Entangling Machine Learning with Quantum Tensor Networks

TL;DR

This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling, and abstracts the problem down to modeling Motzkin spin chains, which exhibit long-range correlations reminiscent of those found in language.

Abstract

This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will abstract the problem down to modeling Motzkin spin chains, which exhibit long-range correlations reminiscent of those found in language. The Matrix Product State (MPS), also known as the tensor train, has a bond dimension which scales as the length of the sequence it models. To combat this, we use the factored core MPS, whose bond dimension scales sub-linearly. We find that the tensor models reach near perfect classifying ability, and maintain a stable level of performance as the number of valid training examples is decreased.

Figures (29)

• Figure 1: Vector decomposition, singular value decomposition, absorbing diagonal matrix.
• Figure 2: Ket and diagrammatic notation.
• Figure 3: Index ordering.
• Figure 4: Contraction loop.
• Figure 5: Cap contraction.