Related papers: A novel SO(3) picture for quantum searching
In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for…
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…
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…
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that…
In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles…
We demonstrate the implementation of Grover's quantum search algorithm on a liquid state nuclear magnetic resonance (NMR) quantum computer using essentially pure states. This was achieved using a two qubit device where the initial state is…
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…
Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The…
There are hamiltonians that solve a search problem of finding one of $N$ items in $O(\sqrt{N})$ steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, $H_{g}$.…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…
We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using simple adiabatic techniques. The…
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently…
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)…
The lackadaisical quantum walk, a quantum analog of the lazy random walk, is obtained by adding a weighted self-loop transition to each state. Impacts of the self-loop weight $l$ on the final success probability in finding a solution make…
We propose a methodology for implementing Grover's algorithm in the digital quantum simulation of disordered Ising models. The core concept revolves around using the evolution operator for the Ising model as the quantum oracle within…
L. K. Grover's search algorithm in quantum computing gives an optimal, square-root speedup in the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbert-space framework that…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
We study the possibility of an implementation of N-qubit (N>3) Grover search in cavity QED, based on a fast operation of N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…