Related papers: Introduction to the multiple-quantum operator spac…
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 show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed for quantum information processing (QIP). Here, we briefly review the use of nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in the…
The whole Hilbert state space of an n-qubit spin system can be divided into (n+1) state subspaces according to the angular momentum theory of quantum mechanics. Here it is shown that any unknown state in such a state subspace, whose…
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…
The analysis of papers on usage NMR in quantum computations is provided and the probable direction of the future investigations are considered.
It is proposed that the state space of a quantum object with a complicated discrete spectrum can be used as a basis for multiqubit recording and processing of information in a quantum computer. As an example, nuclear spin 3/2 is considered.…
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to…
In this work, a connection between some spectral properties of direct integral of operators in the direct integral of Hilbert spaces and their coordinate operators has been investigated.
We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods…
Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
Quantum computing exploits fundamentally new models of computation based on quantum mechanical properties instead of classical physics, and it is believed that quantum computers are able to dramatically improve computational power for…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to…
Quantum computing using two-dimensional NMR has recently been described using scalar coupling evolution technique [J. Chem. Phys.,109,10603 (1998)]. In the present paper, we describe two-dimensional NMR quantum computing with the help of…
Determining the vibrational structure of a molecule is central to fundamental applications in several areas, from atmospheric science to catalysis, fuel combustion modeling, biochemical imaging, and astrochemistry. However, when significant…
Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the…
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".