Near-linear constructions of exact unitary 2-designs
Quantum Physics
2017-01-03 v3
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).
Keywords
Cite
@article{arxiv.1501.04592,
title = {Near-linear constructions of exact unitary 2-designs},
author = {Richard Cleve and Debbie Leung and Li Liu and Chunhao Wang},
journal= {arXiv preprint arXiv:1501.04592},
year = {2017}
}
Comments
30 pages, 10 figures, presentation improved