Deep Ising Born Machine

A quantum neural network (QNN) is a method to find patterns in quantum data and has a wide range of applications including quantum chemistry, quantum computation, quantum metrology, and quantum simulation. Efficiency and universality are two desirable properties of a QNN but are unfortunately contradictory. In this work, we examine a deep Ising Born machine (DIBoM), and show it has a good balance between efficiency and universality. More precisely, the DIBoM has a flexible number of parameters to be efficient, and achieves provable universality with sufficient parameters. The architecture of the DIBoM is based on generalized controlled-Z gates, conditional gates, and some other ingredients. To compare the universality of the DIBoM with other QNNs, we propose a fidelity-based expressivity measure, which may be of independent interest. Extensive empirical evaluations corroborate that the DIBoM is both efficient and expressive.