Can math beat gamers in Quantum Moves?

In a recent work on quantum state preparation, S{\o}rensen and colleagues explore the possibility of using video games to help design quantum control protocols. The authors present a game called "Quantum Moves" in which gamers have to move an atom from A to B by means of optical tweezers. They report that, players succeed where purely numerical optimization fails [1]. Moreover, by harnessing the player strategies they can outperform the most prominent established numerical methods [1]. The aim of this manuscript is to analyze the problem in detail and show that those claims are untenable. In fact a simple stochastic local optimization method can easily find very good solutions to this problem in a few 1000 trials rather than the astronomical $7.4\times 10^{8}$ trials of the most successful optimization method reported in [1]. Next, counter-diabatic driving is used to generate protocols without resorting to numeric optimization; the protocols are shown to outperform virtually all players. The analysis moreover results in an accurate analytic estimate of the quantum speed limit which, apart from zero-point motion, is shown to be entirely classical in nature. The latter might explain why gamers are remarkably good at the game

Stationary ensemble approximations of dynamic quantum states: Optimizing the Generalized Gibbs Ensemble

We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to the time dependent density matrix. Our procedure allows for a systematic construction of the GGE by a constrained minimization of the distance between the latter and the true state. Moreover, we show that the entropy of the GGE is a direct measure for the quality of the approximation. We apply our method to a quenched hard core bose gas. In contrast to the standard GGE, our correlated GGE properly describes the higher order correlation functions

Self-energy correction to dynamic polaron response

We present the first order self-energy correction to the linear response coefficients of polaronic systems within the truncated phase space approach developed by the present authors. Due to the system-bath coupling, the external pertubation induces a retarded internal field which dynamically screens the external force. Whereas the effect on the mobility is of second order, dynamical properties such as the effective mass and the optical absorption are modified in first order. The Fr\"ohlich polaron is used to illustrate the results

Breaks, cuts, and patterns

Wegeneralize the concept of a break by considering pairs of arbitrary rounds.Weshow that a set of homeaway patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P = NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.status: publishe

Variational Truncated Wigner Approximation

In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator