Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data

TL;DR

This paper introduces a permutation invariant quantum encoding for point cloud data that enhances generalisation in quantum machine learning models, demonstrated through improved accuracy on geometric classification tasks.

Contribution

The paper presents a novel permutation invariant quantum encoding method specifically designed for point cloud data, improving generalisation in quantum machine learning.

Findings

Permutation invariant encoding improves accuracy with more points.

Non-invariant encodings decrease in accuracy as points increase.

Enhanced generalisation demonstrated on geometric classification tasks.

Abstract

Quantum Computing offers a potentially powerful new method for performing Machine Learning. However, several Quantum Machine Learning techniques have been shown to exhibit poor generalisation as the number of qubits increases. We address this issue by demonstrating a permutation invariant quantum encoding method, which exhibits superior generalisation performance, and apply it to point cloud data (three-dimensional images composed of points). Point clouds naturally contain permutation symmetry with respect to the ordering of their points, making them a natural candidate for this technique. Our method captures this symmetry in a quantum encoding that contains an equal quantum superposition of all permutations and is therefore invariant under point order permutation. We test this encoding method in numerical simulations using a Quantum Support Vector Machine to classify point clouds drawn from either spherical or toroidal geometries. We show that a permutation invariant encoding improves in accuracy as the number of points contained in the point cloud increases, while non-invariant quantum encodings decrease in accuracy. This demonstrates that by implementing permutation invariance into the encoding, the model exhibits improved generalisation.