Quantum pseudo-randomness from cluster-state quantum computation

Understand

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation.

• By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for optimizing pseudo-random circuits by properly choosing single-qubit rotations.
• A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution.
• Our results may be viewed as an alternative construction of approximate unitary 2-designs.