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Secure multiparty quantum summation, as a critical part of secure multiparty quantum computation, plays a pivotal role in the field of quantum cryptography. In this paper, a hybrid protocol is proposed to implement secure multiparty quantum summation and anonymous ranking simultaneously, which uses d$d$‐level two‐particle entangled states. In the designed protocol, the particles are conveyed in the way of the circle‐type transmission mode, which can compute the sum of the secret and the ranking by analyzing the distribution of participants associated with different secret values. Moreover, random number sequences can be obtained by constructing a fundamental system of solutions, which avoids the transmission of random numbers and reduces the use of quantum resources. According to the analysis, it can be seen that the protocol is secure against known attacks, and the secrets remain undisclosed throughout the protocol's implementation. [ABSTRACT FROM AUTHOR]

Traditional k-means algorithm measures the Euclidean distance between any two data points, but it is not applicable in many scenarios, such as the path information between two cities, or when there are some obstacles between two data points. To solve the problems, we propose a quantum k-means algorithm based on Manhattan distance (QKMM). The main two steps of the QKMM algorithm are calculating the distance between each training vector and k cluster centroids, and choosing the closest cluster centroid. The quantum circuit is designed, and the time complexity is O (log (N d) + 2 n + k) , where N is number of training vectors, d is number of features for each training vector, n is number of bits for each feature, and k is the number of clustering classes. Different from other quantum k-means algorithms, our algorithm has wide applications and reduces the complexity. Compared with classical k-means algorithm, our algorithm reaches quadratic speedup. [ABSTRACT FROM AUTHOR]

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 widely used clustering algorithm, density peak clustering (DPC), assigns different attribute values to data points through the distance between data points, and then determines the number and range of clustering by attribute values. However, DPC is inefficient when dealing with scenes with a large amount of data, and the range of parameters is not easy to determine. To fix these problems, we propose a quantum DPC (QDPC) algorithm based on a quantum D i s t C a l c circuit and a Grover circuit. The time complexity is reduced to O (log (N 2) + 6 N + N) , whereas that of the traditional algorithm is O (N 2) . The space complexity is also decreased from O (N · ⌈ log N ⌉) to O (⌈ log N ⌉) . [ABSTRACT FROM AUTHOR]