Related papers: A computable branching random walk for the many-bo…
The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging however; a…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
The atomic motion controls important features of materials, such as thermal transport, phase transitions, and vibrational spectra. However, the simulation of ionic dynamics is exceptionally challenging when quantum fluctuations are relevant…
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…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
Using quantum parallelism on random walks as original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers -- with internal degrees of freedom which serve as…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
Quantum magnets are never short of novel and fascinating dynamics, yet its simulation by classical computers requires exponentially-scaled computation resources, which renders the research on large-scale many-body dynamics fiendishly…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…
The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. Finding the steady state probability…
In this study we show a way of achieving the reverse evolution of n-dimensional quantum walks by introducing interventions on the coin degree of freedom during the forward progression of the coin-walker system. Only a single intervention is…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the…
We put forward a user-friendly framework of the truncated Wigner approximation (TWA) for dissipative quantum many-body systems. Our approach is computationally affordable and it features a straightforward implementation. The leverage of the…