Nonlinear classical dissipative systems present a rich phenomenology in their “route to chaos,” including period doubling, i.e., the system evolves with a period which is twice that of the driving. However, typically the attractor of a periodically driven quantum open system evolves with a period which exactly matches that of the driving. Here, we analyze a periodically driven many-body open quantum system whose classical correspondent presents period doubling. We show that by studying the dynamical correlations, it is possible to show the occurrence of period doubling in the quantum (period-one) steady state. We also discuss that such systems are natural candidates for clean and intrinsically robust Floquet time crystals.

Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today's available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other commonly used models with significantly less gates and also provide insight on the theoretical gap between quantum reservoir computing and the theory of quantum states' complexity.

There is a remarkable interest in the study of out-of-time ordered correlators (OTOCs) that goes from many-body theory and high-energy physics to quantum chaos. In the latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics. The exponential growth has been verified for many paradigmatic maps and systems. However, less is known for multipartite cases. On the other hand, the recently introduced Wigner separability entropy (WSE) and its classical counterpart provide a complexity measure that treats equally quantum and classical distributions in phase space. We compare the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic, double elliptic, and mixed. In all cases, we find that the OTOCs and the WSE have essentially the same behavior, providing a complete characterization in generic bipartite systems and at the same time revealing them as very good measures of quantum complexity for phase-space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Rényi entropy and OTOCs.

We extend the semiclassical theory of short periodic orbits [M. Novaes et al., Phys. Rev. E 80, 035202(R) (2009)] to partially open quantum maps, which correspond to classical maps where the trajectories are partially bounced back due to a finite reflectivity $R$. These maps are representative of a class that has many experimental applications. The open scar functions are conveniently redefined, providing a suitable tool for the investigation of this kind of system. Our theory is applied to the paradigmatic partially open tribaker map. We find that the set of periodic orbits that belongs to the classical repeller of the open map ($R=0$) is able to support the set of long-lived resonances of the partially open quantum map in a perturbative regime. By including the most relevant trajectories outside of this set, the validity of the approximation is extended to a broad range of $R$ values. Finally, we identify the details of the transition from qualitatively open to qualitatively closed behavior, providing an explanation in terms of short periodic orbits.

We investigate the ratchet current that appears in a kicked Hamiltonian system when the period of the kicks corresponds to the regime of quantum resonance. In the classical analog, a spatial-temporal symmetry should be broken to obtain a net directed current. It was recently discovered that in quantum resonance the temporal symmetry can be kept, and we prove that breaking the spatial symmetry is a necessary condition to find this effect. Moreover, we show numerically and analytically how the direction of the motion is dramatically influenced by the strength of the kicking potential and the value of the period. By increasing the strength of the interaction this direction changes periodically, providing us with un-expected source of current reversals in this quantum model. These reversals depend on the kicking period also, though this behavior is theoretically more difficult to analyze. Finally, we generalize the discussion to the case of a nonuniform initial condition.

It has been recently found that the so-called isoperiodic stable structures (ISSs) have a fundamental role in the classical current behavior of dissipative ratchets [Phys. Rev. Lett. 106, 234101 (2011).]. Here I analyze their quantum counterparts, the quantum ISSs (QISSs), which have a fundamental role in the quantum current behavior. QISSs have the simple attractor shape of those ISSs which settle down in short times. However, in the majority of the cases they are strongly different from the ISSs, looking approximately the same as the quantum chaotic attractors that are at their vicinity in parameter space. By adding thermal fluctuations of the size of $\hbar${}eff to the ISSs I am able to obtain very good approximations to the QISSs. I conjecture that in general, quantum chaotic attractors could be well approximated by means of just the classical information of a neighboring ISS plus thermal fluctuations. I expect to find this behavior in quantum dissipative systems in general.