Multiparticle quantum walk–based error correction algorithm with two-lattice Bose–Hubbard model

Abstract

When the evolution of discrete time quantum walk is carried out for particles, the ramble state is prone to error due to the influence of system noise. A multiparticle quantum walk error correction algorithm based on the two-lattice Bose–Hubbard model is proposed in this study. First, two point Bose–Hubbard models are constructed according to the local Euclidean generator, and it is proved that the two elements in the model can be replaced arbitrarily. Second, the relationship between the transition intensity and entanglement degree of the particles in the model is obtained by using the Bethe hypothesis method. Third, the position of the quantum lattice is coded and the quantum state exchange gate is constructed. Finally, the state replacement of quantum walk on the lattice point is carried out by switching the walker to the lattice point of quantum error correction code, and the replacement is carried out again. The entanglement of quantum particles in the double-lattice Bose–Hubbard model is simulated numerically. When the ratio of the interaction between particles and the transition intensity of particles is close to 0, the entanglement operation of quantum particles in the model can be realized by using this algorithm. According to the properties of the Bose–Hubbard model, quantum walking error correction can be realized after particle entanglement. This study introduces the popular restnet network as a training model, which increases the decoding speed of the error correction circuit by about 33%. More importantly, the lower threshold limit of the convolutional neural network (CNN) decoder is increased from 0.0058 under the traditional minimum weight perfect matching (MWPM) to 0.0085, which realizes the stable progress of quantum walk with high fault tolerance rate.