Scalable Clifford-Based Classical Initialization for the Quantum Approximate Optimization Algorithm

TL;DR

This paper introduces SPIQ, a scalable classical initialization method for QAOA that uses Clifford states to improve convergence, reduce quantum evaluations, and enhance solution quality for large combinatorial problems.

Contribution

The paper presents a novel, scalable framework for classical initialization of QAOA using Clifford-preparable states, significantly improving performance and efficiency over existing methods.

Findings

Achieves up to 80% accuracy improvement over state-of-the-art initialization.

Reduces initial-state diversity by up to 10,000x across various problems.

Demonstrates consistent, scalable improvements on real-world datasets.

Abstract

Variational Quantum Algorithms (VQAs), such as the Quantum Approximate Optimization Algorithm (QAOA), offer a promising route to tackling combinatorial optimization problems on near and intermediate-term quantum devices. However, their performance critically depends on the choice of initial parameters, and the limited expressiveness of the QAOA ansatz makes identifying effective initializations both difficult and unscalable. To address this, we propose a framework, Scalable Parameter Initialization for QAOA (SPIQ), that employs a relaxed QAOA ansatz to enable classical search over a set of Clifford-preparable quantum states that yield high-quality solutions. These states serve as superior QAOA initializations, driving rapid convergence while significantly reducing the quantum circuit evaluations needed to reach high-quality solutions and consequently lowering quantum-device cost. We present a scalable, application-agnostic initialization framework that achieves an absolute accuracy improvement of up to 80% over state-of-the-art initialization and reduces initial-state diversity by up to 10,000x across QUBO, PUBO, and PCBO problems spanning tens to hundreds of qubits. We further benchmark its performance on a wide range of problem formulations and instances derived from real-world datasets, demonstrating consistent and scalable improvements. Furthermore, we introduce two complementary strategies for selecting high-quality Clifford points identified by our search procedure and using them to seed multi-start optimization, thereby enhancing exploration and improving solution quality.