Related papers: Coined Quantum Walks as Quantum Markov Chains
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…
Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a…
We define the discrete-time quantum walk on complex networks and utilize it for community detection. We numerically show that the quantum walk with the Fourier coin is localized in a community to which the initial node belongs. Meanwhile,…
The Grover walk is one of the most well-studied quantum walks on graphs. In this paper, we investigate its periodicity to reveal the relationship between the quantum walk and the underlying graph, focusing particularly on the…
We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples…
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the…
We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…
We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW, and (ii)…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in $2$D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant…
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential…