  This paper introduces quantum circuit $C^*$-algebra net, which provides a
connection between $C^*$-algebra nets proposed in classical machine learning
and quantum circuits. Using $C^*$-algebra, a generalization of the space of
complex numbers, we can represent quantum gates as weight parameters of a
neural network. By introducing additional parameters, we can induce interaction
among multiple circuits constructed by quantum gates. This interaction enables
the circuits to share information among them, which contributes to improved
generalization performance in machine learning tasks. As an application, we
propose to use the quantum circuit $C^*$-algebra net to encode classical data
into quantum states, which enables us to integrate classical data into quantum
algorithms. Numerical results demonstrate that the interaction among circuits
improves performance significantly in image classification, and encoded data by
the quantum circuit $C^*$-algebra net are useful for downstream quantum machine
learning tasks.
