In the search for advantage in Quantum Machine Learning, appropriate encoding of the underlying classical data into a quantum state is a critical step. Our previous work  implemented an encoding method inspired by underlying physics and achieved AUC scores higher than that of classical techniques for a reduced dataset of B Meson Continuum Suppression data. A particular problem faced by these Quantum SVM techniques was overfitting of training data. One possible method of tackling this is by reducing the expressibility of the model by exploiting symmetries in the data using symmetry invariant encodings. There are often several natural symmetries present in Particle Physics data (permutation of particle order and rotational symmetry) that can be targeted. This presentation demonstrates a method of encoding that guarantees invariance under permuting the ordering of particles in the data input. A downside of this model for more general applicability is the quadratic scaling of ancilla qubits as the number of states to be symmetrised increases. However, data from Particle Physics may only contain a small number of particles in each event, meaning this scaling is not too prohibitive and suggests particle data is well suited to this approach. In addition we explore solutions to this scaling using approximately invariant encoding created through genetic algorithms. As quantum technology develops over the coming decade it is hoped the methods discussed here can form a basis for Quantum Machine Learning model development in a Particle Physics context.
 Heredge, J., Hill, C., Hollenberg, L., Sevior, M., Quantum Support Vector Machines for Continuum Suppression in B Meson Decays. Comput Softw Big Sci 5, 27 (2021). https://doi.org/10.1007/s41781-021-00075-x
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