Quantum Circuit $C^*$-algebra Net
This work addresses the integration of classical data into quantum algorithms for researchers in quantum machine learning, representing an incremental advancement by building on existing C*-algebra nets.
The paper tackles the problem of connecting classical machine learning with quantum circuits by introducing quantum circuit C*-algebra nets, which represent quantum gates as neural network parameters and enable interaction among circuits to improve generalization; numerical results show significant performance improvements in image classification and utility for downstream quantum machine learning tasks.
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.