Simulations of Shor’s algorithm using matrix product states
Simulations of Shor’s algorithm using matrix product states
复制标题
使用矩阵乘积状态模拟 Shor 算法
DOI：
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发表时间：
2015
影响因子：
2.5
通讯作者：
L. Hollenberg
中科院分区：
文献类型：
--
作者：
David S. Wang;C. Hill;L. Hollenberg
证明了在矩阵乘积状态形式下，Shor算法中产生的状态可以用O(max(4lr2，22l))DocumentClass[12pt]{Minimum}usepackage{amsath}usepackage{wa ysym}usepackage{amsfonts}usepackage{amsbsy}usepackage{amsbsy}usepackage{upgreek}setlong{oddsidemarin}{-69pt}例如{Document}$$O(max(4lr^2，2^{2l}))$end{Document}空间表示，其中L是要分解的位数，r是相关找序问题的顺序和解。与幅度形式主义方法相比，空间的减少是显著的，允许在具有32 GB RAM的单个处理器上运行多达42个量子比特的模拟。这种方法很容易适应分布式存储环境，我们已经模拟了一个45量子位的情况，使用8个内核和16 GB RAM在大约1小时内完成。
We show that under the matrix product state formalism the states produced in Shor’s algorithm can be represented using O(max(4lr2,22l))documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$O(max (4lr^2, 2^{2l}))$$end{document} space, where l is the number of bits in the number to factorise and r is the order and the solution to the related order-finding problem. The reduction in space compared to an amplitude formalism approach is significant, allowing simulations as large as 42 qubits to be run on a single processor with 32 GB RAM. This approach is readily adapted to a distributed memory environment, and we have simulated a 45-qubit case using 8 cores with 16 GB RAM in approximately 1 h.