Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance.

The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.

Electron spin relaxation near a micron-size ferromagnet.

Magnetic resonance force microscopy was used to study the behavior of small ensembles of unpaired electron spins in silica near a micrometer-size ferromagnetic tip. Using a cantilever-driven spin manipulation protocol and a magnetic field gradient greater than 10(5) T/m, signals from as few as 100 net spins within a 20 nm thick resonant slice could be studied. A sixfold increase in the spin-lattice relaxation rate was found within 800 nm of the ferromagnet, while no effect due to silica surface proximity was detected. The results are interpreted in terms of Larmor-frequency magnetic field fluctuations emanating from the ferromagnet.

Experimental realization of an order-finding algorithm with an NMR quantum computer.

We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.

Force detection of nuclear magnetic resonance.

Micromechanical sensing of magnetic force was used to detect nuclear magnetic resonance with exceptional sensitivity and spatial resolution. With a 900 angstrom thick silicon nitride cantilever capable of detecting subfemtonewton forces, a single shot sensitivity of 1.6 x 10(13) protons was achieved for an ammonium nitrate sample mounted on the cantilever. A nearby millimeter-size iron particle produced a 600 tesla per meter magnetic field gradient, resulting in a spatial resolution of 2.6 micrometers in one dimension. These results suggest that magnetic force sensing is a viable approach for enhancing the sensitivity and spatial resolution of nuclear magnetic resonance microimaging.

Scandium clusters in fullerene cages.

The production and spectroscopic characterization of fullerene-encapsulated metal-atom clusters is reported. In particular, both solution and solid-state electron paramagnetic resonance (EPR) spectra of Sc(3)C(82) have been obtained. ScC(82) also gives an EPR spectrum, but Sc2Cn species-the most abundant metallofullerenes in the mass spectrum-are EPR-silent even though Sc(2) is EPR-active in a rare-gas matrix at 4.2 K. The results suggest that the three scandium atoms in Sc(3)C(82) form an equilateral triangle-as was previously suggested for Sc(3) molecules isolated in a cryogenic rare-gas matrix. The spectrum of ScC(82) has features similar to those found earlier for LaC(82) and YC(82), suggesting that it can also be described as a +3 metal cation within a -3 fullerene radical anion. An implication of this work is that production of macroscopic quantities of clustercontaining fullerenes may make possible the fabrication of exotic new structures with regular arrays of metal-atom clusters isolated in fullerene molecules, resulting in a new type of host/guest nanostructured material.

C60 rotation in the solid state: dynamics of a faceted spherical top.

The rotational dynamics of C(60) in the solid state have been investigated with carbon-13 nuclear magnetic resonance ((13)C NMR). The relaxation rate due to chemical shift anisotropy (1/9T1(CSA)(1)) was precisely measured from the magnetic field dependence of T(1), allowing the molecular reorientational correlation time, tau, to be determined. At 283 kelvin, tau = 9.1 picoseconds; with the assumption of diffusional reorientation this implies a rotational diffusion constant D = 1.8 x 10(10) per second. This reorientation time is only three times as long as the calculated tau for free rotation and is shorter than the value measured for C(60) in solution (15.5 picoseconds). Below 260 kelvin a second phase with a much longer reorientation time was observed, consistent with recent reports of an orientational phase transition in solid C(60). In both phases tau showed Arrhenius behavior, with apparent activation energies of 1.4 and 4.2 kilocalories per mole for the high-temperature (rotator) and low-temperature (ratchet) phases, respectively. The results parallel those found for adamantane.