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In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum…
This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a…
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This…
The main idea in the original Grover search (Phys. Rev. Lett. 79, 325 (1997)) is to single out a target state containing the solution to a search problem by amplifying the amplitude of the state, following the Oracle's job, i.e., a black…
We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general…
The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Grover's algorithm, a well-know quantum search algorithm, allows one to find the correct item in a database, with quadratic speedup. In this paper we adapt Grover's algorithm to the problem of finding a correct answer to a natural language…
Grover's database search algorithm is the optimal algorithm for finding a desired object from an unsorted collection of items. Although it was discovered in the context of quantum computation, it is simple and versatile enough to be…
We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding minimum or maximum solutions on a weighted directed graph. We focus on a geometry of…
We present a novel use case for quantum computation: the sensitivity analysis for a risk model used at Deutsche B\"orse Group. Such an analysis is computationally too expensive to perform on classical computers. We show in detail how the…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…
Grover's algorithm accelerates unstructured database search quadratically compared to classical algorithms. In the NISQ era, distributed quantum computing can decrease circuit depth and reduce noise. In this paper, an algorithm for…
Grover's algorithm searches for data satisfying a desired condition in an unstructured database. This algorithm can search a space of size $N$ in $\sqrt{N}$ queries, thereby achieving a quadratic speedup. However, within the Grover oracle…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a…