  Given the limitations of current hardware, the theoretical gains promised by
quantum computing remain unrealized across practical applications. But the gap
between theory and hardware is closing, assisted by developments in quantum
algorithmic modeling. One such recent development is QuantumCircuitOpt (QCOpt),
an open-source software framework that leverages state-of-the-art
optimization-based solvers to find provably optimal compact circuit
decompositions, which are exact up to global phase and machine precision. The
quantum circuit design problem can be modeled using non-linear, non-convex
constraints. However, QCOpt reformulates these non-linear constraints using
well-known linearization techniques such that the resulting design problem is
solved as a Mixed-Integer Linear Programming (MILP) model. In this work, we
instead explore whether the QCOpt could also be effective with a continuous
Non-Linear Programming (NLP) model obtained via relaxation of the integer
variables in the non-linear constraints. We are able to present not only
multiple significant enhancements to QCOpt, with up to 11.3x speed-up in run
times on average, but also opportunities for more generally exploring the
behavior of gradient-based NLP solvers.
