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Jonathan A Jones - One of the best experts on this subject based on the ideXlab platform.

  • error tolerance in an nmr implementation of grover s fixed point Quantum Search Algorithm
    Physical Review A, 2005
    Co-Authors: Li Xiao, Jonathan A Jones
    Abstract:

    We describe an implementation of Grover's fixed-point Quantum Search Algorithm on a nuclear magnetic resonance Quantum computer, Searching for either one or two matching items in an unsorted database of four items. In this Algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive Search operator, so that the Algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored.

  • Error tolerance in an NMR implementation of Grover’s fixed-point Quantum Search Algorithm
    Physical Review A, 2005
    Co-Authors: Li Xiao, Jonathan A Jones
    Abstract:

    We describe an implementation of Grover's fixed-point Quantum Search Algorithm on a nuclear magnetic resonance Quantum computer, Searching for either one or two matching items in an unsorted database of four items. In this Algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive Search operator, so that the Algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored.

  • implementation of a Quantum Search Algorithm on a Quantum computer
    Nature, 1998
    Co-Authors: Jonathan A Jones, Michele Mosca, R H Hansen
    Abstract:

    In 1982 Feynman1 observed that Quantum-mechanical systems have an information-processing capability much greater than that of corresponding classical systems, and could thus potentially be used to implement a new type of powerful computer. Three years later Deutsch2 described a Quantum-mechanical Turing machine, showing that Quantum computers could indeed be constructed. Since then there has been extensive reSearch in this field, but although the theory is fairly well understood, actually building a Quantum computer has proved extremely difficult. Only two methods have been used to demonstrate Quantum logic gates: ion traps3,4 and nuclear magnetic resonance (NMR)5,6. NMR Quantum computers have recently been used to solve a simple Quantum Algorithm—the two-bit Deutsch problem7,8. Here we show experimentally that such a computer can be used to implement a non-trivial fast Quantum Search Algorithm initially developed by Grover9,10, which can be conducted faster than a comparable Search on a classical computer.

  • implementation of a Quantum Search Algorithm on a nuclear magnetic resonance Quantum computer
    arXiv: Quantum Physics, 1998
    Co-Authors: Jonathan A Jones, Michele Mosca, R H Hansen
    Abstract:

    We demonstrate an implementation of a Quantum Search Algorithm on a two qubit NMR Quantum computer based on cytosine.

Guilu Long - One of the best experts on this subject based on the ideXlab platform.

  • Experimental implementation of a fixed-point duality Quantum Search Algorithm in the nuclear magnetic resonance Quantum system
    Science China Physics Mechanics and Astronomy, 2011
    Co-Authors: Liang Hao, Guilu 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.

  • An N /4 fixed-point duality Quantum Search Algorithm
    Science China Physics Mechanics and Astronomy, 2010
    Co-Authors: Liang Hao, Dan Liu, Guilu Long
    Abstract:

    Here a fixed-point duality Quantum Search Algorithm is proposed. This Algorithm uses iteratively non-unitary operations and measurements to Search an unsorted database. Once the marked item is found, the Algorithm stops automatically. This Algorithm uses a constant non-unitary operator, and requires N/4 steps on average (N is the number of data from the database) to locate the marked state. The implementation of this Algorithm in a usual Quantum computer is also demonstrated.

  • an n 4 fixed point duality Quantum Search Algorithm
    Science China-physics Mechanics & Astronomy, 2010
    Co-Authors: Liang Hao, Dan Liu, Guilu Long
    Abstract:

    Here a fixed-point duality Quantum Search Algorithm is proposed. This Algorithm uses iteratively non-unitary operations and measurements to Search an unsorted database. Once the marked item is found, the Algorithm stops automatically. This Algorithm uses a constant non-unitary operator, and requires N/4 steps on average (N is the number of data from the database) to locate the marked state. The implementation of this Algorithm in a usual Quantum computer is also demonstrated.

  • Quantum DIRECT COMMUNICATION BASED ON Quantum Search Algorithm
    International Journal of Quantum Information, 2010
    Co-Authors: Chuan Wang, Liang Hao, Si Yu Song, Guilu Long
    Abstract:

    Quantum direct communications, including deterministic secure Quantum communication and Quantum secure direct communication protocol using two-qubit Quantum Search Algorithm are proposed in this paper. Secret messages are encoded by two-qubit unitary operations and exchanged by the two communication parties directly. We discussed the security of the protocol under intercept-resend attack and individual attack. We found that the protocols are secure against eavesdropping attacks.

  • Experimental NMR realization of a generalized Quantum Search Algorithm
    Physics Letters A, 2001
    Co-Authors: Guilu Long, H Y Yan, J X Tao, Hongbo Chen, Maili Liu, Xiaoli Zhang, Jun Luo, Li Xiao
    Abstract:

    A generalized Quantum Search Algorithm, where phase inversions for the marked state and the prepared state are replaced by pi /2 phase rotations, is realized in a 2-qubit NMR heteronuclear system. The Quantum Algorithm Searches a marked state with a smaller step compared to standard Grover Algorithm. Phase matching requirement in Quantum Searching is demonstrated by comparing it with another generalized Algorithm where the two phase rotations are pi /2 and 3 pi /2, respectively. Pulse sequences which include non-90 degrees pulses are given. (C) 2001 Elsevier Science B.V. All rights reserved.

Ahmed Younes - One of the best experts on this subject based on the ideXlab platform.

  • towards more reliable fixed phase Quantum Search Algorithm
    Applied Mathematics & Information Sciences, 2013
    Co-Authors: Ahmed Younes
    Abstract:

    Building Quantum devices using fixed operators is a must to simplify hardware construction of a Quantum computer. Quan- tum Search engine is not an exception. In this paper, a fixed phase Quantum Search Algorithm that Searches for M matches in an unstructured list of size N will be proposed. Fixing phase shifts to 1.91684π in the standard amplitude amplification will make the minimum probability of success is 99.58% in O N/M for 0 Quantum Search Algorithm. The Algorithm will be able to handle either a single match or multiple matches in the Search space. The Algorithm will find a match in O N/M whether the number of matches is known or not in advance.

  • Towards More Reliable Fixed Phase Quantum Search Algorithm
    Applied Mathematics & Information Sciences, 2013
    Co-Authors: Ahmed Younes
    Abstract:

    Building Quantum devices using fixed operators is a must to simplify hardware construction of a Quantum computer. Quan- tum Search engine is not an exception. In this paper, a fixed phase Quantum Search Algorithm that Searches for M matches in an unstructured list of size N will be proposed. Fixing phase shifts to 1.91684π in the standard amplitude amplification will make the minimum probability of success is 99.58% in O N/M for 0

  • Strength and Weakness in Grover's Quantum Search Algorithm
    arXiv: Quantum Physics, 2008
    Co-Authors: Ahmed Younes
    Abstract:

    AbstractGrover’s Quantum Search Algorithm is considered as one of the milestone in the field ofQuantum computing. The Algorithm can Search for a single match in a database with Nrecords in O(√N) assuming that the item must exist in the database with quadratic speedupover the best known classical Algorithm. This review paper discusses the performance ofGrover’s Algorithm in case of multiple matches where the problem is expected to be easier.Unfortunately, we will find that the Algorithm will fail for M > 3N/4, where M is the numberof matches in the list. 1 Introduction In 1996, Lov Grover [11] presented an Algorithm for Searching an unstructured list of N itemswith quadratic speed-up over classical Algorithms. His original Algorithm targets the case wherea single match exists within the Search space. Much reSearch effort has gone into analysing andgeneralising his Algorithm for multiple matches [3, 4, 6, 7, 8].This paper will review the work done by others on solving the unstructured Search problemon Quantum computers as follows: Section 2 provides the general definition of the unstructuredSearch problem and some of its applications. Section 3 briefly summarises the work done so far indesigning Algorithms concerning this problem on Quantum computers. Section 4 presents Grover’sAlgorithm in some detail and the work done by others related to his Algorithm, analysing itsperformance and behaviour over the range 1 ≤ M≤ Nfor both known and unknown number ofmatches M. The paper ends up with a general conclusion in Section 5 about Grover’s Algorithm.

  • Fixed Phase Quantum Search Algorithm
    arXiv: Quantum Physics, 2007
    Co-Authors: Ahmed Younes
    Abstract:

    Building Quantum devices using fixed operators is a must to simplify the hardware construction. Quantum Search engine is not an exception. In this paper, a fixed phase Quantum Search Algorithm that Searches for M matches in an unstructured Search space of size N will be presented. Selecting phase shifts of 1.91684\pi in the standard amplitude amplification will make the technique perform better so as to get probability of success at least 99.58% in O(sqrt(N/M)) better than any know fixed operator Quantum Search Algorithms. The Algorithm will be able to handle either a single match or multiple matches in the Search space. The Algorithm will find a match in O(sqrt(N/M)) whether the number of matches is known or not in advance.

  • Quantum Search Algorithm with more reliable behaviour using partial diffusion
    arXiv: Quantum Physics, 2004
    Co-Authors: Ahmed Younes, Jon Rowe, Julian F Miller
    Abstract:

    In this paper, we will use a Quantum operator which performs the inversion about the mean operation only on a subspace of the system (Partial Diffusion Operator) to propose a Quantum Search Algorithm runs in O( p N/M) for Searching unstructured list of size N with M matches such that, 1 ≤ M ≤ N. We will show that the performance of the Algorithm is more reliable than known Quantum Search Algorithms especially for multiple matches within the Search space. A performance comparison with Grover’s Algorithm will be provided.

Ofer Biham - One of the best experts on this subject based on the ideXlab platform.

  • Analysis of Grover's Quantum Search Algorithm as a dynamical system
    Physical Review A, 2003
    Co-Authors: Ofer Biham, Daniel Shapira, Yishai Shimoni
    Abstract:

    Grover's Quantum Search Algorithm is analyzed for the case in which the initial state is an arbitrary pure Quantum state |{phi}> of n qubits. It is shown that the optimal time to perform the measurement is independent of |{phi}>, namely, it is identical to the optimal time in the original Algorithm in which |{phi}>=|0>, with the same number of marked states, r. The probability of success P{sub s} is obtained in terms of the amplitudes of the state |{phi}> and is shown to be independent of r. A class of states, which includes fixed points and cycles of the Grover iteration operator, is identified. The relevance of these results in the context of using the success probability as an entanglement measure is discussed. In particular, the Groverian entanglement measure, previously limited to a single marked state, is generalized to the case of several marked states.

  • Effect of unitary noise on Grover's Quantum Search Algorithm
    Physical Review A, 2003
    Co-Authors: Daniel Shapira, Shay Mozes, Ofer Biham
    Abstract:

    The effect of unitary noise on the performance of Grover's Quantum Search Algorithm is studied. This type of noise may result from tiny fluctuations and drift in the parameters of the (Quantum) components performing the computation. The resulting operations are still unitary, but not precisely those assumed in the design of the Algorithm. Here we focus on the effect of such noise in the Hadamard gate W, which is an essential component in each iteration of the Quantum Search process. To this end W is replaced by a noisy Hadamard gate U. The parameters of U at each iteration are taken from an arbitrary probability distribution (e.g., a Gaussian distribution) and are characterized by their statistical moments around the parameters of W. For simplicity, we assume that the noise is unbiased and isotropic, namely, all noise variables in the parametrization we use have zero average and the same standard deviation {epsilon}. The noise terms at different calls to U are assumed to be uncorrelated. For a Search space of size N=2{sup n} (where n is the number of qubits used to span this space) it is found that as long as {epsilon}

  • effect of unitary noise on grover s Quantum Search Algorithm
    Physical Review A, 2003
    Co-Authors: Daniel Shapira, Shay Mozes, Ofer Biham
    Abstract:

    The effect of unitary noise on the performance of Grover's Quantum Search Algorithm is studied. This type of noise may result from tiny fluctuations and drift in the parameters of the (Quantum) components performing the computation. The resulting operations are still unitary, but not precisely those assumed in the design of the Algorithm. Here we focus on the effect of such noise in the Hadamard gate W, which is an essential component in each iteration of the Quantum Search process. To this end W is replaced by a noisy Hadamard gate U. The parameters of U at each iteration are taken from an arbitrary probability distribution (e.g., a Gaussian distribution) and are characterized by their statistical moments around the parameters of W. For simplicity, we assume that the noise is unbiased and isotropic, namely, all noise variables in the parametrization we use have zero average and the same standard deviation {epsilon}. The noise terms at different calls to U are assumed to be uncorrelated. For a Search space of size N=2{sup n} (where n is the number of qubits used to span this space) it is found that as long as {epsilon}Algorithm maintains significant efficiency, whilemore » above this noise level its operation is hampered completely. It is also found that below this noise threshold, when the Search fails, it is likely to provide a state that differs from the marked state by only a few bits. This feature can be used to Search for the marked state by a classical postprocessing, even if the Quantum Search has failed, thus improving the success rate of the Search process.« less

L. Lara - One of the best experts on this subject based on the ideXlab platform.