On universal and fault-tolerant quantum computing: a novel basis and a new constructive proof of universality for Shor's basis

P. Boykin, T. Mor, M. Pulver, V. Roychowdhury, F. Vatan
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引用次数: 101

Abstract

A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and /spl sigma//sub z//sup 1/4 /) and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of /spl pi/) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by P.W. Shor (1996) and A.Y. Kitaev (1997).
论量子计算的普适性和容错性:肖尔基的一种新的普适性基础和新的建设性证明
描述了一种新的通用的、容错的量子计算基(门组)。这样的集合是在真实的噪声环境中进行量子计算所必需的。新基由两个单量子比特门(Hadamard和/spl sigma//sub z//sup 1/4 /)和一个双量子比特门(Controlled-NOT)组成。由于由Controlled-NOT门和Hadamard门组成的集合不是普遍的,新的基通过只包括一个额外的基本(在这个意义上,它不包括/spl pi/的非理性倍数的角)单量子位门来实现普遍性,因此,它可能是人们可以构建的最简单的普遍基。我们还为P.W. Shor(1996)和A.Y. Kitaev(1997)提出的唯一已知的另一类通用性和容错基提供了另一种普遍性证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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