Local random quantum circuits are approximate polynomial-designs - numerical results
Abstract
We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al., arXiv:1208.0692]. Using a group theory formalism, spectral gaps that give a ratio of convergence to a given t-design are evaluated for a different number of qubits n (up to 20) and degrees t (t=2,3,4 and 5), improving previously known results for n=2 in the case of t=2 and 3. Their values lead to a conclusion that the previously used lower bound that bounds spectral gaps values may give very little information about the real situation and in most cases, only tells that a gap is closed. We compare our results to the another lower bounding technique, again showing that its results may not be tight.
Cite
@article{arxiv.1212.2556,
title = {Local random quantum circuits are approximate polynomial-designs - numerical results},
author = {Piotr Ćwikliński and Michał Horodecki and Marek Mozrzymas and Łukasz Pankowski and Michał Studziński},
journal= {arXiv preprint arXiv:1212.2556},
year = {2013}
}
Comments
9 pages, 6 figures, 1 table, v2: reorganized version, new references added, lenghts of circuts added, submitted to JPA