Yoshiaki Kawase

Yoshiaki Kawase

Quantum neural networks hold promise for tackling computationally challenging tasks that are intractable for classical computers. However, their practical application is hindered by significant optimization challenges, arising from complex loss landscapes characterized by barren plateaus and numerous local minima. These problems become more severe as the number of parameters or qubits increases, hampering effective training. To mitigate these optimization challenges, particularly for quantum machine learning applied to classical data, we employ an approach of distributing overlapping local patches across multiple quantum neural networks, processing each patch with an independent quantum neural network, and aggregating their outputs for prediction. In this study, we investigate how the number of parameters and patches affects the loss landscape geometry of this distributed quantum neural network architecture via Hessian analysis and loss landscape visualization. Our results confirm that increasing the number of parameters tends to lead to deeper and sharper loss landscapes. Crucially, we demonstrate that increasing the number of patches significantly reduces the largest Hessian eigenvalue at minima. This finding suggests that our distributed patch approach acts as a form of implicit regularization, promoting optimization stability and potentially enhancing generalization. Our study provides valuable insights into optimization challenges and highlights that the distributed patch approach is a promising strategy for developing more trainable and practical quantum machine learning models for classical data tasks.

Yoshiaki Kawase, Kosuke Mitarai, Keisuke Fujii

t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while maintaining the relationship, or similarities, between the surrounding points. In t-SNE, the initial position of the low-dimensional data is randomly determined, and the visualization is achieved by moving the low-dimensional data to minimize a cost function. Its variant called parametric t-SNE uses neural networks for this mapping. In this paper, we propose to use quantum neural networks for parametric t-SNE to reflect the characteristics of high-dimensional quantum data on low-dimensional data. We use fidelity-based metrics instead of Euclidean distance in calculating high-dimensional data similarity. We visualize both classical (Iris dataset) and quantum (time-depending Hamiltonian dynamics) data for classification tasks. Since this method allows us to represent a quantum dataset in a higher dimensional Hilbert space by a quantum dataset in a lower dimension while keeping their similarity, the proposed method can also be used to compress quantum data for further quantum machine learning.