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arXiv · 1501.04592

Near-linear constructions of exact unitary 2-designs

Richard Cleve·Debbie Leung·Li Liu·Chunhao Wang
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Abstract

A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be implemented by quantum circuits consisting of ~O(n) elementary gates in logarithmic depth. This is essentially a quadratic improvement in size (and in width times depth) over all previous implementations that are exact or approximate (for sufficiently strong approximations).

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Richard Cleve, Debbie Leung, Li Liu, Chunhao Wang. 2015-01-19. Near-linear constructions of exact unitary 2-designs. https://arxiv.org/abs/1501.04592

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