Costantino S. Yannoni

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 Shors 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 Shors 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.

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 1013 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.

C60 Rotation in the Solid State: Dynamics of a Faceted Spherical Top

The rotational dynamics of C60 in the solid state have been investigated with carbon-13 nuclear magnetic resonance (13C NMR). The relaxation rate due to chemical shift anisotropy (1/9T1CSA1) was precisely measured from the magnetic field dependence of T1, allowing the molecular reorientational correlation time, τ, to be determined. At 283 kelvin, τ = 9.1 picoseconds; with the assumption of diffusional reorientation this implies a rotational diffusion constant D = 1.8 x 1010 per second. This reorientation time is only three times as long as the calculated τ for free rotation and is shorter than the value measured for C60 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 C60. In both phases τ 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.

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 Sc3C82 have been obtained. ScC82 also gives an EPR spectrum, but Sc2Cn species—the most abundant metallofullerenes in the mass spectrum—are EPR-silent even though Sc2 is EPR-active in a rare-gas matrix at 4.2 K. The results suggest that the three scandium atoms in Sc3C82 form an equilateral triangle—as was previously suggested for Sc3 molecules isolated in a cryogenic rare-gas matrix. The spectrum of ScC82 has features similar to those found earlier for LaC82 and YC82, 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.

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 Shors 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.

Three‐dimensional imaging with a nuclear magnetic resonance force microscope

A magnetic resonance force microscope was used to demonstrate three‐dimensional nuclear magnetic resonance imaging with micrometer‐scale spatial resolution. The sample was mounted on a silicon nitride cantilever that served as a micromechanical force sensor. A nearby magnetic tip generated a field gradient of 22 G/μm. A three‐dimensional magnetic resonance force map of the 1H spins in the sample was produced by lateral scanning of the magnetic tip relative to the sample and by varying the rf frequency of the spin excitation. The real‐space spin density of the sample was reconstructed from the force map by means of a deconvolution technique. The spatial resolution achieved in the experiment was ∼3 μm in the axial direction.

Multiple species of La@C82 and Y@C82. Mass spectroscopic and solution EPR studies

Abstract Two dominant electron paramagnetic resonance (EPR) hyperfine patterns for both La and Y fullerenes have been identified and linked to the mass spectroscopic (MS) peaks of La@C 82 and Y@C 82 , respectively, as also observed by Suzuki. Additionally, lower intensity La@C n EPR multiplets are identified which have not, as yet, been correlated with specific MS peaks. The intensity ratios of the two dominant EPR multiplets depend on various parameters such as solvent and temperature, suggesting the species possess different chemical properties.

Implementation of a three-quantum-bit search algorithm

We report the experimental implementation of Grover’s quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of 13C-labeled CHFBr2, in which the three weakly coupled spin-1/2 nuclei behave as the bits and are initialized, manipulated, and read out using magnetic resonance techniques. This quantum computation is made possible by the introduction of two techniques which significantly reduce the complexity of the experiment and by the surprising degree of cancellation of systematic errors which have previously limited the total possible number of quantum gates.

NMR nutation spectroscopy: A method for determining molecular geometry in amorphous solids

A NMR technique for direct determination of internuclear distances in amorphous solids is described and illustrated with a measurement of the carbon–carbon bond length in acetic acid at −190 °C. The result, 1.488 °A, is sufficiently close to the x‐ray value of 1.478 °A to confirm the effectiveness of the overall approach. The pulse sequence used, and the ensuing spectral analysis, ensure a very direct measurement of internuclear distances in amorphour solids.

CPMAS Polarization Transfer Methods for Superposed Chemical Exchange and Spin Diffusion in Organic Solids

Abstract The question of how CPMAS polarization-transfer experiments (CP, cross polarization; MAS, magic-angle spinning) should be conducted in order to distinguish between slow chemical exchange and spin diffusion in the solid state has been studied. Both contributions can be separated by performing different types of polarization-transfer experiments in the laboratory and the rotating frame, since dynamics of spin diffusion but not chemical exchange differs from one experiment to the next. Generally, if both processes are present, polarization transfer is expected to be nonexponential and chemical-exchange as well as spin-diffusion rate constants can be obtained in one series of experiments. If the exchange is symmetric, however, polarization transfer is single exponential and a combination of different pulse experiments is required for obtaining rate constants of both processes. The results for 15N CPMAS NMR polarization-transfer experiments on crystalline meso-tetratolylporphin-15N4 (TTP) are presented. Experiments in the laboratory frame show that spin diffusion between the 15N atoms of TTP is characterized by a temperature-independent rate constant. The nature of this process was established by 1H decoupling during the mixing time, which results in quenching of the polarization transfer. Thus, the role of the 1H spin reservoir for laboratory-frame spin diffusion among chemically inequivalent 15N spins in 15N-enriched material is confirmed. At higher temperatures, polarization transfer in the laboratory and the rotating frame is observed due to a symmetric exchange of the nitrogen atoms arising from a double proton transfer which has been previously established. The double proton transfer rates observed with the different polarization-transfer methods agree well with the values predicted from high-temperature lineshape analysis and are found to be very close to the solution data.