, a quantum computer, returns the minimum value of the quadratic unconstrained binary optimization (QUBO) model. Thus, quantum annealers can be leveraged to solve arbitrary eigenvalue problems by formulating corresponding QUBO models. In this paper, we propose two higher-order unconstrained optimization (HUBO) formulations to solve eigenvalue problems involving n×n general matrices. In addition, we use a formula to reduce the order and convert the HUBO model into a QUBO model. Further, by using a quantum approximate optimization algorithm, this method can be extended to a gate-model quantum computer.