Related papers: Discrete Lorentz covariance for Quantum Walks and …
Quantum walks (QWs) describe particles evolving coherently on a lattice. The internal degree of freedom corresponds to a Hilbert space, called coin system. We consider QWs on Cayley graphs of some group $G$. In the literature,…
We use discrete-event simulation on a digital computer to study two different models of experimentally realizable quantum walks. The simulation models comply with Einstein locality, are as "realistic" as the one of the simple random walk in…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
A Quantum Cellular Automaton (QCA) is essentially an operator driving the evolution of particles on a lattice, through local unitaries. Because $\Delta_t=\Delta_x = \epsilon$, QCAs constitute a privileged framework to cast the digital…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
Discrete-time quantum walks (DTQWs) provide a convenient platform for a realisation of many topological phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian. Nevertheless, researchers…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a…
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 family of 2D discrete-time quantum walks (DTQWs) is presented and shown to coincide, in the continuous limit, with the Dirac dynamics of a spin 1/2 fermion coupled to a constant and uniform magnetic field. Landau levels are…
Quantum-dot cellular automata (QCA) is a likely candidate for future low power nano-scale electronic devices. Sequential circuits in QCA attract more attention due to its numerous application in digital industry. On the other hand,…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
The interest in quantum walks has been steadily increasing during the last two decades. It is still worth to present new forms of quantum walks that might find practical applications and new physical behaviors. In this work, we define…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
A quantum cellular automaton (QCA) or a causal unitary is by definition an automorphism of local operator algebra, by which local operators are mapped to local operators. Quantum circuits of small depth, local Hamiltonian evolutions for…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the…
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical…
Quantum-dot cellular automata (QCAs) offer a diffusive computing paradigm with picosecond transmission speed, making them an ideal candidate for moving diffusive computing to real-world applications. By implementing a trainable associative…
This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a…