Research On And Simulation Of Logic H-gate Implementation Method Based On Surface Code

Due to its powerful parallel computing ability,quantum computing has been a hot and cutting-edge technology in recent years.However,due to the vulnerability of qubits in calculation,they are prone to random errors,so quantum error correction codes are needed to protect them.As one of the types of quantum error-correcting codes,quantum surface code has become one of the most mainstream quantum error-correcting codes because of its nearest neighbor two-dimensional topology and high fault-tolerant threshold.As an important gate in the fault-tolerant general gate set,H-gate is the key to the conversion between two computing bases in quantum computing,which directly affects the implementation of quantum computing.How to design a reliable and efficient fault-tolerant logic H-gate is an urgent problem to be solved.This thesis focuses on the method of realizing logical H-gate based on quantum surface code model,and the methods of realizing logical H-gate based on boundary surface code model and bit defect surface code model.The main contents are as follows:Firstly,this thesis proposes a method to realize logical H-gate based on boundary surface code model.This method realizes the exchange of stabilizer properties through H-transform,and then ensures the correctness of codeword in logical state through data bit exchange under the criterion of less time slots and nearby exchange.Different from the traditional operation of surface code,this method completely avoids the measurement and correction of data bits,is simple to implement and reduces the complexity.In this method,the side length of the model is the same as the code distance,so that all data bits in the model are fully utilized and the resource consumption is reduced.Secondly,this thesis studies the method of realizing logical H-gate based on bit defect surface code model.Firstly,the traditional method of realizing logical H-gate based on double bit defect model,which converts the bit defect model into boundary model by measuring and correcting the data bits.In the boundary model,the exchange of stabilizer properties is realized through H-transform.Again,the boundary model is converted back to the bit defect model through the measurement and correction of data bits.Finally,the correctness of codeword in logical state is guaranteed through bit defect movement.Then this thesis proposes an improved method,that is,the logical H-gate has been realized in the boundary model,and there is no need to move the bit defect after the model is restored.The improved method is to manipulate the smaller boundary model.Compared with the traditional method that needs to move the bit defect at the end,that is,manipulate the larger bit defect model,the improved method improves the implementation efficiency.