Guided-SPSA: Simultaneous Perturbation Stochastic Approximation Assisted by the Parameter Shift Rule

2024-04-24

International Conference on Quantum Computing and Engineering

AI Summary

To address the high sampling overhead and instability in gradient estimation for variational quantum circuits (VQCs) on noisy intermediate-scale quantum (NISQ) devices, this paper proposes Guided-SPSA—a novel method that, for the first time, leverages the parameter-shift rule (PSR) to guide direction updates in simultaneous perturbation stochastic approximation (SPSA). By integrating PSR’s accuracy with SPSA’s low parameter complexity, Guided-SPSA reduces circuit evaluations by 15–25%, achieves more stable convergence—especially under poor initial parameter choices—and outperforms pure PSR in robustness. Across quantum machine learning tasks—including regression, classification, and reinforcement learning—it consistently surpasses standard SPSA while maintaining or improving solution quality. The core contribution lies in a synergistic guidance mechanism that jointly exploits PSR and SPSA, balancing computational efficiency, robustness to noise and initialization, and scalability to larger parameter spaces.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to 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
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

The study of variational quantum algorithms (VQCs) has received significant attention from the quantum computing community in recent years. These hybrid algorithms, utilizing both classical and quantum components, are well-suited for noisy intermediate-scale quantum devices. Though estimating exact gradients using the parameter-shift rule to optimize the VQCs is realizable in NISQ devices, they do not scale well for larger problem sizes. The computational complexity, in terms of the number of circuit evaluations required for gradient estimation by the parameter-shift rule, scales linearly with the number of parameters in VQCs. On the other hand, techniques that approximate the gradients of the VQCs, such as the simultaneous perturbation stochastic approximation (SPSA), do not scale with the number of parameters but struggle with instability and often attain suboptimal solutions. In this work, we introduce a novel gradient estimation approach called Guided-SPSA, which meaningfully combines the parameter-shift rule and SPSA-based gradient approximation. The Guided-SPSA results in a 15% to 25% reduction in the number of circuit evaluations required during training for a similar or better optimality of the solution found compared to the parameter-shift rule. The Guided-SPSA outperforms standard SPSA in all scenarios and outperforms the parameter-shift rule in scenarios such as suboptimal initialization of the parameters. We demonstrate numerically the performance of Guided-SPSA on different paradigms of quantum machine learning, such as regression, classification, and reinforcement learning.

Problem

• Optimizing variational quantum algorithms with scalable gradient estimation
• Reducing circuit evaluations in quantum machine learning training
• Improving stability and optimality in quantum gradient approximation

Innovation

• Combines parameter-shift rule with SPSA
• Reduces circuit evaluations by 15-25%
• Improves stability and solution optimality