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This paper mainly proposes a new method for clustering linear ordinal ranking (LOR) information by agglomerative hierarchical clustering (AHC) algorithm. Considering that the cores of the AHC algorithm for LOR clustering are the difference measure among different LORs and the aggregation of the individual LORs, we firstly systematically analyze the existing studies for LOR distance measure, based on which we extend the method to depict LORs. Subsequently, the corresponding new distance measure is proposed starting from the perspective of utilizing the rankings' position information and relationship information together. In addition, we simplify the dominating index and dominated index-based aggregation method for LORs fusion. Further, we present a numerical case on online financial product recommendation to illustrate the usage of the algorithm and also try to provide a feasible way for online financial product recommendation. Then, we make some discussions on the proposed distance measure and the aggregation method under the framework of the AHC algorithm to show the features of the algorithm proposed in this paper. [ABSTRACT FROM AUTHOR]

Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class of problems where quantum computers possess an advantage is phase estimation, which includes applications like factoring. We introduce a computational model based on a single squeezed state resource that can perform phase estimation, which we call the power of one qumode. This model is inspired by an interesting computational model known as deterministic quantum computing with one quantum bit (DQC1). Using the power of one qumode, we identify that the amount of squeezing is sufficient to quantify the resource requirements of different computational problems based on phase estimation. In particular, we can use the amount of squeezing to quantitatively relate the resource requirements of DQC1 and factoring. Furthermore, we can connect the squeezing to other known resources like precision, energy, qudit dimensionality, and qubit number. We show the circumstances under which they can likewise be considered good resources. [ABSTRACT FROM AUTHOR]