On a Possible Quantum Variational Autoencoder Circuit

Generative Models have always attracted the attention of Machine Learning research community; they are useful and also generally harder than their discriminative counterparts. In these models, we would be looking into learning the probability distribution of the input and sampling from that to generate new data samples. Since quantum computing and algorithms are inherently random, they can facilitate a natural framework in this situation. But, getting a suitable gate circuit to achieve the requisite quantum state which by repeated preparation and measurement leads to the sought-after data samples is not trivial. In this paper, we propose a quantum circuit which has a flavor of Variational Autoencoder with the usual visible and hidden nodes for input data and latent distribution. The encoder portion comprises of a suitably chosen parameterized phase ansatz and Inverse Quantum Fourier Transform blocks. Depending on whether the measurement is carried out on the hidden nodes or not, the decoder circuit, which is just not the inverse of the encoder in our case, is configured. The Kullback-Leibler Divergence is used train the circuit towards the required input distribution. Numerical results presented demonstrate the correct functionality of the approach.