# Probabilistic Modeling with Matrix Product States

## TL;DR

This paper introduces an efficient, gradient-free training algorithm for quantum circuit-inspired probabilistic models, demonstrating their usefulness for classical sequence modeling tasks like parity learning.

## Contribution

It presents a novel, exactly solvable, density matrix renormalization group-based algorithm for training quantum circuit models on classical data.

## Key findings

- Effective modeling of classical datasets using circuit-based models
- Successful application to the parity learning problem
- Supports the usefulness of quantum-inspired models in classical machine learning

## Abstract

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.