Pulse Sequences for NMR Quantum Computers: How to Manipulate Nuclear Spins While Freezing the Motion of Coupled Neighbours

We show how to divide a coupled multi-spin system into a small subset of ``active'' spins that evolve under chemical shift or scalar coupling operators, and a larger subset of ``spectator'' spins which are returned to their initial states, as if their motion had been temporarily frozen. This allows us to implement basic one-qubit and two-qubit operations from which general operations on $N$-qubits can be constructed, suitable for quantum computation. The principles are illustrated by experiments on the three coupled protons of 2,3-dibromopropanoic acid, but the method is applicable to any spin-1/2 nuclei and to systems containing arbitrary numbers of coupled spins.Comment: 11 pages, 5 fig

An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer

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 quantum computer has been investigated using the 400 MHz NMR spectrum of the three coupled protons in 2,3dibromopropanoic acid. It has been employed to implement the Deutsch-Jozsa algorithm for distinguishing between constant and balanced functions. The extension to systems containing more coupled spins is straightforward and does not require a more protracted experiment.

Quantitative Correlation at the Molecular Level of Tumor Response to Docetaxel by Multimodal Diffusion-Weighted Magnetic Resonance Imaging and [F-18]FDG/[F-18]FLT Positron Emission Tomography

We aimed to quantitatively characterize the treatment effects of docetaxel in the HCT116 xenograft mouse model, applying diffusion-weighted magnetic resonance imaging (MRI) and positron emission tomography (PET) using 2-deoxy-2-[ 18 F]fluoro-D-glucose ([ 18 F]FDG) and 3′-deoxy-3′-[ 18 F]-fluorothymidine ([ 18 F]FLT). Mice were imaged at four time points over 8 days. Docetaxel (15 mg/kg) was administered after a baseline scan. Voxel-wise scatterplots of PET and apparent diffusion coefficient (ADC) data of tumor volumes were evaluated with a threshold cluster analysis and compared to histology (GLUT1, GLUT3, Ki67, activated caspase 3a). Compared to the extensive tumor growth observed in the vehicle-treated group (from 0.32 ± 0.21 cm 3 to 0.69 ± 0.40 cm 3 ), the administration of docetaxel led to tumor growth stasis (from 0.32 ± 0.20 cm 3 to 0.45 ± 0.23 cm 3 ). The [ 18 F]FDG/ADC cluster analysis and the evaluation of peak histogram values revealed a significant treatment effect matching histology as opposed to [ 18 F]FLT/ADC. [ 18 F]FLT uptake and the Ki67 index were not in good agreement. Our voxel-based cluster analysis uncovered treatment effects not seen in the separate inspection of PET and MRI data and may be used as an independent analysis tool. [ 18 F]FLT/ADC cluster analysis could still point out the treatment effect; however, [ 18 F]FDG/ADC reflected the histology findings in higher agreement