Symmetry breaking in geometric quantum machine learning in the presence of noise
It addresses the impact of noise on EQNN training, a critical issue for practical quantum machine learning applications, though it is incremental as it builds on existing theoretical work.
This paper investigates how hardware noise affects equivariant quantum neural networks (EQNN) in geometric quantum machine learning, showing that symmetry breaking increases linearly with layers and noise strength, supported by simulations and hardware data up to 64 qubits.
Geometric quantum machine learning based on equivariant quantum neural networks (EQNN) recently appeared as a promising direction in quantum machine learning. Despite the encouraging progress, the studies are still limited to theory, and the role of hardware noise in EQNN training has never been explored. This work studies the behavior of EQNN models in the presence of noise. We show that certain EQNN models can preserve equivariance under Pauli channels, while this is not possible under the amplitude damping channel. We claim that the symmetry breaking grows linearly in the number of layers and noise strength. We support our claims with numerical data from simulations as well as hardware up to 64 qubits. Furthermore, we provide strategies to enhance the symmetry protection of EQNN models in the presence of noise.