Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective

Understand

We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer.

• Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed.
• After briefly discussing some of the standard symmetries relevant for many-particle systems, we discuss the advantage of encoding some symmetries directly in quantum ans\"atze, especially to reduce the quantum register size.
• It is, however, well-known that the use of symmetry-breaking states can also be a unique way to incorporate specific internal correlations when a spontaneous symmetry breaking occurs.