The staggered quantum walk model

The Elephant Quantum Walk

Giuseppe Di Molfetta,1, 2, ∗ Diogo O. Soares-Pinto,3 and Sílvio M. Duarte Queirós4 Aix-Marseille Université, CNRS, École Centrale de Marseille, Laboratoire d’Informatique Fondamentale, Marseille, France Departamento de Física Teórica and IFIC, Universidad de Valencia-CSIC, Dr. Moliner 50, 46100-Burjassot, Spain Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970, São...

Quantum Walk on the Line

Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider quantum walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the “Hadamard walk”. In particular, we show that after t time steps, the probability distribution on the line induced by the Hadamard walk ...

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Quantum lattice Boltzmann is a quantum walk

*Correspondence: [email protected] 1IAC-CNR, Istituto per le Applicazioni del Calcolo ‘Mauro Picone’, Via dei Taurini, 19, Rome, 00185, Italy Full list of author information is available at the end of the article Abstract Numerical methods for the 1-D Dirac equation based on operator splitting and on the quantum lattice Boltzmann (QLB) schemes are reviewed. It is shown that these discretizati...

Efficient quantum walk on a quantum processor.

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to...