Deleting a marked state in quantum database in a duality computing mode

Abstract

In this article, we present a deletion algorithm in the duality computer that deletes a marked state from an even superposition of all basis-states with certainty. This duality computer deletion algorithm requires a single query, and this achieves exponential speedup over classical algorithm. Using a duality mode and recycling quantum computing, we provide a realization of this duality computer deletion algorithm in quantum computer. duality computer, deletion algorithm, search algorithm, database, recycling quantum computing Citation: Liu Y. Deleting a marked state in quantum database in a duality computing mode. Chin Sci Bull, 2013Bull, , 58: 2927Bull, -2931Bull, , doi: 10.1007 Deleting items from a database has been a widely met scientific problem and it has important applications in computing process. In classical computing, deleting is an essential method to preserve certain data structure for convenient searching and visiting, for example, a well-known Google search engine PageRank algorithm [1]. Classical deleting is considered equivalent to classical searching. To delete M marked items from a N-item database usually requires O(MN log N) steps. Fibonacci heaps algorithm [2] which has been shown optimal [3] is the optimal classical deletion algorithm. For arbitrary database, Fibonacci heaps algorithm deletes M marked items from a N-item heap with O(N log N + M) steps. Recently, the deletion algorithm has been extended to quantum computation [4]. A quantum deletion algorithm is proposed that deletes a marked basis-state from an evenly distributed state with only a single query. Compared to its classical counterpart, quantum deletion algorithm can achieve an exponential speedup.Duality computer (DC) is a recently proposed computing model [5]. It exploits particle wave duality property, and it may offer additional computing capability. Two proofof-the-principle designs of duality computer have been presented. Later on, many efforts have been made to duality email: yliu@ncepu.edu.cn computer research. A duality computer can solve an unsorted database search problem [5] and factorization for large integers [6]. Mathematical theory of duality computer has also been worked out [7][8][9][10][11][12][13][14][15]. A quantum computer realization of the duality computer is given in [16], and complex duality quantum computer is proposed in [17]. This realization uses the duality mode and recycling quantum computing. These modes provide new ways and flexibility in quantum algorithm designs, for example, a fixed-point quantum search algorithm based on the duality mode is proposed [18], which can achieve speedup compared to previous fixed-point searching [19]. Later it is experimentally demonstrated [20]. An improved fixed-point duality quantum algorithm is given in [21]. Duality quantum computing has been generalized into more broad range, duality quantum information processing [22,23]. In this article, we explore the problem of deleting marked item using the duality computer, and the duality mode in quantum computer....

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