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Nowadays, quantum simulation schemes come in two flavours.
Continuum Limits of Quantum Lattice Systems, 2019
T. J. Osborne · 1901
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A quantum cellular automaton for one-dimensional qed
Pablo Arrighi, Cédric Bény, and Terry Farrelly · 1903
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Quantum mechanics and path integrals
Hibbs Feynman · 1965
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Hamiltonian formulation of wilson’s lattice gauge theories
John Kogut and Leonard Susskind · 1975
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Simulating physics with computers
R. P. Feynman · 1982
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Quantum mechanical computers
R. P. Feynman · 1986
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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
Iwo Bialynicki-Birula · 1994
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From quantum cellular automata to quantum lattice gases
David A Meyer · 1996
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A note on the correspondence between qubit quantum operations and special relativity
P. Arrighi and C. Patricot · 2003
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Reversible quantum cellular automata
B. Schumacher and R. Werner · 2004
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Connecting the discrete-and continuous-time quantum walks
Frederick W Strauch · 2006
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Supersonic quantum communication
Jens Eisert and David Gross · 2009
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A quantum Game of Life
P. Arrighi and J. Grattage · 2010
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Unitarity plus causality implies localizability
P. Arrighi, V. Nesme, and R. Werner · 2010
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Quantum simulation of the dirac equation
Rene Gerritsma, Gerhard Kirchmair, Florian Zähringer, E Solano, R Blatt, and CF Roos · 2010
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Molecular binding in interacting quantum walks
Andre Ahlbrecht, Andrea Alberti, Dieter Meschede, Volkher B Scholz, Albert H Werner, and Reinhard F Werner · 2012
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Partitioned Quantum Cellular Automata are Intrinsically Universal
P. Arrighi and J. Grattage · 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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Quantum walks as massless dirac fermions in curved space-time
Giuseppe Di Molfetta, Marc Brachet, and Fabrice Debbasch · 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
Quantum walks and non-abelian discrete gauge theory
Pablo Arnault, Giuseppe Di Molfetta, Marc Brachet, and Fabrice Debbasch · 2016
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Quantum walking in curved spacetime
P. Arrighi, S. Facchini, and M. Forets · 2016
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Quantum walks as simulators of neutrino oscillations in a vacuum and matter
Giuseppe Di Molfetta and Armando Pérez · 2016
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Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
Esteban A Martinez, Christine A Muschik, Philipp Schindler, Daniel Nigg, Alexander Erhard, Markus Heyl, Philipp Hauke, Marcello Dalmonte, Thomas Monz, Peter Zoller, et al · 2016
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Quantum walking in curved spacetime: (3+1) dimensions, and beyond
P. Arrighi and F. Facchini · 2017
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The dirac equation as a quantum walk: higher dimensions, observational convergence
P. Arrighi, V. Nesme, and M. 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 simulation
IM Georgescu, Sahel Ashhab, and Franco Nori · 2014
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Quantum Algorithms for Fermionic Quantum Field Theories, 2014
S. P. Jordan, K. S. M. Lee, and J. Preskill · 2014
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Lattice qcd in curved spacetimes
Arata Yamamoto · 2014
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Doubly special relativity from quantum cellular automata
A. Bibeau-Delisle, A. Bisio, G. M. D’Ariano, P. Perinotti, and A. Tosini · 2015
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Alessandro Bisio, Giacomo Mauro D’Ariano, and Paolo Perinotti · 2017
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Fermion confinement via quantum walks in (2+ 1)-dimensional and (3+ 1)-dimensional space-time
Ivan Márquez-Martín, Giuseppe Di Molfetta, and Armando Pérez · 2017
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Thirring quantum cellular automaton
Alessandro Bisio, Giacomo Mauro D’Ariano, Paolo Perinotti, and Alessandro Tosini · 2018
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Quantum walks in external gauge fields, 2018
C. Cedzich, T. Geib, A. H. Werner, and R. F. Werner · 2018
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Action principles for quantum automata and lorentz invariance of discrete time quantum walks
Fabrice Debbasch · 2018
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Quantum-classical computation of schwinger model dynamics using quantum computers
N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage · 2018
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Quantum-classical computation of schwinger model dynamics using quantum computers
N Klco, EF Dumitrescu, AJ McCaskey, TD Morris, RC Pooser, M Sanz, E Solano, P Lougovski, and MJ Savage · 2018
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Discrete-time quantum walks as fermions of lattice gauge theory
Pablo Arnault, Armando Pérez, Pablo Arrighi, and Terry Farrelly · 2019
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Simulating dirac hamiltonian in curved space-time by split-step quantum walk
Arindam Mallick, Sanjoy Mandal, Anirban Karan, and C Madaiah Chandrashekar · 2019
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