Complex duality quantum computers acting on pure and mixed states

Cao, Hongrui; Chen, ZhengLi; Guo, Zhihua; Fang-guo, Ren

doi:10.1007/s11433-012-4916-1

Cited by 10 publications

(4 citation statements)

References 16 publications

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“…Moreover, Gudder has proved that all linear bounded operators in a finite dimensional Hilbert space can be expressed as an element in the positive cone of generalized quantum gates 21 . Many recent studies about the mathematical theory of duality quantum computer have been made 19 20 21 22 23 24 25 26 27 28 29 30 31 34 36 .…”

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confidence: 99%

“…The concept of duality quantum computers is first proposed by Long in 2002 based on the general principle of quantum interference 17 18 , which draw many attentions 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 . It is shown that any bounded linear operator can be expressed as a linear combinations of unitary operators in a duality quantum computer 21 .…”

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Duality quantum algorithm efficiently simulates open quantum systems

Wei

Ruan

Long

2016

Sci Rep

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Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Duality quantum algorithm efficiently simulates open quantum systems

Wei

Ruan

Long

2016

Sci Rep

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“…On the other hand, duality quantum computer, which allows the use of linear combination of unitaries (LCU) for designing quantum algorithms, was proposed [22][23][24][25]. Recently, much interest has been focused on the duality quantum computer [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Besides the common universal gates for quantum computation, two new kinds of computing gates are allowed in duality computer [22].…”

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confidence: 99%

Implementation of a fixed-point quantum search by duality computer

Ding¹,

Zhou²

2019

EPL

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The quantum algorithms where the operations are unitary can be implemented by an ordinary quantum computer, and nonunitary operations can be realized in the duality computer. The operations in the fixed-point quantum search proposed by Mizel (Phys. Rev. Lett., 102 (2009) 150501) are not unitary, and in this paper it is shown that this algorithm can effectively be implemented in duality quantum computer.

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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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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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Complex duality quantum computers acting on pure and mixed states

Cited by 10 publications

References 16 publications

Duality quantum algorithm efficiently simulates open quantum systems

Duality quantum algorithm efficiently simulates open quantum systems

Implementation of a fixed-point quantum search by duality computer

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

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