Some Progress On Quantum Error Correction For Discrete And Continuous Error Models

In the era of rapid development of technology,the increasing demands for computing capability have gained significant attention with the explosive growth of information.The emergence of quantum computing provides great potentiality compared to classical computing.In the realization of quantum computing,it is essential to rely on accurate and reliable quantum information processing.Although the theory of quantum information processing has been put forward since 1970 s,there still remains numerous problems to construct a universal quantum computer.One of the crucial issue is how to protect information from noise interference such that the error rate during quantum information processing can be limited within an acceptable bound.The technique to address this issue is quantum error correction.The research on quantum error correction technology includes the formal definition of noise as an error model and the design and implementation of quantum error correction approaches.Discrete error models and continuous error models are two kinds of definitions of noise.The former assumes noise occurs independently and can be discretized into a set of basic errors,where a specific error model can be described using a tool named quantum operations.The latter describes that noise is continuous in time by using differential equations.As researchers have proposed abundant effective quantum error correction approaches up to now,comparative analysis of these approaches is one of the ways to further study this field.By reviewing and exploring some progress of quantum error correction approaches for discrete and continuous error models,the main contributions of this dissertation are outlined as follows,· First,quantum error correction approaches are categorized into three types according to the different error models.For the basic error set,quantum codes can correct arbitrary errors by first detecting a set of discrete errors and then correcting them.For quantum operations,quantum error correction aims at finding a non-universal approach with better error correction performance for a specific error model.For continuous error models,continuous-time quantum error correction describes continuous error correction procedures by using differential equations.· Second,each category of quantum error correction approaches is reviewed and analyzed.Some challenging directions are proposed and discussed for future research.Furthermore,the perturbed error models are proposed to explore the effect of the perturbation based on the existing error models during quantum information processing.Two possible definitions of the perturbed error models are presented according to the causes of the perturbation.· Third,examples of different quantum error correction approaches are constructed and implemented.Experiments are simulated on the IBM Q Experience,a cloud-based quan-tum platform.The error correction performance of different quantum error correction approaches are embodied by the accuracy of information affected by noise.The feasibility and effectiveness of quantum error correction approaches are validated through experimental results.To sum up,in terms of classification,this dissertation provides a new perspective using the different error models as the starting point.It categorizes quantum error correction approaches into three types: quantum codes,quantum error correction approaches for quantum operations and continuous-time quantum error correction.In terms of content,this dissertation analyzes the recent progress of quantum error correction more comprehensively and proposes possible future directions.In terms of experiment,the error correction procedures of various quantum error correction approaches are simulated for different error models.