Research And Simulation Of High-performance Fault-tolerant System Based On Quantum Error-correcting Codes

This paper explores the problem of exploring new quantum error-correcting decoding schemes with the rapid development of the quantum information industry and the continuous improvement of the manufacturing process and production scale of quantum processors and quantum algorithm chips.Highlighting the advantages of quantum error correction at low cost to reduce hardware losses has become an important direction for both the industry and academia.The efficient error-correcting encoding and decoding in the NISQ(Noisy Intermediate-Scale Quantum)era has become a key issue in the field of quantum computing.This paper proposes a new scalable quantum error-correcting scheme that uses physical qubits to achieve orders of magnitude of scaling,and constructs decoders including a neural network decoder with good expansion,a reinforcement learning decoder with fast path optimization,and a generative adversarial network decoder with high fidelity.Finally,a machine learning-based quantum error-correcting system with a decoding rate of up to 10bit/s and low-threshold fault tolerance of over 18% is generated and simulation-verified,which has important guiding significance.The main research content can be summarized as the exploration and resolution of quantum error-correction methods,which has a positive promoting effect on the future development of quantum information and quantum computing.(1)For medium-scale quantum computing in the environment of noise information protection and data transmission problems,the use of quantum error correction code rotation dimensional expansion technology,reduce the complexity of the detection of stabilizers in quantum error correction code,design scalable topological error correction code dimensional leap scheme,while using Qiskit source library to load data,maximum likelihood estimation algorithm and Dijkstra algorithm to obtain coding matching results,enhance the quantum line.The design contains a variety of quantum gate extension designs,which enable the physical quantum bits to reach the order of magnitude and decoding rate of not less than 10bit/s.The theory demonstrates the specific sparse matrix coding method to achieve the results of degree reduction in information acquisition of multi-dimensional quantum error correction codes under the auxiliary quantum bits of the topological quantum stabilizer,and the fidelity of the error tolerant decoder reaches above 98%.(2)For the quantum computing process of quantum bit information loss due to interference,the use of machine learning chunking algorithm model includes analysis of the internal construction of topological quantum error correction codes,including the operator correlation of the bits themselves and the spatial correlation between different bits to study the mechanism and characteristics of the generation of these vertex operators and lattice operators,reduce the decoder in the process of restoring quantum bit information by the noise containing interference,so that the Quantum decoder iteration depth and output strength in the search for decoding algorithms can be transformed into a variety of complex noise error model by class decoding the optimal noise model reduced to less than 10% of the high-performance decoder,to achieve coding lines effectively restore the topological error correction code coding information to more than 98%,the scale of simulated random electronic lines to reach the physical quantum bit exponential simulation.(3)To address the problem of effective verification of topological quantum error correction codes that are difficult to transmit in fault-tolerant systems at low thresholds.Considering the mature design architectures of convolutional neural networks,dueling networks and long and short-term memory networks,this project proposes to use a composite structure of three decoders to build an easy-to-implement,500-layer deep Rest Net network iteration depth and single-quantum 7-bit quantum variational algorithm on a high-rate network architecture compatible with multidimensional error correction codes.The proposed mapping of error correction lines and quantum Grover algorithms to decoders is completed in conjunction with a specific architecture for scalable topological error correction codes,and noise reduction of quantum error correction lines at low thresholds is performed to accommodate the low noise requirements of specific error correction algorithms using a 10 d B noise limit,leading to the design of stabilisers with decoding rates up to 10bit/s.On this basis,the problem of efficient verification of high-efficiency information under fault-tolerant systems is completed.