Abstract The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence in the quantum “coin” which drives the walk. We find exact analytical expressions for the time dependence of the first two moments of position, and...

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in Quantum Information Theory (such as the well-known Hadamard random...

This note introduces some examples of quantum random walks in R and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the “quantum coin flip” is the Fourier Integral (or Plancherel) Transform. The other examples are the Birkhoff quantum walks, so named because the coin flips are effected by means of measure preservi...

What happens when a quantum system undergoing unitary evolution in time is subject to repeated projective measurements the initial state at random times? A question of general interest is: How does survival probability $S_m$, namely, that an survives even after $m$ number measurements, behave as function $m$? We address these issues context two paradigmatic systems, one, walk evolving discrete ...

Photons can carry orbital angular momentum (OAM), which offers a practical realization of a high-dimensional quantum information carrier. In this paper, by employing OAM of a single photon, we propose an experimental scheme to implement one-dimensional two-state quantum random walks on an infinite line. Furthermore, we show that the scheme can be used to implement one-dimensional three-state qu...

In this report, we present the ideas behind the notion of quantum random walks. We further restrict our attention to the paper ”Search via quantum walk” by Magniez, Nayak, Roland and Santha and give some general insights and intuition behind their work. The report is intended for the final exam evaluation in the subject ”Quantum Information and Computation”.

Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for almost uniform sampling from a state space S of cardinality N : run a symmetric ergodic Markov chain P on S for long enough to obtain a random state from within ǫ total variation distance of the uniform distribution over S. The running time of this algor...

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 measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level o...

The discrete-time quantum walk, the quantum version of classical random walks, were first introduced in 1993 [1] and have since then been a topic of research within the context of quantum information and computation [2]. Some of the algorithms in quantum information has been shown to have a successful implementation using quantum walks. Several systems have been proposed as candidates to implem...