Probabilistic Modeling with Matrix Product States
This work addresses the challenge of leveraging quantum-inspired models for classical machine learning tasks, though it appears incremental as it adapts existing methods.
The authors tackled the problem of training quantum circuit models for sequence modeling by proposing an efficient gradient-free algorithm, a modification of the density matrix renormalization group, and demonstrated its utility on the parity learning problem.
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.