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Parameterized quantum circuits are widely studied approaches for tacklingoptimization problems. A prominent example is the Quantum Alternating OperatorAnsatz (QAOA), an approach that builds off the structure of the QuantumApproximate Optimization Algorithm. Finding high-quality parameters efficientlyfor QAOA remains a major challenge in practice. In this work, we introduce aclassical strategy for parameter setting, suitable for common cases in whichthe number of distinct cost values grows only polynomially with the problemsize. The crux of our strategy is that we replace the cost function expectationvalue step of QAOA with a parameterized model that can be efficiently evaluatedclassically. This model is based on empirical observations that QAOA stateshave large overlaps with states where variable configurations with the samecost have the same amplitude, which we define as Perfect Homogeneity. We thusdefine a Classical Homogeneous Proxy for QAOA in which Perfect Homogeneityholds exactly, and which yields information describing both states andexpectation values. We classically determine high-quality parameters for thisproxy, and use these parameters in QAOA, an approach we label the HomogeneousHeuristic for Parameter Setting. We numerically examine this heuristic forMaxCut on random graphs. For up to $3$ QAOA levels we are easily able to findparameters that match approximation ratios returned by previous globallyoptimized approaches. For levels up to $20$ we obtain parameters withapproximation ratios monotonically increasing with depth, while a strategy thatuses parameter transfer instead fails to converge with comparable classicalresources. These results suggest that our heuristic may find good parameters inregimes that are intractable with noisy intermediate-scale quantum devices.Finally, we outline how our heuristic may be applied to wider classes ofproblems.

A Parameter Setting Heuristic for the Quantum Alternating Operator Ansatz