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The phenomenon of stabilization of highly excited states of a hydrogen atom in a strong monochromatic field is discussed. An approximate description of the dynamics from the introduction of the Kramers map allows one to understand the main properties of this phenomenon through analogy with the Kepler map. The analogy between the stabilization and the channneling of particles in a crystal is also discussed.

We report the results of analytical and numerical investigations on the ionization of a classical atom in a strong, linearly polarized, monochromatic field. We show that the ionization probability decreases with increasing field intensity at field amplitudes much larger than the classical chaos border. This effect should be observable in real laboratory experiments.

We consider the evolution of waves governed by a periodically perturbed nonlinear Schr\"odinger equation. The system is a nonlinear generalization of the quantum kicked rotator. We study the soliton chaotic motion, its destruction and reversibility properties. It is found that nonlinearity does not destroy the quantum suppression of chaotic diffusion.

There is an error in the numerical implementation of the static imperfection model Eq. 21 in the paper , which resulted in an effective reduction of the disorder strength by approximately a factor of 2 for the cases of generic and correlated imperfection models. However, there was no error for the correlated imperfection model with all qubits in the control and computational register coupled by interactions. After correction of the error the dependence of the inverse participation ratio IPR on see Fig. 1 a remains qualitatively the same as in Fig. 6 of the paper. Nevertheless, the values of c fluctuate strongly depending on the arithmetic properties of x, r, and N. These fluctuations remain quite strong even after increasing the number of data points see Table II in 1 and Fig. 1 b as compared to Table I and Fig. 10 of the paper . The algebraic fit c=B / log2 N gives ln B=0.068±0.105, =1.420±0.054 for the generic imperfection model, ln B=0.70±0.19, =1.897±0.097 for the correlated imperfection model, and ln B=−1.22±0.13, =1.523±0.068 for the correlated imperfection model with all qubits coupled. We attribute the deviations of the exponents from the theoretical values to finite size effects in number of qubits and the significant arithmetic fluctuations of c as a function of r, x, and N. In addition after publication we realized there were two typos in Eqs. 22 and 26 which should read

We present a quantum algorithm that allows one to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens additional possibilities for investigation of macroscopic quantum tunneling and realization of semiclassical Schroedinger cat oscillations [E. Schroedinger, Naturwissenschaften 32, 807 (1935)]. Our numerical studies determine the decoherence rate induced by noisy gates for these oscillations and propose a suitable parameter regime for their experimental implementation.

We present theoretical and numerical results showing that the probability distribution on energy levels of highly excited hydrogen atoms produced by a monochromatic field should be exponentially localized in the number of absorbed photons. These results allow for a new interpretation of underthreshold ionization and also for an estimate of the ionization rate.