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A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries.
Simulating physics with computers
R. P. Feynman · 1982
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Lattice boltzmann equation for quantum mechanics
Sauro Succi and Roberto Benzi · 1993
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Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata
I. Bialynicki-Birula · 1994
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From quantum cellular automata to quantum lattice gases
D. A. Meyer · 1996
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A theory of quantum gravity based on quantum computation
S. Lloyd · 2005
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The electronic properties of graphene
AH Castro Neto, Francisco Guinea, Nuno MR Peres, Kostya S Novoselov, and Andre K Geim · 2009
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Spatial search on a honeycomb network
G. Abal, R. Donangelo, F. L. Marquezino, and R. Portugal · 2010
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Any and-or formula of size n can be evaluated in time nˆ1/2+o(1) on a quantum computer
Andris Ambainis, Andrew M Childs, Ben W Reichardt, Robert Špalek, and Shengyu Zhang · 2010
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Exploring topological phases with quantum walks
Takuya Kitagawa, Mark S. Rudner, Erez Berg, and Eugene Demler · 2010
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Spatial quantum search in a triangular network
G. Abal, R. Donangelo, M. Forets, and R. Portugal · 2012
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Numerical solution of the time-dependent dirac equation in coordinate space without fermion-doubling
François Fillion-Gourdeau, Emmanuel Lorin, and André D Bandrauk · 2012
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Two-particle bosonic-fermionic quantum walk via integrated photonics
Linda Sansoni, Fabio Sciarrino, Giuseppe Vallone, Paolo Mataloni, Andrea Crespi, Roberta Ramponi, and Roberto Osellame · 2012
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The Dirac equation as a Quantum Walk: higher-dimensions, convergence
P. Arrighi, M. Forets, and V. Nesme · 2013
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Spinfoam fermions
Eugenio Bianchi, Muxin Han, Carlo Rovelli, Wolfgang Wieland, Elena Magliaro, and Claudio Perini · 2013
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Two-component dirac-like hamiltonian for generating quantum walk on one-, two-and three-dimensional lattices
CM Chandrashekar · 2013
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Electric quantum walks with individual atoms
Maximilian Genske, Wolfgang Alt, Andreas Steffen, Albert H Werner, Reinhard F Werner, Dieter Meschede, and Andrea Alberti · 2013
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Quantum-walk transport properties on graphene structures
Hamza Bougroura, Habib Aissaoui, Nicholas Chancellor, and Viv Kendon · 2016
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Quantum walk on a cylinder
Luis A Bru, German J De Valcarcel, Giuseppe Di Molfetta, Armando Pérez, Eugenio Roldán, and Fernando Silva · 2016
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Quantum walks and gravitational waves
Pablo Arnault and Fabrice Debbasch · 2017
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Quantum walking in curved spacetime: (3+1) dimensions, and beyond
P. Arrighi and F. Facchini · 2017
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Quantum walks, weyl equation and the lorentz group
Alessandro Bisio, Giacomo Mauro D Ariano, and Paolo Perinotti · 2017
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Isotropic quantum walks on lattices and the weyl equation
Giacomo Mauro D’Ariano, Marco Erba, and Paolo Perinotti · 2017
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Discrete lorentz covariance for quantum walks and quantum cellular automata
Pablo Arrighi, Stefano Facchini, and Marcelo Forets · 2014
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Quantum walks in artificial electric and gravitational fields
Giuseppe Di Molfetta, Marc Brachet, and Fabrice Debbasch · 2014
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Quantum walks and quantum search on graphene lattices
Iain Foulger, Sven Gnutzmann, and Gregor Tanner · 2015
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Quantum walks on graphene nanoribbons using quantum gates as coins
I G Karafyllidis · 2015
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Quantum walks on simplicial complexes
Kaname Matsue, Osamu Ogurisu, and Etsuo Segawa · 2015
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An effective hamiltonian approach to quantum random walk
Debajyoti Sarkar, Niladri Paul, Kaushik Bhattacharya, and Tarun Kanti Ghosh · 2017
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Efficient quantum algorithms for analyzing large sparse electrical networks
Guoming Wang · 2017
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Dirac quantum walks on triangular and honeycomb lattices, 2018
Gareth Jay, Fabrice Debbasch, and Jingbo Wang · 2018
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Massive dirac fermions in a ferromagnetic kagome metal
Linda Ye, Mingu Kang, Junwei Liu, Felix von Cube, Christina R Wicker, Takehito Suzuki, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, David C Bell, et al · 2018
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