Related papers: Quantum walk of two anyons across a statistical bo…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
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…
Each step in a quantum random walk is typically understood to have two basic components; a `coin-toss' which produces a random superposition of two states, and a displacement which moves each component of the superposition by different…
Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson…
We study the domain walls which form when Bose condensates acquire a double-well dispersion. Experiments have observed such domain walls in condensates driven across a $\mathbb{Z}_2$ symmetry-breaking phase transition in a shaken optical…
A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A…
We theoretically investigate transport signatures of quantum interference in highly symmetric double quantum dots in a parallel geometry and demonstrate that extremely weak symmetry-breaking effects can have a dramatic influence on the…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
Switching of a single plasmon interacting with equally spaced quantum dots coupled to one-dimensional surface plasmonic waveguide is investigated theoretically via the real-space approach. We showed that the transmission and reflection of a…
We solve exactly the non-equilibrium dynamics of two discrete random walkers moving in channels with transition rates $p \neq q$ that swap positions at a rate $s$. We compute exactly the joint probability distribution $P_{n,m}(t)$ for the…
The many-body state of carriers confined in a quantum dot is controlled by the balance between their kinetic energy and their Coulomb correlation. In coupled quantum dots, both can be tuned by varying the inter-dot tunneling and…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher…
We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
Quantum mechanics introduces the possibility for particles to move in a direction opposite to their momentum -- a counter-intuitive and classically impossible phenomenon known as quantum backflow. The magnitude of this effect is relatively…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
We report on the state of the art of quantum walk experiments with neutral atoms in state-dependent optical lattices. We demonstrate a novel state-dependent transport technique enabling the control of two spin-selective sublattices in a…
We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…