Research On Encoding And Error Correction Scheme Of Quantum Surface Code

The superposition property of quantum states enables quantum computers to have powerful parallel computing capabilities.However,the quantum superposition state is very fragile and will inevitably interact with environmental noise to cause decoherence,which is a major obstacle to the practical application of quantum computers.Until the advent of quantum error-correcting codes,this problem is finally expected to be overcome.Among many quantum error correction code schemes,the quantum surface code has a special topology and a high error rate threshold,which makes it one of the error correction code schemes for realizing large-scale reliable quantum computing.Quantum surface codes encode a few logical qubits into multiple physical qubits,thereby protecting quantum information from environmental noise.The realization of the quantum surface code coding circuit mainly includes the method based on syndrome measurement and the method based on the realization of stabilizer.This paper mainly studies the method based on syndrome measurement.Using the error syndrome extraction circuit of the surface code,the syndromes of the surface code in different error states can be obtained,and on this basis,the quantum state can be corrected according to the error syndromes,and the logical qubit of the surface code can be obtained correctly.However,when the scale of the surface code is very large,the number of error syndromes increases exponentially,and the error correction for a single error syndrome becomes very complicated.Therefore,it is necessary to study a simple error syndrome correction method to complete the encoding of the surface code.After the logical bits of the surface code are obtained by encoding,the influence of environmental noise will cause errors in the logical bits.At this time,it is necessary to perform active error correction on the logical bits of the surface code.The existing surface code error correction schemes are based on the minimum weight perfect matching algorithm.However,due to the special topology of the surface code,errors at different positions may cause the same error syndromes.Ignoring this phenomenon will reduce the accuracy of error correction.,so it is necessary to optimize the existing surface code error correction scheme.Aiming at the above problems,this paper studies the coding and error correction scheme of surface codes.First,the basic knowledge of quantum computing is introduced,including the basic theory of qubit gates and quantum error correction codes.Then,the coding scheme of surface codes is studied.On this basis,combined with a series of theories such as initializing physical bits,selecting corrective operations,and selecting logical operations,a surface code encoding scheme based on syndrome extraction and correction is proposed.This coding scheme corresponds the correction operation to the stabilizer of the surface code one-to-one.When a certain stabilizer is not satisfied,the correction operation is controlled and superimposed by its measurement result,which skillfully corrects all error syndromes and greatly increases the complexity of the coding circuit reduce.Next,the error correction scheme of the surface code is studied.By introducing the plane coordinate system and the boundary node,the error correction model is established on the two-dimensional plane of the surface code.This error correction model classifies and identifies X-type errors and Z-type errors,matches different types of random errors,outputs the most likely error chain,and accurately locates and corrects the data bits that generate errors.The topological property of the surface code determines that the same error syndromes may correspond to many different error chains.This scheme combines this property to optimize the weight formula of error chains,so that the maximum possible error chain output by the error correction model is no longer just the shortest error chain,but the most likely error chain after considering the number of equivalent error chains.This improvement further improves the accuracy of this error correction scheme.