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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…

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…

Grover's search algorithm has attracted great attention due to its quadratic speedup over classical algorithms in unsorted database search problems. However, Grover's algorithm is inefficient in multi-target search problems, except in the…

Quantum computers, which take advantage of the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact, such as factoring large numbers and searching…

In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…

Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is…

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 this article, we give a complete characterization of all the unitary transformations that can be synthesized in a given time for a system of coupled spin-1/2 in presence of general time varying coupling tensor. Our treatment is quite…

NMR is emerging as a valuable testbed for the investigation of foundational questions in quantum mechanics. The present paper outlines the preparation of a class of mixed states, called pseudo-pure states, that emulate pure quantum states…

An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…

The desired interference required for quantum computing may be modified by the wave function oscillations for the implementation of quantum algorithms[Phys.Rev.Lett.84(2000)1615]. To diminish such detrimental effect, we propose a scheme…

We propose an ion trap implementation of Grover's quantum search algorithm for an unstructured database of arbitrary length N. The experimental implementation is appealingly simple because the linear ion trap allows for a straightforward…

Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…

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…

A new approach to the implementation of a quantum computer by high-resolution nuclear magnetic resonance (NMR) is described. The key feature is that two or more line-selective radio-frequency pulses are applied simultaneously. A three-qubit…

Evolution of entanglement with the proceeding of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one.…

Solid state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multi-qubit systems are currently difficult to achieve. We describe a method for programmable…

Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the…

We introduce a novel NMR approach that extends the capabilities of indirect dynamic nuclear polarization (DNP) under magic-angle spinning to probe the local environment of half-integer spin quadrupolar nuclei. Compared to…

We have developed semiconductor point contact devices in which nuclear spins in a nanoscale region are coherently controlled by all-electrical methods. Different from the standard nuclear-magnetic resonance technique, the longitudinal…