Quantum Language Processing

TL;DR

This paper introduces a quantum framework for language processing using Fock-space representations and quantum Boltzmann machines, demonstrating its theoretical richness and practical potential for parsing complex grammars.

Contribution

It develops a novel quantum formalism for linguistic problems, introduces a new training method for quantum Harmony operators, and establishes the computational complexity of quantum language processing.

Findings

Quantum language processing is BQP-complete.

The proposed method can rapidly parse non-trivial grammars.

Quantum Boltzmann machines may be more expressive than classical ones.

Abstract

We present a representation for linguistic structure that we call a Fock-space representation, which allows us to embed problems in language processing into small quantum devices. We further develop a formalism for understanding both classical as well as quantum linguistic problems and phrase them both as a Harmony optimization problem that can be solved on a quantum computer which we show is related to classifying vectors using quantum Boltzmann machines. We further provide a new training method for learning quantum Harmony operators that describe a language. This also provides a new algorithm for training quantum Boltzmann machines that requires no approximations and works in the presence of hidden units. We additionally show that quantum language processing is BQP-complete, meaning that it is polynomially equivalent to the circuit model of quantum computing which implies that quantum language models are richer than classical models unless BPP=BQP. It also implies that, under certain circumstances, quantum Boltzmann machines are more expressive than classical Boltzmann machines. Finally, we examine the performance of our approach numerically for the case of classical harmonic grammars and find that the method is capable of rapidly parsing even non-trivial grammars. This suggests that the work may have value as a quantum inspired algorithm beyond its initial motivation as a new quantum algorithm.