Classifying Data with Local Hamiltonians

TL;DR

This paper introduces a quantum neural network model using local Hamiltonians for data classification, demonstrating a training scheme with quantum annealing and testing on color classification tasks with promising results.

Contribution

It proposes a novel quantum neural network framework based on local Hamiltonians, including a training scheme via quantum annealing and practical implementation details.

Findings

Successfully trained a quantum classifier on color data

Developed a qubit-efficient training optimization

Demonstrated the classifier's performance on a simple task

Abstract

The goal of this work is to define a notion of a quantum neural network to classify data, which exploits the low energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data and then test its performance on a simple classification task. More specifically, we use Microsoft's quantum simulator, Liquid, to construct local Hamiltonians that can encode trained classifier functions in their ground space, and which can be probed by measuring the overlap with test states corresponding to the data to be classified. To obtain such a classifier Hamiltonian, we further propose a training scheme based on quantum annealing which is completely closed-off to the environment and which does not depend on external measurements until the very end, avoiding unnecessary decoherence during the annealing procedure. For a network of size n, the trained network can be stored as a list of O(n) coupling strengths. We address the question of which interactions are most suitable for a given classification task, and develop a qubit-saving optimization for the training procedure on a simulated annealing device. Furthermore, a small neural network to classify colors into red vs. blue is trained and tested, and benchmarked against the annealing parameters.