Ciara Morgan

We study unitary 2-designs and decoupling with random diagonal-unitaries. We first show that the alternate application of random diagonal-unitaries in the Pauli-Z and -X bases constitutes a unitary 2-design after a number of repetitions, implying that the process achieves decoupling. We then go on to show that even fewer repetitions are sufficient for achieving decoupling at the same rate as that with Haar random unitaries. These results imply that precise unitary 2-designs are not necessary for achieving the Haar decoupling rate, indicating the possibility to achieve the rate by random unitaries less uniform than 2-designs. We also provide a simple quantum circuit that implements a unitary 2-design and achieves decoupling, which is partitioned into a constant number of commuting parts.