Related papers: The Wigner branching random walk: Efficient implem…
A branching random walk algorithm for the many-body Wigner equation and its numerical applications for quantum dynamics in phase space are proposed and analyzed. After introducing an auxiliary function, the (truncated) Wigner equation is…
The analysis of a physical problem simplifies considerably when one uses a suitable coordinate system. We apply this approach to the discrete-time quantum walks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wigner walks),…
A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
Particle swarm optimization comes under lot of changes after James Kennedy and Russell Eberhart first proposes the idea in 1995. The changes has been done mainly on Inertia parameters in velocity updating equation so that the convergence…
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total interaction of each particle with the $N-1$ other particles by…
We introduce quantized bipartite walks, compute their spectra, generalize the algorithms of Grover \cite{g} and Ambainis \cite{amb03} and interpret them as quantum walks with memory. We compare the performance of walk based classical and…
The stochastic solutions to the Wigner equation, which explain the nonlocal oscillatory integral operator $\Theta_V$ with an anti-symmetric kernel as {the generator of two branches of jump processes}, are analyzed. All existing branching…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
Our objective is to sample the node set of a large unknown graph via crawling, to accurately estimate a given metric of interest. We design a random walk on an appropriately defined weighted graph that achieves high efficiency by…
Quantization of a random-walk model is performed by giving a qudit (a multi-component wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the…
Random walk based sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as GMD modify the topology of…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by…
Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. Nevertheless, in practice the number of steps required to achieve uniformly distributed samples is rather high. We propose…
"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…