Testing symmetry on quantum computers

Understand

Symmetry is a unifying concept in physics.

• In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks.
• For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation.
• Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels.