Conditional quantum circuit Born machine based on a hybrid quantum–classical​ framework

As a branch of machine learning, generative models are widely used in supervised and unsupervised learning. To speedup certain machine learning tasks, quantum generative adversarial networks, quantum circuit Born machine (QCBM), and quantum Boltzmann machine have been proposed. These generative models can implement some specific generative tasks but have no control over the modes of the generated data. To make the generative model more intelligent and controllable, additional conditional information (such as category labels for MNIST digits) can be added to the model to guide the generation of data. A more in-depth study was carried out based on the QCBM, and a conditional quantum circuit Born machine (CQCBM) based on a hybrid quantum–classical (HQC) framework was proposed. The conditional information was encoded by adding extra qubits to guide the model training process. Experiments were conducted on both mixed Gaussian distribution and MNIST handwritten digit dataset. Numerical and experimental results show that the proposed CQCBM is able to generate the target distribution while satisfying the conditional constraints well. Compared to other conditional quantum generative models only applied to Bars and Stripes (BAS) or Chessboard datasets, the proposed model also performed well on more difficult image-generating tasks.