Existence and construction of a quantum channel with given inputs and outputs

Guo, Zhihua; Cao, Huaixin

doi:10.1007/s11434-012-5506-3

Chin. Sci. Bull.

2012

DOI: 10.1007/s11434-012-5506-3

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Existence and construction of a quantum channel with given inputs and outputs

Zhihua Guo

Huaixin Cao

Abstract: We derive that sufficient and necessary conditions for existence of a quantum channel φ and a generalized unitary operation E sendingof matrices, respectively. As an application, a sufficient and necessary condition for existence of a unitary duality quantum computer with given input-output states is obtained. existence, quantum channel, generalized unitary operation, duality quantum computerCitation: Guo Z H, Cao H X. Existence and construction of a quantum channel with given inputs and outputs.

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Cited by 6 publications

(2 citation statements)

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“…Another project was launched by the Chinese Academy of Sciences (CAS), called CASEarth (http://data.casearth.cn/). The project aims to build a cyberinfrastructure for data on the Earth, environmental, ecological and biological sciences 5 . By collecting data from CAS institutions, the CASEarth repository has now stored more than 5 PB of data, and its data have been downloaded more than 500,000 times.…”

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Boosting geoscience data sharing in China

Cheng

Wang

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Nat. Geosci.

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Boosting geoscience data sharing in China

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Wang

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Nat. Geosci.

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“…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].…”

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

Liu

2013

Chin. Sci. Bull.

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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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Note on the Wigner-Yanase-Dyson Skew Information

Dou

2013

Int J Theor Phys

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Existence and construction of a quantum channel with given inputs and outputs

Cited by 6 publications

References 26 publications

Boosting geoscience data sharing in China

Boosting geoscience data sharing in China

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

Note on the Wigner-Yanase-Dyson Skew Information

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