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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]

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]

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]