Near term algorithms for linear systems of equations

Abstract Finding solutions to systems of linear equations is a common problem in many areas science and engineering, with much potential for speed up on quantum devices. While the Harrow–Hassidim–Lloyd (HHL) algorithm yields an exponential over classical algorithms some cases, it requires fault-tolerant computer, which unlikely be available near-term. Thus, attention has turned investigation noisy intermediate-scale (NISQ) devices where several near-term approaches solving have been proposed. This paper focuses Variational Quantum Linear Solvers (VQLS), other closely related methods adaptions. Several contributions are made this paper, include: first application Evolutionary Ansatz VQLS (EAVQLS), implementation Logical (LAVQLS), based Classical Combination States (CQS) method, proof principle demonstration CQS method real hardware Adiabatic (AAVQLS). These implemented contrasted. The run moderate success device. EAVQLS AAVQLS show promise as possible improvements standard once refined.