Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

Hao, Liang; Long, Gui Lu

doi:10.1007/s11433-011-4327-8

Sci. China Phys. Mech. Astron.

2011

DOI: 10.1007/s11433-011-4327-8

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Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

Liang Hao

Gui Lu Long

Abstract: In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given. quantum search algorithm, fixed-point search algorithm, duality quantum computing, the N1 algorithm, NMR realization

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Cited by 15 publications

(6 citation statements)

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“…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

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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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confidence: 99%

Duality quantum algorithm efficiently simulates open quantum systems

Wei

Ruan

Long

2016

Sci Rep

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“…This also indicates that we can perform duality quantum computing in an ordinary quantum computer, in the so-called duality quantum computing mode [16,17]. There have been intensive interests in the theory of duality computer in recent years [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], and experimental studies have also been reported [31,32].…”

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Duality quantum computer and the efficient quantum simulations

Wei

Long

2016

Quantum Inf Process

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In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 12(11-12): 901-924 (2012)] for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al [Phys. Rev. Lett. 114, 090502 (2015)], which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.

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“…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].…”

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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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Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

Cited by 15 publications

References 43 publications

Duality quantum algorithm efficiently simulates open quantum systems

Duality quantum algorithm efficiently simulates open quantum systems

Duality quantum computer and the efficient quantum simulations

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

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