相关论文: What is random about a quantum random walk?
We extend to the gamut of functional forms of the probability distribution of the time-dependent step-length a previous model dubbed Elephant Quantum Walk, which considers a uniform distribution and yields hyperballistic dynamics where the…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
We study the dynamics of a generalization of quantum coin walk on the line which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations to…
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…
We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…
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 generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…
Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the novel feature that it uses many identical quantum coins keeping at the same time…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Discrete time (coined) quantum walks are produced by the repeated application of a constant unitary transformation to a quantum system. By recasting these walks into the setting of periodic perturbations to an otherwise freely evolving…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying…
The behaviour of random quantum walks is known to be diffusive. Here we study discrete time quantum walks in weak stochastic gauge fields. In the case of position and spin dependent gauge field, we observe a transition from ballistic to…
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…
The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts with pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerrlike nonlinearity of the medium we…
Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schr\"{o}dinger, massive Dirac, and Klein-Gordon equations. Here, two different types of Fibonacci discrete-time…
We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of…
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…