Related papers: Quantum walk on distinguishable non-interacting ma…
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
Many paradoxes of quantum mechanics come from the fact that a quantum system can possess different features at the same time, such as in wave-particle duality or quantum superposition. In recent delayed-choice experiments, a quantum…
The possibility of fine-tuning the couplings between optical modes is a key requirement in photonic circuits for quantum simulations. In these architectures, emulating the long-time evolution of particles across large lattices requires…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can…
We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schr\"odinger-Heisenberg…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
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…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum…
We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin…
We present the method of walk-sum to study the real-time dynamics of interacting quantum many-body systems. The walk-sum method generates explicit expressions for any desired pieces of an evolution operator U independently of any others.…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…
We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles. The main results are devoted to the study of the generating function and the limiting…