Iterative Interpolation Schedules for Quantum Approximate Optimization Algorithm

Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum optimization heuristic with empirical evidence of speedup over classical state-of-the-art for some problems. QAOA solves optimization problems using a parameterized circuit with $p$ layers, with higher $p$ leading to better solutions. Existing methods require optimizing $2p$ independent parameters which is challenging for large $p$. In this work, we present an iterative interpolation method that exploits the smoothness of optimal parameter schedules by expressing them in a basis of orthogonal functions, generalizing Zhou et al. By optimizing a small number of basis coefficients and iteratively increasing both circuit depth and the number of coefficients until convergence, our approach enables construction of high-quality schedules for large $p$. We demonstrate our method achieves better performance with fewer optimization steps than current approaches on three problems: the Sherrington-Kirkpatrick (SK) model, portfolio optimization, and Low Autocorrelation Binary Sequences (LABS). For the largest LABS instance, we achieve near-optimal merit factors with schedules exceeding 1000 layers, an order of magnitude beyond previous methods. As an application of our technique, we observe a mild growth of QAOA depth sufficient to solve SK model exactly, a result of independent interest.