Experimental Research Of Quantum Walks

Unlike the classical world,quantum mechanics,as a discipline that explores the field of quantum science,since its inception,has brought strange phenomena in a counterintuitive manner.The process of an isolated system evolution can be represented by a unitary operator under quantum mechanics.Since the unitary operator is reversible,it inspires us to implement reversible calculations through quantum systems.Quantum walk is one of the important branches of quantum physics and quantum information.It mainly deals with frontier issues such as quantum algorithms and quantum simulation.Quantum walk possesses better than classical characteristics,which offers a quadratic increase in the diffusion speed of quantum states.At present quantum walk has been proved to be able to implement quantum algorithms,quantum communication,quantum measurement,quantum computation and quantum simulation,etc.,thereby quantum walk can realize all steps of quantum information processing.Quantum walk draws people's attention,thus the theoretical and experimental researches of quantum walk become more and more important.In this thesis for the Doctorate,we focus on the experimental implementation of quantum walk.More specifically,we propose a scheme for realizing the quantum walk in the phase space in a specific physical system,introduce the optical components and the commonly techniques required for the experiment to realize quantum walk.Besides,we experimental realize the quantum walk revival with a time-dependent coin,implement a quantum walk on a circle with single photons.At last,we use a one-dimensional photonic quantum walk to realize the singlequbit positive-operator-valued measurement.The main contents are as follows:1.Based on the superconducting resonator-assisted double quantum dots,we propose a scheme for realizing a quantum walk in phase space.In the program,we introduce how each element of the quantum walk is implemented in the actual system in detail.In the specific physical system,we observe the transformation from quantum walk to classical random walk by adjusting the intensity of the applied driven field.2.The principle and application of optical components commonly used in optical systems.We briefly analyze the spontaneous parametric down conversion in nonlinear crystals and introduce the preparation of single photon sources and entanglement photon sources.Through the design scheme by optical components,we describe the methods of preparation,unitary operation and quantum measurement of quantum states.3.Demonstration a quantum walk with time-dependent coin bias.With this technique we observe the propagation and recovery of information in quantum walk.The theoretical scheme and the experiment show the quantum state which encoded information can be restored to the initial state after any evolutionary time.Our work fundamentally solves the problem of whether the information can be restored and how it is restored in quantum walk and provides exact evidence that quantum walk can be applied to quantum communication.4.Experimental implementation of a quantum walk on a circle with single photons.We use two beam displacers and some half-wave plates to achieve the conditional shift operator for an N-node circle,which realizes clockwise-cycling and counterclockwise-cycling walks.Compared with the quantum walk on the circle realized by other systems in the phase space,we realize the quantum walk on the circle in the real position space.5.Realization of single-qubit positive-operator-valued measurement via a one-dimensional photonic quantum walk.In the experiment,we construct the positive-operator-valued measurement via a quantum walk,which is used to implement an unambiguous state discrimination of two single-qubit states.The process of constructing the measurement by quantum walk is programmable.Through this procedural scheme,we use a 5-step quantum walk to experimentally construct a symmetric informationally complete positive-operator-valued measurement.In short,the subject will help us to develop more applications of quantum walk.Quantum walk will be a universal method applied to quantum computing,quantum simulation,quantum measurement,and quantum communication.