Related papers: Direct Probe of Topological Invariants Using Bloch…
The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on…
We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atom in optical lattices.…
We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann…
We study a quantum walk of a single particle that is subject to stroboscopic projective measurements on a graph with two sites. This two-level system is the minimal model of a measurement induced quantum walk. The mean first detected…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin…
Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we will call an electric TBH; this phenomenon will be referred…
Mathematically, topological invariants arise from the parallel transport of eigenstates on the energy bands, which, in physics, correspond to the adiabatic dynamical evolution of transient states. It determines the presence of boundary…
Topological gapless phases of matter have been a recent interest among theoretical and experimental condensed matter physicists. Fermionic chains with extended nearest neighbor couplings have been observed to show unique topological…
Spatially resolved local quantum geometric markers play a crucial role in the diagnosis of topological phases without long-range translational symmetry, including amorphous systems. Here, we focus on the nonlocality of such markers. We…
We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…