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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]

With the rapid growth of video and image technology, the binary classification of matrices has attracted much attention. In 2017, Duan et al. proposed a quantum algorithm for support matrix machines (QSMM) that efficiently addresses image classification problems. The QSMM consists of two core subroutines: an HHL algorithm and a quantum singularity threshold (QSVT) algorithm with complexities of O κ 3 ϵ - 3 log (N m n) and O log (m n) , respectively, where κ is the condition number of the corresponding matrix of the HHL algorithm, ϵ is the expected accuracy of the output state, N is the number of samples in the training set and mn is the size of the feature space. The QSMM achieves an exponential increase in speed over classical counterparts. However, we find that Duan's QSMM can be improved by applying an improved quantum matrix inversion (QMI) algorithm instead of the HHL algorithm. Compared with that of Duan's QSMM, the dependence on precision of our improved QSMM (IQSMM) is exponentially improved, and the complexity of our first subroutine is as low as O [ κ 2 log 1.5 (κ / ϵ) log (N m n) ] . [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]

Different from the existing quantum key distribution (QKD)-based quantum private query (QPQ) protocols, we propose a secure multi-party quantum private information query protocol utilizing universal blind quantum computation in quantum cloud computing. Due to the blindness and correctness of blind quantum computation, our protocol guarantees the privacy and security for all the clients and the servers. The clients obtain values corresponding to their queries only, and nothing else from the servers, while the servers can not get any information about the queries. In our protocols, the only thing that the clients do is to need the ability to perform single-qubit measurement or to prepare single-qubit states. [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]

Blind quantum computation (BQC) enables the client, who has few quantum technologies, to delegate her quantum computation to a server, who has strong quantum computabilities and learns nothing about the client’s quantum inputs, outputs and algorithms. In this article, we propose a single-server BQC protocol with quantum circuit model by replacing any quantum gate with the combination of rotation operators. The trap quantum circuits are introduced, together with the combination of rotation operators, such that the server is unknown about quantum algorithms. The client only needs to perform operations X and Z, while the server honestly performs rotation operators. [ABSTRACT FROM AUTHOR]