What can we learn from quantum convolutional neural networks?

TL;DR

This paper investigates quantum convolutional neural networks (QCNNs), revealing how they implicitly embed physical features through ground-state feature maps, leading to improved quantum data analysis and applications in fluid dynamics.

Contribution

It provides a new interpretation of QCNNs via hidden feature maps and demonstrates their effectiveness in quantum phase recognition and fluid dynamics problems.

Findings

High performance in phase recognition arises from effective basis sets with sharp features.

Quantum data enhances generalization, especially with limited samples.

Ground-state feature maps can be applied successfully to fluid dynamics.

Abstract

Quantum machine learning (QML) shows promise for analyzing quantum data. A notable example is the use of quantum convolutional neural networks (QCNNs), implemented as specific types of quantum circuits, to recognize phases of matter. In this approach, ground states of many-body Hamiltonians are prepared to form a quantum dataset and classified in a supervised manner using only a few labeled examples. However, this type of dataset and model differs fundamentally from typical QML paradigms based on feature maps and parameterized circuits. In this study, we demonstrate how models utilizing quantum data can be interpreted through hidden feature maps, where physical features are implicitly embedded via ground-state feature maps. By analyzing selected examples previously explored with QCNNs, we show that high performance in quantum phase recognition comes from generating a highly effective basis set with sharp features at critical points. The learning process adapts the measurement to create sharp decision boundaries. Our analysis highlights improved generalization when working with quantum data, particularly in the limited-shots regime. Furthermore, translating these insights into the domain of quantum scientific machine learning, we demonstrate that ground-state feature maps can be applied to fluid dynamics problems, expressing shock wave solutions with good generalization and proven trainability.