Theoretical Study Of Coherent Ising Machine With Squeezed Feedback System

With the passage of time,more and more non-deterministic polynomial-hard(NPhard)problems that require huge amount of computation are found in daily production,including artificial intelligence,transportation,drug research,very large scale integration design and other fields.However,traditional Von Neumann computers can not find precise solutions to these problems in an acceptable time.Coherent Ising Machine(CIM)based degenerate optical parametric oscillator(DOPO)is a non-Von Neumann calculation scheme using the photonic technology.The ground-state-search problem of the Ising model can be solved by using a degenerate optical parametric oscillator network.CIM can be used as a solver for such problems based on the reducibility of NP-hard problems.However,as a new photonic computing technology,there are still many scientific problems waiting to be solved.In this paper,a squeezed feedback coherent Ising Machine(S-CIM)with better computational performance is proposed by using the squeezed vacuum injection and phase sensitive amplifier(PSA).Afterwards,the self-feedback iterative coherent Ising Machine with better stability is obtained on the basis of the S-CIM.The specific work is as follows:1.The calculation model of S-CIM is formulated and analyzed in detail,then the truncated Wigner representation and the Ito rules will be used to obtain the c-number stochastic differential equations of the S-CIM containing N-coupled DOPOs.The quantum inseparability and quantum fluctuation in the fiber ring cavity with 2-coupled DOPO pulses are investigated under different pumping schedule.In addition,the spin configuration corresponding to the coupled DOPO pulse is used to divide the optimization process of S-CIM into four stages accurately,which is compared with the CIM.2.The computation experiments of S-CIM are performed by using the small-scale(vertex number N = 4)and the large-scale(vertex number N = 800-20000)Max-Cut problems respectively.The large-scale instances with 0.02%-6% edge density and random geometry are obtained by using the G-set graphs which are randomly constructed by the machine-independent graph generator.The computation performance of S-CIM system is evaluated.Numerical results demonstrate that in the optimal result of large-scale instances,S-CIM increases the approximate ratio of the normalized output by 2.27% and significantly reduces the computational time by 75.12%.3.On the basis of S-CIM,a coherent Ising machine scheme with self-feedback iterative system is proposed by using a Mach-Zehnder modulator instead of the ring fiber cavity.Because it no longer relies on the PSA in the long ring cavity,the new system is less affected by the environment,the global stability is further enhanced.The computation experiments on M?bius Ladder graph with N = 16 show that the computation success rate of the coherent Ising machine based on a self-feedback iterative system is 9.68%-11.36% better than that of the S-CIM.