Unraveling the emergence of quantum state designs in systems with symmetry

Understand

Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics.

• Symmetries, on the other hand, are expected to reduce the randomness of a state.
• Despite being ubiquitous, the effects of symmetry on quantum state designs remain an outstanding question.
• The recently introduced projected ensemble framework generates efficient approximate state $t$-designs by hinging on projective measurements and many-body quantum chaos.