Computational speed-up with a single qudit.

Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart.

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR.

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl(2). The spectra were obtained with the sample at 4.2K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the (27)Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from (155)Gd and (157)Gd nuclei.

Asymmetrical gradient coil for head imaging.

This work presents a novel approach to develop dedicated transverse gradient coils for head imaging. The proposed coil design is based on the stochastic optimization of an asymmetrical stream function and improves the matching between the region-of-interest and the homogeneous gradient volume. Additionally, the electric field produced by these asymmetrical coils is 30% lower than that produced by standard symmetrical designs, which minimizes the risk of magnetostimulation of nerves in fast imaging techniques. A prototype of the asymmetrical gradient coil was built to test the method and magnetic field produced by the prototype was measured. Magnetic field measurements and electrical parameters of coils are in good agreement with theoretical calculations.