IMPACT OF QUANTUM CIRCUIT DEPTH AND ENTANGLEMENT ON HYBRID QUANTUM-CLASSICAL CLASSIFICATION PERFORMANCE: A CASE STUDY ON WISCONSIN BREAST CANCER DATASET

Abstract

Variational Quantum Circuits (VQCs) are a strong candidate architecture for quantum machine learning algorithms that can be run on Noisy Intermediate-Scale Quantum (NISQ) devices. However, many design decisions still need exploration, such as the influence that circuit depth and entanglement topology have on training and accuracy. Here we explore circuit depth and entanglement for hybrid quantum-classical neural networks by benchmarking 12 combinations of 4 circuit depths (1-4 layers) and 3 entanglement types (linear, circular, full) on an 8-dimensional reduced Wisconsin Diagnostic Breast Cancer dataset. For each depth and entanglement type we train over 10 random seeds. We find significant effects of circuit depth and entanglement type on classification accuracy (p<0.001 and p=0.002 respectively, via ANOVA). For circuit depth we observe steadily increasing accuracy as depth is increased. All three types of entanglement show similar trends with depth, however circular consistently outperforms linear and full entanglement at all depths (94.3% mean test set accuracy at depth 4). Performance saturates at depth 4 for circular entanglement. Full entanglement shows poorer performance compared to linear and circular, as well as having higher variance as depth increases. This may indicate trainability issues due to barren plateaus which has been shown to scale with circuit expressibility. As such, we recommend circuit designs that implement circular entanglement and caution the use of highly expressive circuits like full entanglement. Circular circuitry provides a good trade-off between accuracy and resources with an accuracy of 96.1% at depth 3.