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Quantum Computing offers a potentially powerful new method for performingMachine Learning. However, several Quantum Machine Learning techniques havebeen shown to exhibit poor generalisation as the number of qubits increases. Weaddress this issue by demonstrating a permutation invariant quantum encodingmethod, which exhibits superior generalisation performance, and apply it topoint cloud data (three-dimensional images composed of points). Point cloudsnaturally contain permutation symmetry with respect to the ordering of theirpoints, making them a natural candidate for this technique. Our method capturesthis symmetry in a quantum encoding that contains an equal quantumsuperposition of all permutations and is therefore invariant under point orderpermutation. We test this encoding method in numerical simulations using aQuantum Support Vector Machine to classify point clouds drawn from eitherspherical or toroidal geometries. We show that a permutation invariant encodingimproves in accuracy as the number of points contained in the point cloudincreases, while non-invariant quantum encodings decrease in accuracy. Thisdemonstrates that by implementing permutation invariance into the encoding, themodel exhibits improved generalisation.

Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data