Enabling Quantum Machine Learning Simulations

Quantum machine learning (QML) and variational quantum algorithms (VQAs) are broad families of quantum algorithms that rely on classical optimisation to solve learning tasks. These quantum algorithms typically use gradient-based optimisers such as Adam or stochastic gradient descent (SGD) to tune free parameters in quantum computation. Gradient-based optimisers perform well in small, noiseless systems but struggle in realistic simulations with a large number of quantum bits (qubits), especially when gradients become unreliable to estimate. In this project, we explore gradient-free methods as an alternative approach for performing black-box optimisation on quantum learning problems. Specifically, we apply insights from a recent direct search algorithm, which employs random subspace projections to reduce the dimensionality of the parameter search space. Our results show that this direct search algorithm outperforms Adam for modest qubit numbers when finite-sampling errors are negligible. We additionally show that this algorithm can theoretically accommodate a finite number of quantum measurements, i.e., when sampling errors dominate. Building on this, we propose a doubly stochastic direct search approach that combines subspace sampling with finite-shot estimation, offering a scalable and error-resilient optimisation strategy for future QML and variational protocols.