Physical Review A - Atomic, Molecular, and Optical Physics
We show how to efficiently generate pseudorandom states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudorandom algorithms in the cluster-state picture, we identify a strategy for optimizing pseudorandom 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.
Brown, Winton G.; Weinstein, Yaakov S.; and Viola, Lorenza, "Quantum Pseudorandomness from Cluster-State Quantum Computation" (2008). Open Dartmouth: Faculty Open Access Articles. 1922.