Probabilistic Interpolation of Quantum Rotation Angles.

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of B bits of resolution, i.e., it might support only 2^{B} possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher B can greatly complexify hardware. Here, we explore an alternative: probabilistic angle interpolation (PAI). This effectively implements any desired, continuously parametrized rotation by randomly choosing one of three discretized gate settings and postprocessing individual circuit outputs. The approach is particularly relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that (a) the approach is optimal in the sense that PAI achieves the least possible overhead and (b) the overhead is remarkably modest even with thousands of parametrized gates and only seven bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers where even 5-6 bits of resolution may suffice and, as we demonstrate, the approach is many orders of magnitude more efficient than prior techniques. Moreover we conclude that, even for more mature late noisy intermediate-scale quantum era hardware, no more than nine bits will be necessary.

A novel pulse scheme for multiple quantum excitation, SFAM to enhance the sensitivity of MQMAS experiments.

The basic MQMAS sequence consists of two hard pulses, one excites the equilibrium population to MQ (Multiple Quantum) coherence, and the other converts back to detectable coherence after some evolution time t1 (Medek et al., 1995). Unfortunately the MQ excitation and conversion processes are very inefficient due to the nonlinear nature of MQ processes. MQ conversion (converting MQ back to detectable coherence) efficiency can significantly be enhanced with DFS (Double Frequency Sweep) or FAM (Fast Amplitude Modulation) type pulses instead of rectangular pulse irradiation (Goldbourt and Madhu, 2002). In contrary to conversion, it is more challenging to enhance MQ excitation in MQMAS experiments, since most methods result in distorted lineshapes (Goldbourt and Madhu, 2002; Lim and Grey, 1998). In the present work MQ excitation of single crystals was studied, and the understanding of the process led to a principle, which was extended to the excitation of powder samples as well. The resulting method was implemented into the MQMAS sequence to enhance MQ excitation of powder samples under MAS condition. The new sequence called SFAM (Shifted Fast Amplitude Modulation) can provide high enhancements at low RF powers (ϵ>4 at νrf=40 kHz) compared to rectangular pulses. Although simulated lineshapes of SFAM predict only minor deviations from ideal lineshapes, experimentally obtained lineshapes along the anisotropic dimension show rather strong distortions. SFAM is relatively simple to optimize, and shows robustness with respect to the miscalibration or inhomogeneity of the RF power as well as to other parameters of the pulse scheme. A good agreement was found between numerically and experimentally optimized parameters.

An alternative solution for computer controlled tuning and matching of existing NMR probes.

Tuning and matching of NMR probes is necessary for many fields of NMR application including temperature dependent NMR, thermoporometry and cryoporometry, or when significantly different types of samples are measured in automation using sample changers. Mismatch of the probe is an especially critical issue in the case of high magnetic fields, polar or ionic solvents, or extreme thermal conditions. Careful tuning is particularly important for quantitative NMR measurements. Manual tuning and matching of the NMR probe is not possible in the case of automated or remotely controlled measurements. Spectrometer manufacturers offer modern probes equipped with automatic tuning/matching mechanics, like Bruker ATM™, suitable for these experiments. The disadvantages of probes with built-in ATM™ are the significantly higher price, and the non-detachable and non-portable construction. Computer controlled tuning and matching is highly desirrable in solid state NMR since no industrial solution has been developed yet for MAS NMR probes. We present an alternative solution for computer controlled tuning and matching of existing Bruker probes. Building costs are significantly lower, since only commercially available components and ICs are used.

PIC microcontroller based external fast analog to digital converter to acquire wide-lined solid NMR spectra by BRUKER DRX and Avance-I spectrometers.

Concerning many former liquid or hybrid liquid/solid NMR consoles, the built in Analog-to-Digital Converters (ADCs) are incapable of digitizing the fids at sampling rates in the MHz range. Regarding both strong anisotropic interactions in the solid state and wide chemical shift dispersion nuclei in solution phase such as (195)Pt, (119)Sn, (207)Pb etc., the spectrum range of interest might be in the MHz range. As determining the informative tensor components of anisotropic NMR interactions requires nonlinear fitting over the whole spectrum including the asymptotic baseline, it is prohibited by low sampling rates of the ADCs. Wide spectrum width is also useful in solution NMR, since windowing of wide chemical shift ranges is avoidable. We built an external analog to digital converter with 10 MHz maximal sampling rate, which can work simultaneously with the built in ADC of the spectrometer. The ADC was tested on both Bruker DRX and Avance-I NMR consoles. In addition to the analog channels it only requires three external digital lines of the NMR console. The ADC sends data to PC via USB. The whole process is controlled by software written in JAVA which is implemented under TopSpin.