IQI Weekly Seminar

Haar-random unitary matrices facilitate many analysis
in quantum information. However, they are highly inefficient to implement or to sample. Unitary 2-designs are distributions on finite sets of unitary matrices that have some specific properties in common with
the Haar measure. We present exact unitary 2-designs on n qubits that can be
implemented with circuits of Clifford gates, with size O(n log^2 n log log n), depth O(log^2 n), and can be sampled with 5n random bits.

 

Joint work with Richard Cleve, Li Liu, and Chunhao Wang.