Iterative Interpolation Schedules for Quantum Approximate Optimization Algorithm

2025-04-02

AI Summary

QAOA suffers from severe parameter optimization challenges at high circuit depth (large $p$), hindering its practical deployment. This work introduces an iterative interpolation parameterization method grounded in orthogonal function bases: QAOA parameters are modeled as low-dimensional expansions of smooth functions, and efficient parameter scheduling is achieved via progressive depth extension coupled with gradient-based optimization. Our approach enables, for the first time, the construction of QAOA parameters for circuits exceeding 1000 layers—surpassing prior scalability limits by an order of magnitude. On benchmark problems—including the Sherrington–Kirkpatrick (SK) spin glass, portfolio optimization, and the low-autocorrelation binary sequence (LABS) problem—it achieves superior solutions with fewer optimization iterations; notably, LABS instances attain near-optimal merit factors. Furthermore, our analysis uncovers a mild growth law governing the minimal QAOA depth required for exact SK model solution, offering new theoretical insight into QAOA’s expressivity.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

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.

Problem

• Reduces QAOA parameter optimization complexity for large p
• Improves solution quality with iterative interpolation schedules
• Demonstrates effectiveness on SK model, portfolio, LABS problems

Innovation

• Iterative interpolation for QAOA schedules
• Orthogonal basis for parameter optimization
• Scalable to over 1000 QAOA layers