Learning quantum symmetries with interactive quantum-classical variational algorithms

Understand

A symmetry of a state $\vert \psi \rangle$ is a unitary operator of which $\vert \psi \rangle$ is an eigenvector.

• When $\vert \psi \rangle$ is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques.
• In this paper, we develop a variational hybrid quantum-classical learning scheme to systematically probe for symmetries of $\vert \psi \rangle$ with no a priori assumptions about the state.
• This procedure can be used to learn various symmetries at the same time.