由量子神经网络启发的改进Shor算法
首发时间:2020-03-04
摘要:Shor算法是著名的量子大数因子分解算法,对经典密码带来了严峻挑战。分析表明在量子计算机上执行Shor算法需要应用到多项式级别的基本量子门,而且实际实现Shor算法需要较深的量子线路,结合含有误差的量子门以及有限的相干时间的物理硬件,因此算法的输出结果保真度较低。基于Shor算法存在的上述问题,我们将利用量子神经网络模型实现从模幂酉操作的特征基映射到计算基的过程,进而降低Shor算法所需的量子线路深度。最后我们在HiQ量子云平台上对Shor算法和改进算法进行模拟,结果表明我们提出改进方案比原Shor算法效率更高。
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The improved Shor algorithm based on the quantum neural network model
Abstract:The Shor algorithm is a well-known quantum algorithm that concentrates on decomposing the large-scale integer, which takes serious challenges to the classical cryptography system. According to the resource analysis, implementing the Shor algorithm takes polynomial scale of quantum gates, which suggests that the Shor algorithm is supported by a deep quantum circuit. Considering the bounded-error quantum gate as well as the physic devices with limited coherence time, the output value of the Shor algorithm has poor fidelity. Based on these problems, we in this paper utilize the quantum neural network model to construct the map from the eigen-vector of the modular exponentiation operator to the computational basis, therefore we sharply reduce the circuit depth of the quantum algorithm. Finally, we test the improved Shor algorithm on the HiQ platform, and the simulation results illustrate our schema outperforms the original Shor algorithm.
Keywords: Quantum physics Quantum computing Quantum algorithm
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