  Inspired by the possibility that generative models based on quantum circuits
can provide a useful inductive bias for sequence modeling tasks, we propose an
efficient training algorithm for a subset of classically simulable quantum
circuit models. The gradient-free algorithm, presented as a sequence of exactly
solvable effective models, is a modification of the density matrix
renormalization group procedure adapted for learning a probability
distribution. The conclusion that circuit-based models offer a useful inductive
bias for classical datasets is supported by experimental results on the parity
learning problem.
