Experimental Research On Grover’s Quantum Search Algorithm

Quantum computing,utilizing quantum mechanics principles such as entanglement and superposition,is a popular research field worldwide due to its natural parallel computing capabilities that differ from classical physics.Its main goal is to break the inevitable development limit of traditional silicon chip electronic computers and achieve data processing capabilities beyond classical computers.Grover’s algorithm,as one of the important algorithms in the field of quantum computing,can exponentially accelerate the enumeration search problem of classical system and has greatly promoted the development of quantum computing.However,at present,Grover’s search experiments in databases with element numbers below 16 have only been demonstrated in some quantum systems.In practical applications,the Grover’s algorithm can be used to solve a variety of search problems,such as word search,pattern recognition,and password cracking.Additionally,in fields such as machine learning and image processing,the Grover’s algorithm also has broad application prospects.It is expected that with the continuous development of quantum computing technology and algorithms,the application prospects of the Grover’s algorithm will become even broader.In summary,the emergence of quantum computing and the Grover’s algorithm will bring disruptive changes to traditional computer models and algorithms,and provide more extensive and in-depth development space for scientific research and industrial production in human society.With the continuous development of quantum computing technology,many optimization and experimental studies have been carried out for the Grover’s algorithm.Recently,the optimization of the Grover’s search algorithm,such as gradient descent and machine learning techniques,has been of great significance for improving the efficiency of the algorithm and reducing errors.Furthermore,researchers have attempted to use different types of quantum hardware,such as superconducting qubits and ion traps,to implement the Grover’s search algorithm,providing strong support and impetus for the development of quantum computing.However,currently,researchers have only demonstrated Grover’s search experiments in databases with up to 16 elements using some quantum systems.In this thesis,we mainly propose an efficient quantum search scheme based on the optimized Grover’s algorithm and a new non-orthogonal state encoding method.Then,we experimentally verify the search scheme in a linear optical system and demonstrate the exploration of the target element in a database of 40 elements.The experimental results and theory are highly consistent,with all experimental fidelity over 99.7%.Finally,we theoretically analyze and experimentally verify the upper limit of the number of elements that can be encoded in a single quantum bit,and provide a formula for the relationship between the number of elements and experimental accuracy and measurement times.The search scheme proposed in this thesis mainly has the following features:(i)The theoretical search probability of the target element reaches 100%.(ii)A single quantum bit can encode a large number of elements,greatly saving experimental resources.(iii)The experimental implementation and operation are very simple,requiring only one search step to complete the search.(iv)It has strong universality and can be applied to most quantum systems,such as cavity QED systems.