相关论文: One dimensional quantum walk with unitary noise

The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…

We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in…

The universal quantum computation model based on quantum walk by Childs has opened the door for a new way of studying the limitations and advantages of quantum computation, as well as for its intermediate-term simulation. In recent years,…

Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…

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 walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the…

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…

We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which…

The question of witnessing or quantifying nonclassicality of quantum systems has been addressed in various ways. For a given system or theory, we propose identifying it with the incompatibility of admissible states. We quantify the…

The discrete-time quantum walk (QW) is a quantum version of the random walk (RW) and has been widely investigated for the last two decades. Some remarkable properties of QW are well known. For example, QW has a ballistic spreading, i.e., QW…

This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial…

First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion.…

We study the dynamics of discrete-time quantum walk using quantum coin operations, $\hat{C}(\theta_1)$ and $\hat{C}(\theta_2)$ in time-dependent periodic sequence. For the two-period quantum walk with the parameters $\theta_1$ and…

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 implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an…

The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…

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…

We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…

In this paper, we present a quantum Bernoulli noises approach to quantum walks on hypercubes. We first obtain an alternative description of a general hypercube and then, based on the alternative description, we find that the operators…