Exploring Quantum Control Landscape and Solution Space Complexity through Dimensionality Reduction&Optimization Algorithms

2025-02-17

AI Summary

This study investigates the structural complexity and solvability of quantum control landscapes (QCLs) in high-dimensional parameter spaces. Focusing on single-qubit systems, we systematically evaluate optimization performance and solution-space distribution using principal component analysis (PCA), genetic algorithms (GA), stochastic gradient descent (SGD), and multiple reinforcement learning (RL) methods—including Q-learning (QL), deep Q-networks (DQN), and proximal policy optimization (PPO). We propose a novel cluster density index (CDI) to quantify the concentration quality of optimal solutions. Results show GA outperforms SGD; QL significantly surpasses DQN and PPO under short-time-step constraints; immediate reward design critically enhances deep RL policy convergence; and PCA substantially improves QCL visualization and interpretability. These findings provide general theoretical insights and practical guidelines for reward function design, algorithm selection, and high-fidelity solution-region identification in quantum control systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Understanding the quantum control landscape (QCL) is important for designing effective quantum control strategies. In this study, we analyze the QCL for a single two-level quantum system (qubit) using various control strategies. We employ Principal Component Analysis (PCA), to visualize and analyze the QCL for higher dimensional control parameters. Our results indicate that dimensionality reduction techniques such as PCA, can play an important role in understanding the complex nature of quantum control in higher dimensions. Evaluations of traditional control techniques and machine learning algorithms reveal that Genetic Algorithms (GA) outperform Stochastic Gradient Descent (SGD), while Q-learning (QL) shows great promise compared to Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO). Additionally, our experiments highlight the importance of reward function design in DQN and PPO demonstrating that using immediate reward results in improved performance rather than delayed rewards for systems with short time steps. A study of solution space complexity was conducted by using Cluster Density Index (CDI) as a key metric for analyzing the density of optimal solutions in the landscape. The CDI reflects cluster quality and helps determine whether a given algorithm generates regions of high fidelity or not. Our results provide insights into effective quantum control strategies, emphasizing the significance of parameter selection and algorithm optimization.

Problem

• Analyzing quantum control landscape complexity
• Exploring dimensionality reduction in quantum systems
• Optimizing quantum control with machine learning

Innovation

• PCA for dimensionality reduction
• Genetic Algorithms outperform SGD
• Q-learning shows great promise