Related papers: Continuum Limits of the 1D Discrete Time Quantum W…
The two major discrete time formulations for quantum walks, coined and scattering, are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology (PRA {\bf 80}, 052301 (2009)). Although the proof explicit…
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…
Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental…
A relativistic Wigner function for free Discrete Time Quantum Walks (DTQWs) on the square $2D$ space-time lattice is defined. Useful concepts such as discrete derivatives and discrete distributions are also introduced. The transport…
In this paper, we study the recurrence of Open Quantum Walks induced by finite-dimensional coins on the line ($\mathbb{Z}$) and on the grid ($\mathbb{Z}^2$). Two versions are considered: discrete-time open quantum walks (OQW) and…
The continuous limit of quantum walks (QWs) on the line is revisited through a recently developed method. In all cases but one, the limit coincides with the dynamics of a Dirac fermion coupled to an artificial electric and/or relativistic…
Discrete-time quantum walks (QWs) represent robust and versatile platforms for the controlled engineering of single particle quantum dynamics, and have attracted special attention due to their algorithmic applications in quantum information…
Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom---called the coin and represented by a finite-dimensional Hilbert space---is associated to each node. Scalar quantum walks are QWs with…
In this dissertation we demonstrate that the continuous-time quantum walk models remain powerful for nontrivial graph structures. We consider two aspects of this problem. First, it is known that the standard Continuous-Time Quantum Walk…
Quantum processes of inherent dynamical nature, such as quantum walks (QWs), defy a description in terms of an equilibrium statistical physics ensemble. Up to now, it has remained a key challenge to identify general principles behind the…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
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…
Implementation of discrete-time quantum walk (DTQW) with superconducting qubits is difficult since on-chip superconducting qubits cannot hop between lattice sites. We propose an efficient protocol for the implementation of DTQW in circuit…
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.
For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that…
Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to…