Related papers: On the class of diffusion operators for fast quant…
We consider the quantum search problem with a continuous time quantum walk for networks of finite spectral dimension d_{s} of the network Laplacian. For general networks of fractal (integer or non-integer) dimension d_{f}, for which in…
Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a…
$ $In its usual form, Grover's quantum search algorithm uses $O(\sqrt{N})$ queries and $O(\sqrt{N} \log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to…
We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced…
A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schr\"odinger's quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in…
Although strongly regular graphs and the hypercube are not complete, they are "sufficiently complete" such that a randomly walking quantum particle asymptotically searches on them in the same $\Theta(\sqrt{N})$ time as on the complete…
It is known that the continuous-time variant of Grover's search algorithm is characterized by quantum search frameworks that are governed by stationary Hamiltonians, which result in search trajectories confined to the two-dimensional…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it…
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
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…
In this paper, we study decoherence in Grover's quantum search algorithm using a perturbative method. We assume that each two-state system (qubit) that belongs to a register suffers a phase flip error (\sigma_{z} error) with probability p…
Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…
The multiple-quantum operator algebra formalism has been exploited to construct generally an unsorted quantum search algorithm. The exponential propagator and its corresponding effective Hamiltonian are constructed explicitly that describe…
In this summary we discuss two new algorithms for Grover's unsorted database search problem that claimed to have reached exponential speedup over Grover's original algorithm. One is in the quantum setting with "power queries" that allow for…
Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…
An attempt has been made in this paper to modify Grover's Algorithm to find the binary string solutions approximating a target cost value. In that direction, new Controlled Oracle and the Local Diffusion Operator are suggested, apart from…
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…