Learning Unitary Transformation by Quantum Machine Learning Model

Quantum machine learning (QML) is a rapidly rising research field that incorporates ideas from quantum computing and machine learning to develop emerging tools for scientific research and improving data processing. How to efficiently control or manipulate the quantum system is a fundamental and vexing problem in quantum computing. It can be described as learning or approximating a unitary operator. Since the success of the hybrid-based quantum machine learning model proposed in recent years, we investigate to apply the techniques from QML to tackle this problem. Based on the Choi-Jamiolkowski isomorphism in quantum computing, we transfer the original problem of learning a unitary operator to a min-max optimization problem which can also be viewed as a quantum generative adversarial network. Besides, we select the spectral norm between the target and generated unitary operators as the regularization term in the loss function. Inspired by the hybrid quantum-classical framework widely used in quantum machine learning, we employ the variational quantum circuit and gradient descent based optimizers to solve the min-max optimization problem. In our numerical experiments, the results imply that our proposed method can successfully approximate the desired unitary operator and dramatically reduce the number of quantum gates of the traditional approach. The average fidelity between the states that are produced by applying target and generated unitary on random input states is around 0.997.