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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…

After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A…

We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple pi-pulse excitation sequences between ground and Rydberg excited states readily produce the…

A new approach to the classical limit of Grover's algorithm is discussed by assuming a very rapid dephasing of a system between consecutive Grover's unitary operations, which drives pure quantum states to decohered mixed states. One can…

In this work we experimentally study the efficiency of various dynamical decoupling sequences for suppressing decoherence of single as well as multiple quantum coherences on large spin-clusters. The system involves crystallites of a…

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant…

We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of efficiently emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but…

The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic…

This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric introduction to the NMR of an ensemble of indistinguishable spins, and then show how this…

We discuss methods of quantum state tomography for solid-state systems with a large nuclear spin $I=3/2$ in nanometer-scale semiconductors devices based on a quantum well. Due to quadrupolar interactions, the Zeeman levels of these…

Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…

Grover's algorithm for quantum search can also be applied to classical energy transfer. The procedure takes a system in which the total energy is equally distributed among $N$ subsystems and transfers most of the it to one marked subsystem.…

The success probability of a search of $M$ targets from a database of size $N$, using Grover's search algorithm depends critically on the number of iterations of the composite operation of the oracle followed by Grover's diffusion…

The nuclear spin is a prime candidate for quantum information applications due to its weak coupling to the environment and inherently long coherence times. However, this weak coupling also challenges the addressability of the nuclear spin.…

A proposal for applying non-adiabatic geometric phases to quantum computing, called the double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A {\bf 67}, 022319 (2003)], is demonstrated in a liquid state NMR quantum computer. Using a…

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…

Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain…

We present a study of the prospects for coherence preservation in solid-state spin qubits using dynamical decoupling protocols. Recent experiments have provided the first demonstrations of multipulse dynamical decoupling sequences in this…

The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…

Using nuclear magnetic resonance (NMR) techniques with three-qubit sample, we have experimentally implemented the highly structured algorithm for the 1-SAT problem proposed by Hogg. A simplified temporal averaging procedure was employed to…