Dynamical decoupling

Gianturco F. A., Serna S., Sanna N. Dynamical decoupling in the quantum calculations of transport coefficients. I. Coupled state results for He-N2 gaseous mixture, Mol. Phys. 74, 1071-87 (1991). 

This paper extends previous studies on the control of a polystyrene reactor by including (1) a dynamic lag on the manipulated flow rate to improve dynamic decoupling, and (2) pole placement via state variable feedback to improve overall response time. Included from the previous work are optimal allocation of resources and steady state decoupling. Simulations on the non-linear reactor model show that response times can be reduced by a factor of 6 and that for step changes in desired values the dynamic decoupling is very satisfactory. 

A control algorithm has been derived that has improved the dynamic decoupling of the two outputs MW and S while maintaining a minimum "cost of operation" at the steady state. This algorithm combines precompensation on the flow rate to the reactor with state variable feedback to improve the overall speed of response. Although based on the linearized model, the algorithm has been demonstrated to work well for the nonlinear reactor model. 

Another practical tool is dynamical decoupling, a technique that uses sequences of fast qubit rotations to mitigate the effects of decoherence. The pulse sequences are designed such that the interactions of each qubit with its environment tend to average out [34, 35]. While still a major concern, decoherence may thus not be the strong impediment it originally seemed to represent for the advent of QC. 

Dynamical decoupling DD is one of the best known approaches to combat decoherence, especially dephasing [39-52,55,56]. We present its essential aspects and how it can be incorporated into the general framework described above. 

Aperiodic DD sequences such as Uhrig dynamical decoupling (UDD) [55] suppress low-frequency components (to the left of the main peak) in the system spectrum, which retain the system-bath coupling even if the main peak of the system spectrum has been shifted beyond the bath cutoff frequency (Figure 4.11). The plots indicate that this suppression of low-frequency components is achieved at the price of a smaller shift of the main peak, that is, shifting the main peak beyond a given cutoff requires more pulses in UDD than in FDD. Note that optimized DD sequences with improved asymptotics exist [91], which we will not consider here. 

For the calculation of the normal mode spectra external and internal coordinates were assumed to be dynamically decoupled. Translational and rotational coordinates were extracted from the trajectories while all vibrational coordinates were set to zero. Dynamical matrices were set up for 50 configurations generated by molecular dynamics simulation. Long-range Coulombic interactions were treated using the Ewald summation technique. In Figure 2 the instantaneous normal mode spectra are depicted while in Table 3 some of their integral properties are compiled. 

Future studies are aimed at simple dynamic decoupling so that transient swings of the "non-changing" parameters can be reduced. 

Conformational motions have been studied." Other line shape experiments include 13c 481,482 P in freeze-dried liposomes,DNA," " cytochrome" and spectra of lipids. The complex dynamics in lipid bilayers was studied by H-2D exchange." Dynamic decoupling found its application" as well as multipulse experiments." SLF experiments like LG-CP," DIPSHIFT" " and determine the amplitudes of fast... 

We expand the summations over the internal modes emd recognise that in the harmonic approximation the modes are dynamically decoupled and no cross terms can result. The sum of the arguments in the exponential... 

These nonresonant couplings may be dealt with by a Van Vleck (see Section 4.2) or contact transformation (Nielsen, 1951), which folds their effects into systematically quasi-degenerate groups of states called polyads (see Section 9.4.5). The polyad Heff fit model accounts accurately for the observed energy levels (and many other properties) of an entire family of scaling-related polyads. In effect, the dimensionality of the exact H is drastically reduced in the polyad Heff. This reduction is due to the existence of several approximate constants of motion which permit H to be block diagonalized into families of dynamically decoupled polyad Heff matrices. 

It is interesting that the band due to Vas(C=C) has not been observed experimentally, or calculated on the twisted model (Figure 8.11). This is explained on the basis of increasing dynamic decoupling upon rotation of the motions of the C=C bonds located on different rings. By contrast, this normal mode displays considerable IR activity for the TT-Me2T [84]. 

Gupta AK, Tembulkar JM (1984a) Dynamic decoupling of secondary systems. Nucl Eng Des 81 359-373 Gupta AK, Tembulkar JM (1984b) Dynamic decoupling of multiply connected MDOF secondary systems. Nucl Eng Des 81 375-383... 

Fig. 3 S i P nuclear spin coherence with XY-16 dynamic decoupling. The 1.9 K and 4.2 K data were fit using biexponentials, with the longer component set to 180 min. Reprinted" from K. Saeedi eta/.. Science, 2013, 342, 830. Reprinted with permission from AAAS.

The proximity of the donor to an oxide interface and nearby electrostatic gates did not introduce additional decoherence. Some coherence measurements are shown in Fig. 5, and the same group have even more recently reported electron Tz times of around 1 ms (with a spin echo) and 0.56 s (with dynamic decoupling), as well as a Tz time for the nucleus with a neutral donor of 1.5 ms for one device and 20 ms for another (both with a spin echo). Ionizing the donor provided a nuclear Tz time of 1.75 s (spin echo) and 35.6 s (with dynamic decoupling). These times are shorter than those measured in bulk Si samples for electrons and nuclei,which was attributed to Johnson-Nyquist thermal noise due to the microwave source. High fidelity control pulses were achieved, reaching 97% for the electron and 99.99% for the nuclear spin. 

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