Research On The Rate Scalable Construction Of Quantum LDPC Codes Based On Balanced Incomplete Block Design

Quantum computing has shown far greater ability than classical computing on issues such as large prime number decomposition,which has attracted great attention from researchers and has become a current research hotspot.However,due to the presence of noise,quantum computing cannot perform an effective calculation process without error control.As an important means to combat quantum noise,the research of quantum error correction coding technology becomes crucial.At present,quantum error correction coding has become an important research direction in the field of quantum information,especially in the field of quantum computing.Low-density parity-check code(LDPC)is a widely used classic error correction coding scheme,which has the characteristics of simple coding and decoding algorithms and performance close to Shannon limit.With the development of quantum coding technology,transplanting classic error correction codes with excellent performance into the field of quantum error correction coding is called a common technique for constructing quantum error correction codes with excellent performance.In this thesis,based on the classic LDPC code,combined with the current quantum LDPC code encoding technology,we will do the following work:First,this thesis systematically analyzes several current methods for constructing quantum LDPC codes based on classic LDPC codes,and analyzes and discusses the structure of the check matrix in detail,including dual-containing CSS code,entanglement-assisted code and non-dual-containing CSS code.On this basis,this paper uses Balanced Incomplete Block Design(BIBD)to construct a classic LDPC code example that can be transformed into a quantum error correction code,and constructs the corresponding quantum LDPC code according to the coding principle of quantum error correction coding And,iterative decoding algorithm based on confidence propagation is used to simulate the performance of the constructed quantum LDPC code,and its advantages and disadvantages are analyzed in detail.Second,we provide a rate scalable way to construct non-homogeneous quantum LDPC codes of CSS type based on Balanced Incomplete Block Design(BIBD).By fixing the so-called expanding coefficienta,one can obtain a new quantum LDPC code with rate1-2a/ m from the one that with rate 1-2 / m(mother code).Further,our method provide a flexible way to construct and switch quantum codes with good trade-offs between rates and error-correcting performances,adapting to various application scenarios.Moreover,as the expanded codes and the mother codes share same non-identity submatrices,no hardware overhead will be increased along with the codes switch.