Related papers: Infinite reduction in absorbing time in quantum wa…
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…
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very…
We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We employ Quantum Fisher Information, as a figure of merit, to quantify extractable information about an unknown parameter…
Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson…
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…
In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $\tau$ self-loops. We derive an…
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…
Quantum versions of random walks on the line and cycle show a quadratic improvement in their spreading rate and mixing times respectively. The addition of decoherence to the quantum walk produces a more uniform distribution on the line, and…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and…
We analyze the response to incorporation of glassy disorder in the coin operation of a discrete-time quantum walk in one dimension. We find that the ballistic spread of the disorder-free quantum walker is inhibited by the insertion of…
A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time…
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…
In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number…
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 show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time…