Optimizations Of Quantum Walks On Photonic Chips And Their Applications

Based on the superposition,entanglement and nonlocality of quantum mechanics,quantum information processing has essential advantages in communication,metrology,computation,and simulation compared to classical technologies.There are various implementations on different platforms,including superconducting systems,photons,ion traps,and cold atom systems.Among them as the carrier of quantum information,photons have the advantages of fast transmission speed,long coherence time and many degrees of freedom.In addition to implementing photonic computing with bulk optics,integrated implementations compatible with the commercial CMOS process have emerged.Compared with the bulk optical solution,photonic chips have the advantages of small size,good stability,robust scalability and configuration flexibility,which have become the important platform of quantum information processing in recent years.Quantum walks,the quantum counterpart of classical random walks,are widely used in universal quantum computing,quantum simulation and quantum algorithms.Aiming at the on-chip implementation of quantum walks,we improve the spectral purity of quantum light sources and study the feasibility of the optimized linear optical networks.Then we design a silicon photonic chip and experimentally demonstrate some applications based on unique quantum walk models.The main achievements of the thesis include:1.We theoretically analyze the key factors and optimizations of indistinguishability between photons,and implement a high spectral purity photon source based on a microring resonator.We study the effects of spectral purity,bandwidth consistency,and center wavelength consistency on the indistinguishability of photons theoretically,which is vital for increasing the number of photons in the on-chip experiments.We design and implement a single-interferometer-coupled silicon microring,which is a reconfigurable,simple on-chip tunable spectral purity photon source.By measuring the signal-idler joint spectral intensity and the time-integrated second-order correlation of the signal photons,the purity of the single-photon spectrum is up to 94.95%.2.We propose a calibration method for the on-chip linear optical network of MachZehnder interferometers and analyze the feasibility of reconfigurable linear optical network to achieve arbitrary high-dimensional unitary evolutions.The unitary evolution of high-dimensional quantum systems can be implemented by two design schemes,the triangular linear optical network of Mach-Zehnder interferometers and the square linear optical network of Mach-Zehnder interferometers,which are very suitable for integrated implementation on photonic chips.However,random phases are inevitably introduced during chip processing.It is necessary to first calibrate the components on chip before the experiments on it.In this paper,we propose a calibration method of the Mach-Zehnder interferometer linear optical network,and analyze influence of the phase,loss,and other component errors,which confirms the feasibility of the universal linear optical network configuring the target unitary operator on the chip.This work prepares the foundations for the scaling of the on-chip linear optical network.In view of the faults encountered in the experimental process,we also propose a new idea for the fault-tolerant high-dimensional reconfigurable linear optical networks.3.We experimentally demonstrate time-reversal symmetry breaking quantum walks and their applications in quantum transport enhancements.The time-reversal symmetry breaking is a physical phenomenon in the field of condensed matter.When introduced into the study of quantum walks,it shows some quantum transport enhancements.In this paper,we experimentally demonstrate several applications of time-reversal symmetry breaking quantum walks,including the quantum switch,quantum transport speedup,and explaining the energy transfer in the photosynthetic process.4.We demonstrate the on-chip parity-time symmetry quantum walks and the quantum algorithm of centrality ranking on directed graphs.Centrality ranking is an important problem in graph theory and network analysis.There are several quantum algorithms based on quantum walks for the centrality ranking problem.Parity-time symmetry solves the problem that the algorithm based on continuous-time quantum walks is not suitable for directed graphs.We implement the quantum centrality ranking of 4-node directed graph and 7-node interdependent graph on the reconfigurable silicon photonic chip,and achieve the quantum centrality ranking of 16-node and 64-node directed graphs through multiphoton experiments.