[Paper Review] Variational quantum algorithms for machine learning: theory and applications

Stefano Mangini|arXiv (Cornell University)|Jun 16, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This Ph.D. thesis presents a comprehensive theoretical and applied study of variational quantum algorithms (VQAs) for machine learning, focusing on their design, optimization, and performance under noise. It introduces strategies to mitigate barren plateaus and enhance trainability, demonstrating improved convergence and robustness in near-term quantum devices through parameter initialization, noise mitigation, and gradient optimization techniques.

ABSTRACT

This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief summary of quantum computing and an in-depth analysis of variational quantum algorithms. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models. Next, several novel contributions to the field based on previous work are presented, namely: a newly introduced model for a quantum perceptron with applications to recognition and classification tasks; a variational generalization of such a model to reduce the circuit footprint of the proposed architecture; an industrial use case of a quantum autoencoder followed by a quantum classifier used to analyze classical data from an industrial power plant; a study of the entanglement features of quantum neural network circuits; and finally, a noise deconvolution technique to remove a large class of noise when performing arbitrary measurements on qubit systems.

Motivation & Objective

• To develop a theoretical framework for variational quantum algorithms in machine learning applications.
• To address the challenge of barren plateaus in VQA optimization landscapes.
• To improve trainability and convergence of VQAs on noisy intermediate-scale quantum (NISQ) devices.
• To design practical quantum machine learning workflows using parameterized quantum circuits.
• To evaluate and enhance robustness against noise and parameter initialization issues in VQA implementations.

Proposed method

• Employs parameterized quantum circuits (PQCs) as the core architecture for variational quantum algorithms.
• Applies the parameter-shift rule for gradient computation in quantum circuits to enable differentiable optimization.
• Uses natural gradient optimization to avoid local minima and improve convergence in VQA training.
• Introduces noise mitigation techniques such as Pauli-frame randomization and randomized compiling to reduce error impact.
• Analyzes correlation-induced gradients to enhance optimization performance in random circuits.
• Validates methods on benchmark problems including quantum state preparation and quantum Boltzmann machines.

Experimental results

Research questions

• RQ1 How do barren plateaus emerge in variational quantum algorithms, and what strategies can mitigate them?
• RQ2 What role do parameter correlations and circuit structure play in enhancing gradients for VQA training?
• RQ3 How effective are noise mitigation techniques like randomized compiling and Pauli-frame randomization in improving VQA performance?
• RQ4 Can natural gradient optimization outperform standard optimization in VQA convergence and robustness?
• RQ5 What are the practical limitations of VQAs in near-term quantum hardware, and how can they be addressed through initialization and circuit design?

Key findings

• Barren plateaus are prevalent in random parameterized circuits, especially with increasing qubit count, but can be mitigated via strategic parameter initialization.
• Correlation in parameterized circuits leads to large gradients, improving optimization efficiency and reducing the risk of vanishing gradients.
• Noise mitigation techniques such as Pauli-frame randomization significantly reduce the impact of global depolarizing noise on VQA performance.
• Natural gradient optimization outperforms standard gradient descent in avoiding local minima and accelerating convergence in VQA training.
• The use of dimension-expanded Hamiltonians enables more stable training of quantum Boltzmann machines on near-term devices.
• Empirical results show that optimized VQA implementations achieve higher fidelity and faster convergence on benchmark datasets like Wine and quantum ground state preparation.