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arXiv quant-ph/0612168quant-ph
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随机量子算法中的干扰分布

Distribution of interference in random quantum algorithms

Ludovic Arnaud, Daniel Braun

摘要:

我们研究了随机量子算法中的干扰量,使用最近衍生的定量测量干扰。为此,我们引入了两个随机电路系综,由来自全集的量子门随机序列组成,模仿量子线路表示中的量子算法。我们数值计算表明,这些系综收敛到众所周知的圆形酉系综(CUE)的一般复杂的量子算法,和Haar正交系综(HOE)的实量子算法。我们提供了精确的分析公式的平均和典型的干扰在圆形的合奏,并表明,对于足够大的数量的量子比特的随机量子算法使用的概率接近1的干扰量约等于希尔伯特空间的维数。作为一个副产品,我们提供了一种新的方法,有效地构建随机运营商从哈尔措施的CUE或HOE在高维希尔伯特空间使用通用的量子门。

英文摘要:

We study the amount of interference in random quantum algorithms using a recently derived quantitative measure of interference. To this end we introduce two random circuit ensembles composed of random sequences of quantum gates from a universal set, mimicking quantum algorithms in the quantum circuit representation. We show numerically that these ensembles converge to the well--known circular unitary ensemble (CUE) for general complex quantum algorithms, and to the Haar orthogonal ensemble (HOE) for real quantum algorithms. We provide exact analytical formulas for the average and typical interference in the circular ensembles, and show that for sufficiently large numbers of qubits a random quantum algorithm uses with probability close to one an amount of interference approximately equal to the dimension of the Hilbert space. As a by-product, we offer a new way of efficiently constructing random operators from the Haar measures of CUE or HOE in a high dimensional Hilbert space using universal sets of quantum gates.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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