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Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak…
Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We…
We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two…
The Polya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability to return to the origin. This result is extremely…
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, via numerical simulations, that the fidelity decay behavior of quasi-integrable systems is strongly dependent on the location of the initial coherent state with respect to the underlying classical phase space. In parallel to…
Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The…
The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…
Weak quantum measurements enable real-time tracking and control of dynamical quantum systems, producing quantum trajectories -- evolutions of the quantum state of the system conditioned on measurement outcomes. For classical systems, the…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
We discuss the dephasing induced by the internal classical chaotic motion in the absence of any external environment. To this end we consider a suitable extension of fidelity for mixed states which is measurable in a Ramsey interferometry…
This paper researches how the systematic errors in phase inversions affect the success rate and the number of iterations in optimized quantum random-walk search algorithm. Through geometric description of this algorithm, the model of the…
Random walks behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can…
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…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…