Extension of nonorthogonal multistate ansätze to variational quantum simulation

Establish how a nonorthogonal multistate ansatz, in which a target state is represented as a linear combination of multiple nonorthogonal parameterized quantum states, can be extended from the nonorthogonal variational quantum eigensolver to variational quantum simulation.

Background

The paper motivates nonorthogonal variational quantum simulation (NOVQS) by noting that a single shallow parameterized quantum circuit may have insufficient expressive power under near-term circuit-depth constraints. In the nonorthogonal variational quantum eigensolver, linear combinations of several nonorthogonal quantum states have been used to enlarge the variational space. Before this work, whether and how that construction could be transferred to dynamical variational simulation had not been resolved.

The paper presents NOVQS as a resolution of this question by deriving equations of motion for the coefficients and circuit parameters and applying the framework to real- and imaginary-time evolution. Because the question is explicitly identified as open immediately before the paper introduces its proposed framework, it qualifies as an explicitly stated open problem even though the paper subsequently addresses it.