ℤ₂ × ℤ₂ Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks

This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub><mo>×</mo><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.