Application Of Quantum Error Correction Coding In High Efficiency Quantum Repeaters

Benefiting from the rapid development of quantum information technology,quantum communication is widely used in cryptography,quantum metro networks,and large-scale distributed quantum computing.However,the photonic states used for transmitting information in quantum communication will be greatly attenuated as the transmission distance increases,which results in short distance of quantum communication and low transmission rate.In order to solve such problems,many schemes with quantum repeaters have been proposed to increase the communication distance.Initially,quantum repeaters were based on heralded entanglement purification and required two-way classical communication.Then,quantum repeaters based on one-way classical communication can be achieved using a teleportation error correction protocol.Now,quantum repeaters can theoretically implement the communication distance and transmission rate of classical optical communication.Because quantum information has the characteristics of being difficult to store and requiring a large number of auxiliary resources during generation,there are still many problems to be solved in the design and implementation of quantum repeaters.At present,most of the research focuses on improving the precision of quantum state manipulation to improve the physical realization mechanism of quantum repeaters.Few solutions are proposed realizing long-range efficient quantum repeaters from the perspective of error correction design with quantum error-correcting codes.Therefore,combining the theory of quantum error-correcting code and the efficient quantum repeater communication model,this thesis completes specific theoretical research and innovative work from the following aspects:Firstly,the existing three types of quantum repeater models are analyzed in detail and compared in performance.According to the results,the one-way all-optical Bell Measurement quantum repeater communication scheme with quantum error-correcting codes is selected as the theoretical model of this thesis.Based on the model,the design requirements of quantum error-correcting codes for the quantum teleportation-based error-correction protocol are proposed.Secondly,up to now,the quantum error-correcting codes used in the teleportation-based error correction protocol are mostly quantum parity codes,which have the defects of large physical resource overhead and low Bell Measurement fault tolerance.In order to improve the above performance,according to Calderbank-Shor-Steane(CSS)Codes construction method,this thesis designs quantum Reed-Muller codes which can be decomposed by Bell basis vectors.Then this thesis analyzes quantum Reed-Muller codes' basic parameters.In addition,this thesis proves that this kind of quantum error-correcting codes can be applied to the quantum repeater model by constructing a decomposition example of quantum Reed-Muller code on Bell bases.Thirdly,in order to analyze the error correction and fault tolerance of quantum Reed-Muller codes in the quantum repeater model,combined with the MAP decoding algorithm,this thesis proposes the upper limit of fault tolerance of Bell measurement that can be achieved by quantum Reed-Muller codes in error photon detectors.Finally,constructing the coding examples of quantum Reed-Muller codes and quantum parity codes,and comparing their performance,the results show that this high-efficiency quantum repeater with quantum error-correcting codes has better performance.