Related papers: Localization of two-dimensional quantum walks defi…
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. [1] showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle [2], expresses the…
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…
We analyze discrete-time quantum walks on Sierpinski gaskets using a flip-flop shift operator with the Grover coin. We obtain the scaling of two important physical quantities: the mean-square displacement and the mixing time as function of…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak…
Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the…
We present an in-depth analytic study of discrete-time quantum walks driven by a non-reflective coin. Specifically, we compare the properties of the widely-used Grover coin ${\cal C}_{G}$ that is unitary and reflective (${\cal…
We study the motion of M particles performing a quantum walk on the line. Under various conditions on the initial coin states for quantum walkers controlled by the Hadamard operator, we give theoretical criterion to observe the quantum…
Properties of one dimensional discrete-time quantum walks are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position dependent coin operators. Deterministic aperiodic sequences of two or…
We implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
We focus on a 2-period time-dependent quantum walk on the half line in this paper. The quantum walker launches at the edge of the half line in a localized superposition state and its time evolution is carried out with two unitary operations…
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…
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 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…