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Quantum walks are the quantum corresponding version of classical random walks, providing polynomial and even exponential acceleration for some classical difficult problems. In recent years, there have been numerous researches on quantum walks, among which the hitting probabilities problem is another crucial problem. In 2021, Guan et al. have proposed an HHL-based algorithm to calculate the hitting probabilities of quantum walks, which can effectively transform the original problem into an inverse matrix problem, then achieve an acceleration effect on the corresponding classical algorithm under some specific conditions. However, we propose a new algorithm consisting of an improved quantum matrix inversion algorithm with complexity O κ 2 log 1. 5 (κ / ε) p o l y log (n) , where κ is the condition number of the matrix, n + 1 is the number of positions of the one-dimensional quantum walks, and ε is the expected accuracy of the output state. Compared to the HHL-based algorithm, our improved algorithm achieves an exponential improvement in the dependence on accuracy. [ABSTRACT FROM AUTHOR]

A delegated quantum computation protocol that includes three servers Bob1, Bob2 and Bob3 and a client Alice is proposed, which is with four-particle χ -type entangled states that have a good property is the other two particles can collapse into a certain Bell state if the first two particles are measured. Alice only needs to be capable of getting access to quantum channels and perform Pauli operation and also has a memory of two graph states brickwork state and blind topological entangled state, but she does not need to prepare any quantum state in this paper. Our protocol is without a trusted center which will save funds, sources and quantum devices, and can verify the correctness of measurement outcomes by quantum entanglement of | χ ij 〉 3124 . At last, we also give blind analysis and proof rigorously. [ABSTRACT FROM AUTHOR]