• Corpus ID: 199064190

Exact quantum search based on analytical multiphase matching for known number of target items and the experimental demonstration on IBM Q

@article{Li2019ExactQS,
  title={Exact quantum search based on analytical multiphase matching for known number of target items and the experimental demonstration on IBM Q},
  author={Tan Li and Xiangqun Fu and Yang Wang and Shuo Zhang and Xiang Wang and Yungang Du and Wansu Bao},
  journal={arXiv: Quantum Physics},
  year={2019}
}
In [Phys. Rev. Lett. 113, 210501 (2014)], to achieve the optimal fixed-point quantum search in the case of unknown fraction (denoted by $\lambda$) of target items, the analytical multiphase matching (AMPM) condition has been proposed. In this paper, we find out that the AMPM condition can also be used to design the exact quantum search algorithm in the case of known $\lambda$, and the minimum number of iterations reaches the optimal level of existing exact algorithms. Experiments are performed… 

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References

SHOWING 1-10 OF 33 REFERENCES
Complementary-multiphase quantum search for all numbers of target items
TLDR
A complementary-multiphase quantum search algorithm, %with general iterations, in which multiple phases complement each other so that the overall high success probability can be maintained.
Fixed-point adiabatic quantum search
TLDR
It is shown that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of theFixed-point property, and an explicit upper bound on the error in the adiABatic approximation is justified.
Tight bounds on quantum searching
TLDR
A lower bound on the efficiency of any possible quantum database searching algorithm is provided and it is shown that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table.
Multiphase matching in the Grover algorithm
Phase matching has been studied for the Grover algorithm as a way of enhancing the efficiency of the quantum search. Recently Li and Li found that a particular form of phase matching yields, with a
Quantum search with certainty based on modified Grover algorithms: optimum choice of parameters
TLDR
The algorithm proposed by Long is the simplest in the sense that it has only one adjustable phase and that the phase can be obtained in a closed form and it is shown that other more general algorithms with additional phases are not more efficient than Long's version with a single phase.
Quantum Search Algorithm Based on Multi-Phase
TLDR
A multi-phase quantum search algorithm whose success probability rises with the increase of the number of phases with just a single iteration, and it tends to be 100% when the fraction of target items is over a lower limit is proposed.
Generalized Grover's Algorithm for Multiple Phase Inversion States.
TLDR
The underlying structure in terms of the eigenspectrum of the generalized Hamiltonian is shown, and an appropriate initial state is derived to perform the Grover evolution, and a time complexity of this case of sqrt[D/M^{α}], where D is the search space dimension, M is the number of target states, and α≈1, which is close to the optimal scaling.
Fixed-point quantum search.
TLDR
By replacing the selective inversions by selective phase shifts of pi/3, the algorithm preferentially converges to the target state irrespective of the step size or number of iterations, this feature leads to robust search algorithms and also to new schemes for quantum control and error correction.
Family of sure-success quantum algorithms for solving a generalized Grover search problem
TLDR
An infinite family of sure-success quantum algorithms are introduced here to solve Grover's search problem, each member for a different range of f, and are particularly useful when the cost of failure of a search is very high, and for multistage searches with a different search criterion for each stage.
Fixed-point quantum search with an optimal number of queries.
TLDR
This work provides the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup and incorporates an adjustable bound on the failure probability and guarantees that this bound is satisfied over the broadest possible range of λ.
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