  Parameterized quantum circuits (PQCs), as one of the most promising schemes
to realize quantum machine learning algorithms on near-term quantum computers,
have been designed to solve machine earning tasks with quantum advantages. In
this paper, we explain why PQCs with different structures can achieve
generative tasks in the discrete case from the perspective of probability
estimation. Although different kinds of PQCs are proposed for generative tasks,
the current methods often encounter the following three hurdles: (1) the mode
contraction problem; (2) unexpected data are often generated with a high
proportion; (3) target data cannot be sampled directly. For the purpose of
tackling the above hurdles, we devise Bayesian quantum circuit (BQC) through
introducing ancillary qubits to represent prior distributions. BQC advances
both generative and semi-supervised quantum circuit learning tasks, where its
effectiveness is validated by numerical simulations using the Rigetti Forest
platform.
