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Exploring Non-Linear Programming Formulations in QuantumCircuitOpt for Optimal Circuit Design
DescriptionThe theoretical gains promised by quantum computing remain unrealized across practical applications given the limitations of current hardware. 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 commercial optimization-based solvers to find provably optimal compact circuit decompositions, which are exact up to global phase and machine precision. While such circuit design problems can be posed using non-linear, non-convex constraints, QCOpt implements a Mixed-Integer Linear Programming model, where non-linear constraints are reformulated using well-known linearization techniques. In this work, we instead explore whether the QCOpt model could be effective with continuous Non-Linear Programming (NLP) formulations. We are able to present not only multiple potential enhancements to QCOpt's run times, but also opportunities for more generally exploring the behavior of gradient-based NLP solvers.
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