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2^(n)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16 GB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。
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 16 GB of memory can simulate up to 24 bit quantum states at most,while when the entanglement of the quantum state is limited,it can simulate hundreds of qubits of quantum Fourier transform.
作者
刘晓楠
廉德萌
杜帅岐
刘正煜
LIU Xiaonan;LIAN Demeng;DU Shuaiqi;LIU Zhengyu(State Key Laboratory of Mathematical Engineering and Advanced Computing(Information Engineering University),Zhengzhou 450000,China;National Supercomputing Center in Zhengzhou,Zhengzhou 450000,China;School of Computer and Artificial Intelligence,Zhengzhou University,Zhengzhou 450000,China)
出处
《计算机科学》
CSCD
北大核心
2024年第9期80-86,共7页
Computer Science
基金
国家自然科学基金(61972413,61701539)。
