Related papers: Quantum walks with memory - goldfish, elephants an…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
We show how to search N items arranged on a $\sqrt{N}\times\sqrt{N}$ grid in time $O(\sqrt N \log N)$, using a discrete time quantum walk. This result for the first time exhibits a significant difference between discrete time and continuous…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks…
Random walks simulate the randomness of objects, and are key instruments in various fields such as computer science, biology and physics. The counter part of classical random walks in quantum mechanics are the quantum walks. Quantum walk…
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform…
We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
We provide an explanation of recent experimental results of Xue et al., where full revivals in a time-dependent quantum walk model with a periodically changing coin are found. Using methods originally developed for "electric" walks with a…
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…
The properties of the coinless quantum walk model have not been as thoroughly analyzed as those of the coined model. Both evolve in discrete time steps but the former uses a smaller Hilbert space, which is spanned merely by the site basis.…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
We introduce history-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying Hamiltonian of the walker to include couplings with memory-keeping agents. We next numerically study the…
This note introduces some examples of quantum random walks in d-dimensional Eucilidean space and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the "quantum…