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Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the…
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…
The discovery of derivatives and integrals was a tremendous leap in scientific knowledge and completely revolutionized many fields, including mathematics, physics, and engineering. The existence of higher-order derivatives means better…
Grover's algorithm is a well-known unstructured quantum search algorithm run on quantum computers. It constructs an oracle and calls the oracle O($\sqrt N$) times to locate specific data out of N unsorted data. This represents a quadratic…
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…
We propose a novel paradigm of integration of Grover's algorithm in a machine learning framework: the inductive Grover oracular quantum neural network (IGO-QNN). The model defines a variational quantum circuit with hidden layers of…
With the advent of powerful quantum computers, the quest for more efficient quantum algorithms becomes crucial in attaining quantum supremacy over classical counterparts in the noisy intermediate-scale quantum era. While Grover's search…
Quantum computing is an exciting non-Von Neumann paradigm, offering provable speedups over classical computing for specific problems. However, the practical limits of classical simulatability for quantum circuits remain unclear, especially…
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…
Grover's algorithm is a cornerstone of quantum search algorithm, offering quadratic speedup for unstructured problems. However, limited qubit counts and noise in today's noisy intermediate-scale quantum (NISQ) devices hinder large-scale…
We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand.…
Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a…
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…
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…
Here we extend the concept of blind client-server quantum computation, in which a client with limited quantum power controls the execution of a quantum computation on a powerful server, without revealing any details of the computation. Our…
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…
We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in…
Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a…