An Exploration of Solution Curves in Feedback-Based Quantum Algorithms*

There is a great interest in using parameterized quantum circuits to solve combinatorial optimization problems, and recently, the Feedback-based ALgorithm for Quantum OptimizatioN (FALQON) was introduced as an optimization-free framework for this purpose. In FALQON, circuit parameter values are set layer-by-layer according to a deterministic, measurement based feedback law. The output parameters can be plotted as a function of layer, producing FALQON solution curves. In this talk, I will explore the characteristics and generality of these curves with a focus on curves produced for solving MaxCut on regular graphs. In particular, I analyze the relationships between the solution curves and the corresponding problem instances, highlighting the observation that FALQON solution curves tend towards a universal form. Motivated by this observation, I will also discuss the transferability of solution curves across different MaxCut problem instances, and conclude with a discussion of how FALQON solution curves may be used to inspire quantum annealing schedules.

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND Number: SAND2022-14341 A