Related papers: Strength and Weakness in Grover's Quantum Search A…
We consider the Grover search algorithm implementation for a quantum register of size $N = 2^k$ using k (or k +1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by M{\o}lmer, Isenhower, and Saffman [J. Phys. B…
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 quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is shown that the optimal time to perform the measurement is independent of $| \phi>$,…
Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…
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,…
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
In this work, we present a multi-layer quantum search method that generates an exponential speedup of the standard Grover's algorithm. As direct applications, any NP problems can be solved efficiently on a quantum circuit with only…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a 50% probability, any classical algorithm (whether deterministic or probabilistic) will need to look at a…
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…
The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain…
Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a…
Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial…
Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both…
We examine how amplitude noise in queries to the oracle degrades a performance of quantum search algorithm. The Grover search and similar techniques are widely used in various quantum algorithms, including cases where rival parties are…
A generalized quantum search algorithm, where phase inversions for the marked state and the prepared state are replaced by $\pi/2$ phase rotations, is realized in a 2-qubit NMR heteronuclear system. The quantum algorithm searches a marked…
Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…
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…