Symmetry breaking in geometric quantum machine learning in the presence
  of noise
Cenk Tüysüz Su Yeon Chang Maria Demidik Karl Jansen Sofia Vallecorsa Michele Grossi
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.