相关论文: Hitting time expressions for quantum channels: bey…

Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other vertex in finite time, provided they are connected. Discrete-time quantum walks on finite connected graphs however, can have…

We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the…

We consider open quantum walks on a graph, and consider the random variables defined as the passage time and number of visits to a given point of the graph. We study in particular the probability that the passage time is finite, the…

We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special…

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an…

Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…

In the present paper, we give the exact formula for the average hitting time (HT, as an abbreviation) of random walks from one vertex to any other vertex on the some weighted Cayley graphs.

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics is recorded…

In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS…

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 new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…

We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's bound of hitting times for general graphs, prove a sharp bound…

Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…

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…

Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of…

Using the results of Ding, Lee, Peres [3], we develop formulas to compute the hitting times and cover times for random walks on groups. We developed an explicit formula for hitting times in terms of the irreducible representations of the…