Modeling Sequences with Quantum States: A Look Under the Hood

TL;DR

This paper explores modeling sequence data using pure, entangled quantum states, leveraging reduced density matrices to capture more information than classical methods, and analyzes the generalization capabilities of the resulting tensor network models.

Contribution

It introduces a quantum state-based approach for sequence modeling using entanglement and DMRG, providing insights into the mechanics and generalization error of such models.

Findings

Quantum models retain more information via entanglement.

The DMRG-based training organizes information into tensor networks.

Generalization error depends on training dataset size.

Abstract

Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the classical marginal distributions on a subsystem in which information about the complementary system has been integrated out and lost. A training algorithm based on the density matrix renormalization group (DMRG) procedure uses the extra information contained in the reduced densities and organizes it into a tensor network model. An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model. As an illustration, we work with the even-parity dataset and produce an estimate for the generalization error as a function of the fraction of the dataset used in training.