Realization of allowable qeneralized quantum gates

Zhang, Ye; Cao, Huaixin; Li, Li

doi:10.1007/s11433-010-4078-y

Cited by 24 publications

(20 citation statements)

References 12 publications

(11 reference statements)

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“…It has been shown recently by Cao et al [10] that it is necessary and sufficient to decompose a generalized quantum gate in the form in (16) in terms of two unitary operators V and W in (15) if the coefficients satisfies…”

Section: Duality Quantum Computing Mode In a Quantum Computermentioning

confidence: 99%

“…The mathematical descriptions can be found in [1][2][3][4][5][6][7][8][9][10]. Concise mathematical expressions together with the studies of the properties of divider and combiner, and duality gates are given.…”

Section: Mathematical Theory Of Duality Quantum Computingmentioning

confidence: 99%

“…There have been intensive interests in the theory of duality computer in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Here in this review article we will briefly describe the main results.…”

Section: Introductionmentioning

confidence: 99%

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Duality Quantum Computing and Duality Quantum Information Processing

Long

2010

Int J Theor Phys

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Quantum mechanical systems exhibit wave-particle duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called duality quantum computing mode. In this article, the main structure of duality quantum computing, their mathematical description and applications are reviewed.

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Section: Duality Quantum Computing Mode In a Quantum Computermentioning

confidence: 99%

Section: Mathematical Theory Of Duality Quantum Computingmentioning

confidence: 99%

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Duality Quantum Computing and Duality Quantum Information Processing

Long

2010

Int J Theor Phys

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“…An evolution of the system is called a quantum operation and denoted by a unitary operator (called a quantum gate) or a completely positive trace-preserving (CPTP) mapping (called a quantum channel). A convex combination of unitary operators is called a generalized quantum gate [2][3][4], which came from a duality quantum computer [5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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

Guo

Cao

2012

Chin. Sci. Bull.

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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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“…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].…”

mentioning

confidence: 99%

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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Realization of allowable qeneralized quantum gates

Cited by 24 publications

References 12 publications

Duality Quantum Computing and Duality Quantum Information Processing

Duality Quantum Computing and Duality Quantum Information Processing

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

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

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