Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data

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.

arXiv comment10 pages, 9 figures

References in corpus (18)

• Quantum Machine Learning
• Supervised learning with quantum enhanced feature spaces
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Power of data in quantum machine learning
• A rigorous and robust quantum speed-up in supervised machine learning
• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Exploiting symmetry in variational quantum machine learning
• Point-E: A System for Generating 3D Point Clouds from Complex Prompts
• Quantum Machine Learning for Chemistry and Physics
• Point Cloud Transformers applied to Collider Physics
• Provably Trainable Rotationally Equivariant Quantum Machine Learning
• Grammar-aware sentence classification on quantum computers
• Optimal manipulations with qubits: Universal quantum entanglers
• Stabilisation of Quantum Computations by Symmetrisation
• Quantum support vector machines for aerodynamic classification
• Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers
• Quantum Image Processing
• GASP -- A Genetic Algorithm for State Preparation

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