CRC Press eBooks

Optimization Methods for Quantum Machine Learning

Hamid D. Ismail

Published Nov 4, 2026• 0 citations

Abstract

This chapter examines optimization as the central practical bottleneck in quantum machine learning (QML), emphasizing that the usefulness of parameterized quantum models depends not only on expressivity but also on whether they can be trained reliably under realistic conditions. It formulates QML training as a constrained, stochastic optimization problem on curved state manifolds, where parameters define unitary evolutions rather than unconstrained Euclidean weights. This geometric perspective is used to analyze the roles of parameterized quantum circuits, generator structure, circuit depth, and quantum Fisher information in shaping trainability and convergence behavior. This chapter develops the main classes of quantum loss functions and gradient-evaluation methods, including the parameter-shift rule, Hadamard-test-based approaches, and finite-shot estimation, and then surveys both gradient-based and gradient-free optimization methods relevant to hybrid quantum-classical training. Particular attention is given to major optimization pathologies, including barren plateaus, noise-induced flat landscapes, hyperparameter sensitivity, and parameter redundancy. The discussion also emphasizes hardware-aware optimization, accounting for finite shot budgets, noise, measurement overhead, and simulation strategies. Taken together, this chapter provides a systematic framework for understanding how geometry, stochastic measurement, ansatz design, optimizer choice, and hardware constraints jointly determine the practical limits of trainability in QML.

DOI: 10.1201/9781042002818-7

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