Quantum Circuit Training with Growth-Based Architectures

TL;DR

Three distinct methods are developed that incrementally increase parameterized quantum circuit depth during training, mitigating overfitting and managing model complexity dynamically, demonstrating that dynamic growth methods outperform traditional, fixed-depth approaches, achieving lower final losses and reduced variance between runs.

Abstract

This study introduces growth-based training strategies that incrementally increase parameterized quantum circuit (PQC) depth during training, mitigating overfitting and managing model complexity dynamically. We develop three distinct methods: Block Growth, Sequential Feature Map Growth, and Interleave Feature Map Growth, which add reuploader blocks to PQCs adaptively, expanding the accessible frequency spectrum of the model in response to training needs. This approach enables PQCs to achieve more stable convergence and generalization, even in noisy settings. We evaluate our methods on regression tasks and the 2D Laplace equation, demonstrating that dynamic growth methods outperform traditional, fixed-depth approaches, achieving lower final losses and reduced variance between runs. These findings underscore the potential of growth-based PQCs for quantum scientific machine learning (QSciML) applications, where balancing expressivity and stability is essential.

Figures (8)

• Figure 1: PQC growing method block growth where both feature maps and ansatzs blocks are added during training, with some specified block being added $\ell$ times every time the PQC grows.
• Figure 2: Sequential feature map growth, where feature map gates are added to the PQC when it grows, adding these gates from left to right in between existing ansatz gates.
• Figure 3: Interleave feature map growth, where feature map gates are added to the PQC when it grows, adding these gates from the middle out in between existing ansatz gates.
• Figure 4: Teacher circuit architecture for $2$ qubits, randomly initialized to create a dataset for PQCs learn the output of which also follow this circuit architecture.
• Figure 5: Mean squared error performance for different training methods on the student-teacher regression tasks. Each boxplot shows the distribution of MSE values across $50$ random seeds for seven models: 5-layer CDL (RAND), 20-layer CDL (RAND), 5-layer CDL (identity initialization), 20-layer CDL (identity initialization), Block Growth, Sequential Feature Map Growth, and Interleave Feature Map Growth. The blue dots represent the MSE values for each of the runs, green horizontal lines represent the median, red triangles the mean.