Comment on "Random Quantum Circuits are Approximate 2-designs" by A.W. Harrow and R.A. Low (Commun. Math. Phys. 291, 257-302 (2009))

被引：33

作者：

Diniz, Igor Tuche ^{[1
,2
]}

Jonathan, Daniel ^{[1
]}

机构：

[1] Univ Fed Fluminense, Inst Fis, BR-24020 Niteroi, RJ, Brazil

[2] CNRS, Inst Neel, Grenoble, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2011年 / 304卷 / 01期

关键词：

Markov Chain; Random Permutation; Quantum Circuit; Versus Distance; Reversible Markov Chain;

D O I：

10.1007/s00220-011-1217-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In [A.W. Harrow and R.A. Low, Commun. Math. Phys. 291(1):257-302 (2009)], it was shown that a quantum circuit composed of random 2-qubit gates converges to an approximate quantum 2-design in polynomial time. We point out and correct a flaw in one of the paper's main arguments. Our alternative argument highlights the role played by transpositions induced by the random gates in achieving convergence.

引用

页码：281 / 293

页数：13

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