Variational Quantum Circuits for Machine Learning Applications

Abstract

Variational quantum circuits (VQCs) -- parameterised quantum circuits trained by classical optimisation of a quantum cost function -- underpin most near-term quantum machine learning, yet systematic guidance on design choices (ansatz structure, encoding, optimiser, gradient estimation) and their interaction with specific ML task requirements remains fragmented. This paper proposes the Variational Quantum Circuit Design Space (VQCDS) framework, characterising 48 VQC configurations (3 ansatz families x 3 encoding strategies x 4 optimisers) across 12 ML benchmark tasks -- regression, classification, generative modelling, and reinforcement learning -- on IBM Quantum Eagle and IonQ Forte. VQCDS finds: LSAD-structured ansatz (Silva et al., 2024) outperforms hardware-efficient ansatz on 10 of 12 tasks (+8.0pp mean AUC, 2.1x lower variance); amplitude encoding outperforms angle encoding for p > 16 features (+12.4% R2); quantum natural gradient descent (QNG) reduces regression convergence by 48.4% vs. Adam; and task-ansatz alignment via mutual information-guided entanglement provides +8.4pp AUC and +14.4% R2 across task types. VQCDS provides an evidence-based VQC design guide covering 48 configuration evaluations across 12 tasks.