Prime factorization using magnonic holographic devices
Prime factorization using magnonic holographic devices
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DOI：
10.1063/1.4962740
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发表时间：
2016-09-28
影响因子：
3.2
通讯作者：
Khitun, Alexander
中科院分区：
文献类型：
--
作者：
Khivintsev, Yuri;Ranjbar, Mojtaba;Khitun, Alexander
确定给定数N的素因子对于传统数字计算机来说是需要超多项式时间的问题。Shor为量子计算机发明了一种多项式时间算法。在本文中，我们提出了实验数据，证明素数分解使用自旋波干涉，但没有量子纠缠。素因子分解包括三个主要步骤。首先，通用型计算机计算数列m（k）mod（N），其中N是要因式分解的数，m是随机选择的正整数，并且k = 1，2，3，4，5，6.接下来，通过利用自旋波干涉来确定所计算的序列r的周期。最后，通用型计算机基于所获得的r来确定素数。在六端Y_3Fe_2（FeO_4）（3）器件上进行了周期发现实验。我们选择了15号进行测试，并使用一系列测量来确定它的素数。所获得的微米级原型的实验数据旨在证明使用自旋波器件解决复杂计算问题的好处。可扩展性是这种基于波的器件固有的主要优势之一，它可以为纳米尺寸的逻辑电路提供一条途径。我们讨论了这种方法的物理和技术限制，它定义了N的最大尺寸和计算速度。虽然这种经典方法在效率上无法与量子算法竞争，但磁振子全息装置可以用作互补逻辑单元，旨在加速经典计算机的素因子分解。由AIP出版社出版。
Determining the prime factors of a given number N is a problem that requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by Shor for quantum computers. In this paper, we present experimental data that demonstrate prime factorization using spin-wave interference but without quantum entanglement. Prime factorization includes three major steps. First, a general-type computer calculates the sequence of numbers m(k)mod(N), where N is the number to be factorized, m is a randomly chosen positive integer, and k = 1, 2, 3, 4, 5, 6 ... Next, the period of the calculated sequence r is determined by exploiting spin-wave interference. Finally, the general-type computer determines the primes based on the obtained r. The experiment for period finding was conducted on a six-terminal Y3Fe2(FeO4)(3) device. We chose number 15 for testing and determined its primes using a sequence of measurements. The obtained experimental data for a micrometer-sized prototype aimed to demonstrate the benefits of using spin-wave devices to solve complex computational problems. Scalability is one of the major strengths inherent in this type of wave-based device, which may provide a route to nanometer-sized logic circuits. We discuss the physical and technological limitations of this approach, which define the maximum size of N and the computational speed. Although this classical approach cannot compete with the quantum algorithm in terms of efficiency, magnonic holographic devices can potentially be used as complementary logic units aimed at speeding up prime factorization for classical computers. Published by AIP Publishing.