Simone Montangero — Page 9

arXiv2001

Efficient Quantum Computing of Complex Dynamics

We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The numerical study of the effect of static imperfections in the quantum computer hardware shows that the main elements of the phase space structures are accurately reproduced up to a time scale which is polynomial in the number of qubits. The errors generated by these imperfections are more dangerous than the errors of random noise in gate operations.

quant-ph↗

arXiv1999

Non-extensive thermodynamics and stationary processes of localization

We focus our attention on dynamical processes characterized by an entropic index Q<1. According to the probabilistic arguments of Tsallis and Bukman [C.Tsallis, D.J. Bukman, Phys. Rev. E 54,R2197 (1996)] these processes are subdiffusional in nature. The non-extensive generalization of the Kolmogorov-Sinai entropy yielding the same entropic index implies the stationary condition. We note, on the other hand, that enforcing the stationary property on subdiffusion has the effect of producing a localization process occurring within a finite time scale. We thus conclude that the stationary dynamic processes with Q<1 must undergo a localization process occurring at finite time. We check the validity of this conclusion by means of a numerical treatment of the dynamics of the logistic map at the critical point.

cond-mat.stat-mech↗