  Symmetries in a Hamiltonian play an important role in quantum physics because
they correspond directly with conserved quantities of the related system. In
this paper, we propose quantum algorithms capable of testing whether a
Hamiltonian exhibits symmetry with respect to a group. We demonstrate that
familiar expressions of Hamiltonian symmetry in quantum mechanics correspond
directly with the acceptance probabilities of our algorithms. We execute one of
our symmetry-testing algorithms on existing quantum computers for simple
examples of both symmetric and asymmetric cases.
