Related papers: Grover's search algorithm for $n$ qubits with opti…
A misunderstanding that an arbitrary phase rotation of the marked state together with the inversion about average operation in Grover's search algorithm can be used to construct a (less efficient) quantum search algorithm is cleared. The…
The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
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…
In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP…
Conditions on sure-success decidability of weights of Boolean functions are presented for a given number of generalized Grover iterations. It is shown that the decidability problem reduces to a system of algebraic equations of a single…
An SO(3) picture of the generalized Grover's quantum searching algorithm,with arbitrary unitary transformation and with arbitrary phase rotations, is constructed. In this picture, any quantum search operation is a rotation in a 3…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms…
Grover's search algorithm is renowned for its dramatic speedup in solving many important scientific problems. The recently proposed Variational Quantum Search (VQS) algorithm has shown an exponential advantage over Grover's algorithm for up…
Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…
Grover's quantum search algorithm evolves a quantum system from a known source state $|s\rangle$ to an unknown target state $|t\rangle$ using the selective phase inversions, $I_{s}$ and $I_{t}$, of these two states. In one of the…
Quantum Algorithms have long captured the imagination of computer scientists and physicists primarily because of the speed up achieved by them over their classical counterparts using principles of quantum mechanics. Entanglement is believed…
Let Boolean function $f:\{0,1\}^n\longrightarrow \{0,1\}$ where $|\{x\in\{0,1\}^n| f(x)=1\}|=a\geq 1$. To search for an $x\in\{0,1\}^n$ with $f(x)=1$, by Grover's algorithm we can get the objective with query times $\lfloor…
Demonstration of quantum advantage remains challenging due to the increased overhead of controlling large quantum systems. While significant effort has been devoted to qubit-based devices, qudits ($d$-level systems) offer potential…
We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger…
Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…
We show that iteration of a few ( $\sim N^{1/4}$) unitary steps of Grover's algorithm suffices to perfectly prepare a Dicke state of $N$ atoms in a cavity. We also show that a few subsequent Grover steps can be employed to generate GHZ and…
A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching…
We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our…
We implement Grover's quantum search algorithm on a nuclear spin chain quantum computer, taking into Ising type interactions between nearest and second nearest neighbours into account. The performance of the realisation of the algorithm is…