Abstract
The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It’s very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for calculating intersection set \({\text{C}=\text{A}\cap \text{B}}\) is presented. Its runtime is \({O\left( {\sqrt{\left| A \right|\times \left| B \right|\times \left|C \right|}}\right)}\) for case \({\left| C \right|\neq \phi}\) and \({O\left( {\sqrt{\left| A \right|\times \left| B \right|}}\right)}\) for case \({\left| C \right|=\phi}\) (i.e. C is empty set), while classical computation needs O (|A| × |B|) steps of computation in general, where |.| denotes the size of set. The presented algorithm is the combination of Grover’s algorithm, classical memory and classical iterative computation, and the combination method decrease the complexity of designing quantum algorithm. The method can be used to design other set operations as well.
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Pang, CY., Zhou, RG., Ding, CB. et al. Quantum search algorithm for set operation. Quantum Inf Process 12, 481–492 (2013). https://doi.org/10.1007/s11128-012-0385-8
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DOI: https://doi.org/10.1007/s11128-012-0385-8