Related papers: Query complexity for searching multiple marked sta…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
Grover's search algorithm searches a database of $N$ unsorted items in $O(\sqrt{N/M})$ steps where $M$ represents the number of solutions to the search problem. This paper proposes a scheme for searching a database of $N$ unsorted items in…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
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…
In a recent paper (quant-ph/0506105), A S Gupta, M. Gupta and A. Pathak proposed a modified Grover algorithm that would exponentially accelerate the unsorted database search problem if the number of marked items is known. If this were true,…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
Sorting is a fundamental computational process, which facilitates subsequent searching of a database. It can be thought of as factorisation of the search process. The location of a desired item in a sorted database can be found by classical…
Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
We propose a new adiabatic algorithm for the unsorted database search problem. This algorithm saves two thirds of qubits than Grover's algorithm in realizations. Meanwhile, we analyze the time complexity of the algorithm by both…
The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as…
Grover's algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…