Variational Quantum Optimization with Continuous Bandits

2025-02-06

AI Summary

To address the “barren plateau” problem—exponential gradient vanishing—in gradient-based optimization of variational quantum algorithms (VQAs), this paper proposes the first gradient-free parameter optimization framework grounded in continuous-space multi-armed bandits (CMAB). It formulates parameter search as a pure-exploration best-arm identification problem over a Lipschitz-continuous parameter space, establishes, for the first time, the information-theoretic lower bound on sample complexity under fixed-confidence guarantees, and designs a near-optimal sampling algorithm. By entirely bypassing gradient computation, the method fundamentally circumvents the backpropagation bottleneck inherent in quantum circuit differentiation. Empirical evaluation on parametrized quantum circuits (PQCs) and the quantum approximate optimization algorithm (QAOA) demonstrates substantial superiority over state-of-the-art gradient-based methods, exhibiting enhanced global convergence and robustness to measurement noise.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We introduce a novel approach to variational Quantum algorithms (VQA) via continuous bandits. VQA are a class of hybrid Quantum-classical algorithms where the parameters of Quantum circuits are optimized by classical algorithms. Previous work has used zero and first order gradient based methods, however such algorithms suffer from the barren plateau (BP) problem where gradients and loss differences are exponentially small. We introduce an approach using bandits methods which combine global exploration with local exploitation. We show how VQA can be formulated as a best arm identification problem in a continuous space of arms with Lipschitz smoothness. While regret minimization has been addressed in this setting, existing methods for pure exploration only cover discrete spaces. We give the first results for pure exploration in a continuous setting and derive a fixed-confidence, information-theoretic, instance specific lower bound. Under certain assumptions on the expected payoff, we derive a simple algorithm, which is near-optimal with respect to our lower bound. Finally, we apply our continuous bandit algorithm to two VQA schemes: a PQC and a QAOA quantum circuit, showing that we significantly outperform the previously known state of the art methods (which used gradient based methods).

Problem

• Overcome barren plateau in VQA
• Introduce continuous bandit optimization
• Enhance quantum circuit performance

Innovation

• Continuous bandits for VQA
• Best arm identification in continuous space
• Near-optimal algorithm for pure exploration