Related papers: Observing Topological Invariants Using Quantum Wal…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…
The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases and quantum information. While recent studies suggest that…
We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the…
For harnessing the full potential of quantum phenomena, light-matter interfaces and complexly connected quantum networks are required, relying on the joint quantum operation of different physical platforms. In this work, we analyze the…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators in the space of functions on a Hilbert space which are square integrable with respect to…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
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…
The topology of one-dimensional chiral systems is captured by the winding number of the Hamiltonian eigenstates. Here we show that this invariant can be read-out by measuring the mean chiral displacement of a single-particle wavefunction…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
We report an experimental implementation of a single-qubit generalised measurement scenario(POVM) based on a quantum walk model. The qubit is encoded in a single-photon polarisation. The photon performs a quantum walk on an array of optical…
From studies of exotic quantum many-body phenomena to applications in spintronics and quantum information processing, topological materials are poised to revolutionize the condensed matter frontier and the landscape of modern materials…
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…
Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…
We have experimentally realized novel space-time inversion (P-T) invariant Z2-type topological semimetal-bands, via an analogy between the momentum space and a controllable parameter space in superconducting quantum circuits. By measuring…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…