Related papers: A note on Ito's formula for discrete-time quantum …
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…
We explore a continuous-time quantum walk starting at a single vertex on the discrete path and cycle with a cubic nonlinearity. Such nonlinearities arise in Bose-Einstein condensates described by the Gross-Pitaevskii equation or by…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-face walks. For the transition matrix of a quantum walk,…
The present letter gives a rigorous way from quantum to classical random walks by introducing an independent random fluctuation and then taking expectations based on a path integral approach.
We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…
We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
Quantum walks are expected to provide useful algorithmic tools for quantum computation. This paper introduces absorbing probability and time of quantum walks and gives both numerical simulation results and theoretical analyses on Hadamard…
We propose an implementation scheme for the continuous-time quantum walk using a diatomic molecule and an optical frequency comb. We show an analogy between the quantum walk and the cascade rotational transitions induced by the optical…
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$…
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…
A new family of discrete-time quantum walks (DTQWs) on the line with an exact discrete $U(N)$ gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac…
Estimation of the coin parameter(s) is an important part of the problem of implementing more robust schemes for quantum simulation using quantum walks. We present the estimation of the quantum coin parameter used for one-dimensional…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The…
We present an experimental implementation of the coined discrete time quantum walk on a square using a three qubit liquid state nuclear magnetic resonance (NMR) quantum information processor (QIP). Contrary to its classical counterpart, we…