A simple method for the preparation of pseudopure states in nuclear magnetic resonance quantum information processing.

The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of pseudopure states (POPS) as a basis for QIP is very convenient because of the simplicity in experimental execution. It is now further demonstrated that the product of the NMR spectra corresponding to two sets of POPS that share a common pseudopure state has the same peak frequencies as those of the common (single) pseudopure state. Examples of applying two different quantum logic gates to a 5-qubit system are given.

Selective excitation in spin systems with homogeneous broadening.

We have found that the application of a weak radio frequency (rf) pulse to a spin system with indirect spin-spin (J) couplings can produce a narrow inverted peak in spectral regions where there are many overlapping peaks. Examples of three compounds with (1)H-(1)H J couplings and one with (1)H-(13)C J couplings are given. The dependences of the signals on the frequency, duration, and amplitude of the weak rf irradiation have been studied. For an rf power of gammaB(1)/2pi=1.0 Hz, pulse widths longer than 0.25 s consistently produce inverted narrow peaks in spectral regions with unresolved peaks. An interpretation of the origin of this unusual result of selective excitation in spin systems with homogeneous broadening is given: the inverted signal observed can be considered as a cumulative effect of the weak rf irradiation acting on many uncorrelated transitions that are slightly off resonance on both sides of the irradiating frequency; the only role of the J couplings (or dipolar couplings in liquid crystals) is to produce a large number of closely spaced peaks that overlap with each other. Computer simulations of both coupled and noninteracting spin systems have been carried out, and the results support this interpretation.

The presence of long-lived spin states in organic solids with rapid molecular motions.

For organic solids with sufficiently mobile molecular segments, the application of a long and weak pulse (gammaB1/2pi approximately Hz) can yield inverted sharp peaks with linewidths of approximately 100 Hz in the 1H NMR spectra, and the use of multi-frequency weak pulses can excite multiple inverted sharp peaks. For these compounds, the normal 1H free induction decay (FID) of a static sample contains a slowly decaying part, which can be detected by acquisition delay up to about 2 ms. The presence of highly mobile molecular segments can also be identified by using a "dipolar filter."

A simple method for NMR photography.

The application of a multi-frequency weak pulse to a liquid crystal can excite narrow 1H NMR peaks at the applied frequencies. By using two-level amplitude coding, namely setting the amplitudes of some of the harmonics to zero, this method can be used to store up to 1024 bits of binary information in the liquid crystal molecules. When the information is retrieved in the form of a spectrum, which is plotted as an array of 32 or 16 segments, the stack of spectral segments reproduces a 2D input pattern quite well. This technique is called "NMR photography." The original method was a pseudo-2D technique that applies the 1024-frequency pulse in the first step, and reads the signal row-by-row in the second step. The present improvement involves subtracting two spectra obtained with the same 1024-frequency pulse but with different durations, so that the method becomes a 1D technique, with a tremendous saving of experimental time. Several examples are given to illustrate the results.

NMR implementation of a parallel search algorithm.

Recently it has been shown that the dynamics of a cluster of dipolar-coupled spins can be manipulated to store and process a large amount of information in a parallel way [Chem. Phys. Lett. 360, 161 (2002)]]. Here it is further demonstrated that it is possible to realize a cascade of parallel bitwise operations on a spin cluster so that an algorithm of parallel search can be experimentally implemented by means of nuclear magnetic resonance.