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For the unsorted database quantum search with the unknown fraction $lambda$ of target items, there are mainly two kinds of methods, i.e., fixed-point or trail-and-error. (i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett. 113, 210501 (2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoders algorithm is actually in $O(1/sqrt{lambda_0})$ rather than $O(1/sqrt{lambda})$, where $lambda_0$ is a known lower bound of $lambda$. (ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoders algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in $lambda$ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides an new idea for the research on fixed-point and trial-and-error quantum search.
We consider a database separated into blocks. Blocks containing target items are called target blocks. Blocks without target items are called non-target blocks. We consider a case, when each target block has the same number of target items. We presen
Grovers algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $lambda$ is the fraction o
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, w
The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate secure key rate, while it still considers that only single-photon pulses can generate secure keys in any
In the treatment plan optimization for intensity modulated radiation therapy (IMRT), dose-deposition coefficient (DDC) matrix is often pre-computed to parameterize the dose contribution to each voxel in the volume of interest from each beamlet of uni