More global randomness from less-random local gates

Understand

Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics.

• In this work, we investigate a class of random quantum circuits with a specific gate structure.
• Within this framework, we prove that one-dimensional structured random circuits with non-Haar random local gates can exhibit substantially more global randomness compared to Haar random circuits with the same underlying circuit architecture.
• In particular, we derive all the exact eigenvalues and eigenvectors of the second-moment operators for these structured random circuits under a solvable condition, by establishing a link to the Kitaev chain, and show that their spectral gaps can exceed those of Haar random circuits.