On the Trainability and Classical Simulability of Learning Matrix Product States Variationally

TL;DR

This paper investigates the trainability of matrix product states in quantum machine learning, showing that local observables avoid barren plateaus and that certain problems are classically simulable due to sparse operators.

Contribution

The study reveals how local observables improve trainability and demonstrates classical simulability of specific quantum learning tasks involving matrix product states.

Findings

Global observables lead to barren plateaus in training.

Local observables prevent vanishing gradients.

Objective functions often involve sparse operators, enabling classical simulation.

Abstract

We prove that using global observables to train the matrix product state ansatz results in the vanishing of all partial derivatives, also known as barren plateaus, while using local observables avoids this. This ansatz is widely used in quantum machine learning for learning weakly entangled state approximations. Additionally, we empirically demonstrate that in many cases, the objective function is an inner product of almost sparse operators, highlighting the potential for classically simulating such a learning problem with few quantum resources. All our results are experimentally validated across various scenarios.