Related papers: Decoherence and classicalization of continuous-tim…
In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple…
We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}= L + \lambda L^2$, being $L$ the Laplacian matrix of the underlying graph and being the perturbation $\lambda L^2$ motivated by its…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
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…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the…
We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk, obtaining explicit macroscopic evolution equations for a three state model in the presence of decoherence. While continuum limits of two state…
Open quantum walks (OQWs) describe a quantum walker on an underlying graph whose dynamics is purely driven by dissipation and decoherence. Mathematically, they are formulated as completely positive trace preserving (CPTP) maps on the space…
A continuous-time quantum walk (CTQW) is sedentary if the return probability in the starting vertex is close to one at all times. Recent results imply that, when starting from a maximal degree vertex, the CTQW dynamics generated by the…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
A distinguishability operator is defined for the continuous-time quantum walk (CTQW) of a bipartite quantum walker on two simply connected graphs, $W_{G_i,G_j} = U_{G_i}\left(t\right) \otimes U_{G_j}\left(t'\right) - U_{G_j}\left(t'\right)…
History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
Quantum-circuit implementations of continuous-time quantum walks (CTQWs) can provide an efficient route to model graph-based algorithms. However, constructing circuits that faithfully reproduce CTQW dynamics across arbitrary graphs remains…
This manuscript gathers and subsumes a long series of works on using QW to simulate transport phenomena. Quantum Walks (QWs) consist of single and isolated quantum systems, evolving in discrete or continuous time steps according to a…
In this work we study several models of decoherence and how different quantum maps and algorithms react when perturbed by them. Following closely Ref. [1], generalizations of the three paradigmatic one single qubit quantum channels (these…