Grover algorithm circuit optimization and noise analysis on integer factorization

The classical computer is restricted by Moore's law and other factors into the development bottleneck, quantum computer by virtue of its natural acceleration advantage into the field of vision. Quantum computing can achieve the acceleration effect compared with classical computing in many fields. In the field of integer decomposition, Shor algorithm can be solved in polynomial time, which breaks the security of RSA public key cryptosystem. However, the quantum bits (logn + 2, where n is the integer to be decomposed) required by Shor algorithm are difficult to be realized on today's quantum computers. Therefore, the hybrid quantum algorithm model of "classical + quantum (Grover algorithm)" is tried to realize the decomposition of large integers. In this paper, based on the previous hybrid quantum algorithm model, considering that the continuous accumulation of errors in the circuit of the quantum algorithm will lead to the failure of the algorithm as the depth increases, part of the circuit of the quantum algorithm oracle is optimized to reduce the consumption of the depth, quantum gate and quantum bit in the circuit of the quantum algorithm, so as to make it easier to run on the actual quantum computer. By running the optimized quantum circuit on the back end of the simulator of IBM Q quantum cloud platform, and trying to add thermal relaxation and depolarization noises to the circuit, the influence of different noises on the circuit under different iterations was explored.