On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

Phase ordering in chaotic map lattices with conserved dynamics

Dynamical scaling in a two-dimensional lattice model of chaotic maps, in contact with a thermal bath, is numerically studied. The model here proposed is equivalent to a conserved Ising model with coupligs which fluctuate over the same time scale as spin moves. When couplings fluctuations and thermal fluctuations are both important, this model does not belong to the class of universality of a Langevin equation known as model B; the scaling exponents are continuously varying with the temperature and depend on the map used. The universal behavior of model B is recovered when thermal fluctuations are dominant.Comment: 6 pages, 4 figures. Revised version accepted for publication on Physical Review E as a Rapid Communicatio

Experimental Study of the Shortest Reset Word of Random Automata

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length of the shortest reset word of a random finite automaton with $n$ states and 2 input letters with high probability is sublinear with respect to $n$ and can be estimated as $1.95 n^{0.55}.

Very-high energy gamma-ray astronomy: A 23-year success story in high-energy astroparticle physics

Very-high energy (VHE) gamma quanta contribute only a minuscule fraction - below one per million - to the flux of cosmic rays. Nevertheless, being neutral particles they are currently the best "messengers" of processes from the relativistic/ultra-relativistic Universe because they can be extrapolated back to their origin. The window of VHE gamma rays was opened only in 1989 by the Whipple collaboration, reporting the observation of TeV gamma rays from the Crab nebula. After a slow start, this new field of research is now rapidly expanding with the discovery of more than 150 VHE gamma-ray emitting sources. Progress is intimately related with the steady improvement of detectors and rapidly increasing computing power. We give an overview of the early attempts before and around 1989 and the progress after the pioneering work of the Whipple collaboration. The main focus of this article is on the development of experimental techniques for Earth-bound gamma-ray detectors; consequently, more emphasis is given to those experiments that made an initial breakthrough rather than to the successors which often had and have a similar (sometimes even higher) scientific output as the pioneering experiments. The considered energy threshold is about 30 GeV. At lower energies, observations can presently only be performed with balloon or satellite-borne detectors. Irrespective of the stormy experimental progress, the success story could not have been called a success story without a broad scientific output. Therefore we conclude this article with a summary of the scientific rationales and main results achieved over the last two decades.Comment: 45 pages, 38 figures, review prepared for EPJ-H special issue "Cosmic rays, gamma rays and neutrinos: A survey of 100 years of research

Search for the QCD critical point at SPS energies

Lattice QCD calculations locate the QCD critical point at energies accessible at the CERN Super Proton Synchrotron (SPS). We present average transverse momentum and multiplicity fluctuations, as well as baryon and anti-baryon transverse mass spectra which are expected to be sensitive to effects of the critical point. The future CP search strategy of the NA61/SHINE experiment at the SPS is also discussed.Lattice QCD calculations locate the QCD critical point at energies accessible at the CERN Super Proton Synchrotron (SPS). We present average transverse momentum and multiplicity fluctuations, as well as baryon and anti-baryon transverse mass spectra which are expected to be sensitive to effects of the critical point. The future CP search strategy of the NA61/SHINE experiment at the SPS is also discussed

NA49 Results on Single Particle and Correlation Measurements in Central Pb+Pb Collisions

Single-particle spectra and two-particle correlation functions measured by the NA49 collaboration in central Pb+Pb collisions at 158 GeV/nucleon are presented. These measurements are used to study the kinetic and chemical freeze-out conditions in heavy ion collisions. We conclude that large baryon stopping, high baryon density and strong transverse radial flow are achieved in central Pb+Pb collisions at the SPS.Single-particle spectra and two-particle correlation functions measured by the NA49 collaboration in central Pb+Pb collisions at 158 GeV/nucleon are presented. These measurements are used to study the kinetic and chemical freeze-out conditions in heavy ion collisions. We conclude that large baryon stopping, high baryon density and strong transverse radial flow are achieved in central Pb+Pb collisions at the SPS

Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

Peer reviewe

Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos, and b quarks

Peer reviewe