Related papers: Optimal co-adapted coupling for the symmetric rand…
We consider one-dimensional excited random walks with finitely many cookies at each site. There are certain natural monotonicity results that are known for the excited random walk under some partial orderings of the cookie environments. We…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
We consider the coupling from the past implementation of the random-cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster…
Full control over the dynamics of interacting, indistinguishable quantum particles is an important prerequisite for the experimental study of strongly correlated quantum matter and the implementation of high-fidelity quantum information…
We apply theoretically open-loop quantum optimal control techniques to provide methods for the verification of various quantum coherent transport mechanisms in natural and artificial light-harvesting complexes under realistic experimental…
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its…
Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…
Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
This work focuses on the quantum mixing time, which is crucial for efficient quantum sampling and algorithm performance. We extend Richter's previous analysis of continuous time quantum walks on the periodic lattice $\mathbb{Z}_{n_1}\times…
Control scenarios have been identified where the use of randomized design may substantially improve the performance of dynamical decoupling methods [L. F. Santos and L. Viola, Phys. Rev. Lett. {\bf 97}, 150501 (2006)]. Here, by focusing on…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a…
We study the classical cubic-lattice double dimer model, consisting of two coupled replicas of the close-packed dimer model, using a combination of theoretical arguments and Monte Carlo simulations. Our results establish the presence of a…
We study a large class of amenable locally compact groups containing all solvable algebraic groups over a local field and their discrete subgroups. We show that the isoperimetric profile of these groups is in some sense optimal among…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…
Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…
We study certain self-interacting walks on the set of integers, that choose to jump to the right or to the left randomly but influenced by the number of times they have previously jumped along the edges in the finite neighbourhood of their…