Related papers: The uniform measure for quantum walk on hypercube:…
Quantum Bernoulli noises are annihilation and creation operators acting on Bernoulli functionals, which satisfy the canonical anti-commutation relations (CAR) in equal-time. In this paper, we use quantum Bernoulli noises to introduce a…
In this paper, we introduce and investigate a model of magnetic quantum walk on a general hypercube. We first construct a set of unitary involutions associated with a magnetic potential $\nu$ by using quantum Bernoulli noises. And then,…
We obtain the uniform measure as a stationary measure of the one-dimensional discrete-time quantum walks by solving the corresponding eigenvalue problem. As an application, the uniform probability measure on a finite interval at a time can…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
We perform generalized measurements of a qubit by realizing the qubit as a coin in a photonic quantum walk and subjecting the walker to projective measurements. Our experimental technique can be used to realize photonically any rank-1…
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean…
We demonstrate an implementation of unambiguous state discrimination of two equally probable single-qubit states via a one-dimensional photonic quantum walk experimentally. Furthermore we experimentally realize a quantum walk algorithm for…
We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing…
We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention is focused on the noise generated by a Gaussian Ornstein…
A connection between the asymptotic behavior of the open quantum walk and the spectrum of a generalized quantum coins is studied. For the case of simultaneously diagonalizable transition operators an exact expression for probability…
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…
In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let $\mathfrak{h}$ be the space of square integrable…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
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…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of…
In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…
We present a generalized definition of discrete-time quantum walks convenient for capturing a rather broad spectrum of walker's behavior on arbitrary graphs. It includes and covers both: the geometry of possible walker's positions with…
We treat three types of measures of the quantum walk (QW) with the spatial perturbation at the origin, which was introduced by [1]: time averaged limit measure, weak limit measure, and stationary measure. From the first two measures, we see…
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…