Related papers: Decoherence in Two-Dimensional Quantum Random Walk…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean…
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution…
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum…
In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the…
An overview is presented of recent work on some statistical problems on multiparticle random walks. We consider a Euclidean, deterministic fractal or disordered lattice and N >> 1 independent random walkers initially (t=0) placed onto the…
We introduce the quantum Levy walk to study transport and decoherence in a quantum random model. We have derived from second order perturbation theory the quantum master equation for a \textit{Levy-like particle}that moves along a lattice…
We investigate quantum walks which play an important role in the modelling of many phenomena. The detailed and thorough description is given to the discrete quantum walks on a line, where the total quantum state consists of quantum states…
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.
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
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…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
Quantum walks represent an excellent testbed for investigating the interplay between unitary coherent and incoherent dissipative processes. Thanks to photonic quantum interferometers of considerable size, experimental studies could be…