Related papers: A note on the spectral mapping theorem of quantum …
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the…
Gramsch and Lay [10] gave spectral mapping theorems for the Dunford-Taylor calculus of a closed linear operator $T$, $$\widetilde{\sigma}_i(f(T)) = f(\widetilde{\sigma}_i(T)), $$ for several extended essential spectra…
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…
Andreka and her colleagues have described various geometrically inspired first-order theories of special and general relativity, while Szekely's PhD dissertation focuses on an intermediate logic of accelerated observers. In this paper we…
The lackadaisical quantum walk is a discrete-time, coined quantum walk on a graph with a weighted self-loop at each vertex. It uses a generalized Grover coin and the flip-flop shift, which makes it equivalent to Szegedy's quantum Markov…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
We analyze the equivalence between discrete-time coined quantum walks and Szegedy's quantum walks. We characterize a class of flip-flop coined models with generalized Grover coin on a graph $\Gamma$ that can be directly converted into…
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…
The aim of this paper is to show a connection between an extended theory of statistical experiments on the one hand and the foundation of quantum theory on the other hand. The main aspects of this extension are: One assumes a hyperparameter…
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…
In this paper we prove and apply a theorem of spectral expansion for Schwartz linear operators which have an S-linearly independent Schwartz eigenfamily. This type of spectral expansion is the analogous of the spectral expansion for…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
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…
We consider the Szegedy walk on graphs adding infinite length tails to a finite internal graph. We assume that on these tails, the dynamics is given by the free quantum walk. We set the $\ell^\infty$-category initial state so that the…
We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing…
This paper is a continuation of the paper \cite{W} by the third author, which studied quantum walks with special long-range perturbations of the coin operator. In this paper, we consider general long-range perturbations of the coin operator…
This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…
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.…
Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…