相关论文: Non-Unitary Quantum Walks on Hyper-Cycles

We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…

We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles, which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is…

Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples…

We prove analytical results showing that decoherence can be useful for mixing time in a continuous-time quantum walk on finite cycles. This complements the numerical observations by Kendon and Tregenna (Physical Review A 67 (2003), 042315)…

We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…

For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that…

We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…

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 present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is…

Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…

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…

A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following: - The…

The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…

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 study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

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…

The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…

Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…

We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…

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…