基于矩阵乘积态的有限纠缠量子傅里叶变换模拟

doi:10.11896/jsjkx.230300215

计算机科学 ›› 2024, Vol. 51 ›› Issue (9): 80-86.doi: 10.11896/jsjkx.230300215

基于矩阵乘积态的有限纠缠量子傅里叶变换模拟

刘晓楠^1,2, 廉德萌^2,3, 杜帅岐^2,3, 刘正煜^2,3

1 数学工程与先进计算国家重点实验室(信息工程大学) 郑州 450000
2 国家超级计算郑州中心郑州 450000
3 郑州大学计算机与人工智能学院郑州 450000

收稿日期:2023-03-29 修回日期:2023-07-28 出版日期:2024-09-15 发布日期:2024-09-10
通讯作者: 廉德萌(dm.lian@outlook.com)
作者简介:(prof.liu.xn@foxmail.com)
基金资助:
国家自然科学基金(61972413,61701539)

Simulation of Limited Entangled Quantum Fourier Transform Based on Matrix Product State

LIU Xiaonan^1,2, LIAN Demeng^2,3, DU Shuaiqi^2,3, LIU Zhengyu^2,3

1 State Key Laboratory of Mathematical Engineering and Advanced Computing(Information Engineering University),Zhengzhou 450000,China
2 National Supercomputing Center in Zhengzhou,Zhengzhou 450000,China
3 School of Computer and Artificial Intelligence,Zhengzhou University,Zhengzhou 450000,China

Received:2023-03-29 Revised:2023-07-28 Online:2024-09-15 Published:2024-09-10
About author:LIU Xiaonan,born in 1977,Ph.D,associate professor,master's supervisor.His main research interests include quantum algorithm and high-perfor-mance parallel computation.
LIAN Demeng,born in 1999,postgra-duate.His main research interests include quantum algorithm and high-performance computing.
Supported by:
National Natural Science Foundation of China(61972413,61701539).

摘要/Abstract

摘要： 与经典计算不同,在量子计算中量子比特可以处于叠加态,多个量子比特之间还可以形成纠缠态。表示n个量子比特组成的量子态需要存储2ⁿ个振幅,这种指数级的存储开销使得大规模的量子模拟难以进行。然而当量子态的纠缠程度有限时,使用矩阵乘积态表示量子态仅需要线性的空间复杂度,可以扩大模拟的规模。使用HIP-Clang语言,基于CPU+DCU的异构编程模型,使用矩阵乘积态表示量子态,对量子傅里叶变换进行模拟。结合矩阵乘积态的特点,对量子傅里叶变换线路进行分析,减少模拟实现时不必要的张量缩并运算与正交化构建。对模拟过程中的张量缩并进行分析,使用TTGT算法完成张量缩并运算,同时利用DCU的并行处理能力来提高效率。对模拟结果进行分析,分别通过振幅误差与半经典Draper量子加法器的结果验证了模拟的正确性。对模拟规模进行分析,当量子态的纠缠熵最大时,使用16GB的内存空间最多只能模拟24位的量子态,而当量子态内部纠缠程度较低时,可以对上百位的量子态进行量子傅里叶变换模拟。

关键词: 量子模拟, 量子傅里叶变换, 矩阵乘积态, 异构计算, DCU, HIP-Clang

Abstract: Unlike classical computing,qubits in quantum computing can be in the superposition state and entangled state can be formed between multiple qubits.Representing a quantum state composed of n qubits requires storing 2 to the n^th power amplitudes.The exponential memory cost makes large-scale quantum simulation difficult.Using the HIP-Clang language,based on the heterogeneous programming model of CPU+DCU and representing the quantum state with the matrix product state,quantum Fourier transform is simulated.By combining the characteristics of the matrix product state and analyzing the quantum Fourier transform circuit,unnecessary tensor contraction operations and orthogonalization construction are reduced during simulation implementation.Tensor contraction during simulation is analyzed and the TTGT algorithm is used to complete tensor contraction operations while utilizing DCU's parallel processing capabilities to improve efficiency.Simulation results are analyzed and the correctness of the simulation is verified through amplitude error and semi-classical Draper quantum adder results.Analyzing simulation scale,when the entanglement entropy of the quantum state is maximum,using 16GB of memory can simulate up to 24bit quantum states at most,while when the entanglement of the quantum state is limited,it can simulate hundreds of qubits of quantum Fourier transform.

Key words: Quantum simulation, Quantum Fourier transform, Matrix product state, Heterogeneous computing, DCU, HIP-Clang

中图分类号:

TP385

刘晓楠, 廉德萌, 杜帅岐, 刘正煜. 基于矩阵乘积态的有限纠缠量子傅里叶变换模拟[J]. 计算机科学, 2024, 51(9): 80-86. https://doi.org/10.11896/jsjkx.230300215

LIU Xiaonan, LIAN Demeng, DU Shuaiqi, LIU Zhengyu. Simulation of Limited Entangled Quantum Fourier Transform Based on Matrix Product State[J]. Computer Science, 2024, 51(9): 80-86. https://doi.org/10.11896/jsjkx.230300215

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基于矩阵乘积态的有限纠缠量子傅里叶变换模拟

Simulation of Limited Entangled Quantum Fourier Transform Based on Matrix Product State

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