The Multi-Agent Programming Contest: A r\'esum\'e

The Multi-Agent Programming Contest, MAPC, is an annual event organized since 2005 out of Clausthal University of Technology. Its aim is to investigate the potential of using decentralized, autonomously acting intelligent agents, by providing a complex scenario to be solved in a competitive environment. For this we need suitable benchmarks where agent-based systems can shine. We present previous editions of the contest and also its current scenario and results from its use in the 2019 MAPC with a special focus on its suitability. We conclude with lessons learned over the years.Comment: Submitted to the proceedings of the Multi-Agent Programming Contest 2019, to appear in Springer Lect. Notes Computer Challenges Series https://www.springer.com/series/1652

Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

Recurrence for discrete time unitary evolutions

We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to \phi. We also show that in the recurrent case the expected first return time is an integer or infinite, for which we give a topological interpretation. A key role in our theory is played by the first arrival amplitudes, which turn out to be the (complex conjugated) Taylor coefficients of the Schur function of the spectral measure. On the one hand, this provides a direct dynamical interpretation of these coefficients; on the other hand it links our definition of first return times to a large body of mathematical literature.Comment: 27 pages, 5 figures, typos correcte

Derivatives of 1-phenyl-3-methylpyrazol-2-in-5-thione and their oxygen analogues in the crystalline phase and their tautomeric transformations in solutions and in the gas phase

1-Phenyl-3-methylpyrazol-2-in-5-thione, crystallised from methanol, was shown to exist in the tautomeric NH-form, stabilised by intermolecular NH···S hydrogen bonds. In solutions, however, the molecule is found predominantly as the SH-tautomer, accompanied (in low-polar solvents) by a small amount of the CH-tautomer. 1-Phenyl-3-methyl-4-benzoylpyrazol-2-in-5-thione occurs in the crystal as well as in solution in the SH-tautomeric form, stabilised by an intramolecular SH···O bridge. In dimethylsulfoxide solution indications were found for an additional SH-tautomer in a conformation lacking the intramolecular H-bridge. The structure of 1-phenyl-3-methylpyrazol-2-in-5-one was redetermined by X-ray single crystal diffraction at 120°K in order to obtain more accurate geometry and hydrogen bonding parameters. © 2001 Elsevier Science B.V. All rights reserved

Random Time-Dependent Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ when the sequence of unitary updates is given by an i.i.d. sequence of random matrices. When averaged over the randomness, this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a diffusive behavior with a diffusion matrix we compute. A moderate deviation principle is also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. A generalization to unitary updates distributed according to a Markov process is also provided. An example of i.i.d. random updates for which the analysis of the distribution can be performed without averaging is worked out. The distribution also displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. A large deviation principle is shown to hold for this example. We finally show that, in general, the expectation of the random diffusion matrix equals the diffusion matrix of the averaged distribution.Comment: Typos and minor errors corrected. To appear In Communications in Mathematical Physic

Experimental simulation and limitations of quantum walks with trapped ions

We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (PRA 2002) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (PRL 2009), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb--Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higher-order terms of the quantum evolution. It turns out that these become dominant after a few steps already, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that the new scheme is not subject to the above-mentioned restrictions, and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing the protocol with state-of-the-art techniques should allow for substantially increasing the number of steps to 100 and beyond and should be extendable to higher-dimensional QWs.Comment: 29 pages, 15 figue

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Intertemporal Efficiency and Equity Under Hyperbolic Preferences. Ex Ante Versus Ex Post Procrastination

In this paper I extend the well known result that a hyperbolically discounting agent postpones costs into the future. If society has hyperbolic inter-temporal preferences, it may be optimal from an ex ante point of view to postpone structural change from a polluting to a non polluting production sector into the future (ex ante procrastination). The consequences of ex ante procrastination are discussed for three different behavioral patterns. I show that, depending on the assumed behavioral regime, ex ante procrastination may lead to ex post procrastination, i.e. de facto no investment in the non polluting sector is undertaken over the whole time horizon, although investment was optimal from an ex ante point of view. Furthermore, the ex post implemented investment plan may be inefficient if it is not dictatorial. Hence, in the case of hyperbolic preferences there is a potential trade-off between inter-temporal efficiency and equity