Related papers: Restart expedites quantum walk hitting times
In a measurement-induced continuous-time quantum walk, we address the problem of detecting a particle in a subspace, instead of a fixed position. In this configuration, we develop an approach of bright and dark states based on the unit and…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of…
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…
We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known…
Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these…
We consider the problem of the first passage time to the origin of a spatially non-homogeneous random walk with a position-dependent drift, known as the Gillis random walk, in the presence of resetting. The walk starts from an initial site…
Recurrence in the classical random walk is well known and described by the P\'olya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under…
The effect of decoherence on the continuous-time quantum walk on the hypercube is revisited. Previously, an exact solution was found for a decoherence model that preserved the effective tensor-product form of the dynamics. Here a new model…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
In recent years, it has been well-established that adding a restart mechanism can alter the firstpassage statistics of a stochastic processes in useful and interesting ways. Though different mecha-nisms have been investigated, we derive a…
In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform…
The first detection of a quantum particle on a graph has been shown to depend sensitively on the sampling time {\tau} . Here we use the recently introduced quantum renewal equation to investigate the statistics of first detection on 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…
We investigate the first passage time beyond a barrier located at $b\geq0$ of a random walk with independent and identically distributed jumps, starting from $x_0=0$. The walk is subject to stochastic resetting, meaning that after each step…
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…