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A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk.
Simple quantum computer
Isaac L. Chuang and Yoshihisa Yamamoto · 1995
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Quantum computation and decision trees
Edward Farhi and Sam Gutmann · 1998
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Quantum logic gates in optical lattices
Gavin K. Brennen, Carlton M. Caves, Poul S. Jessen, and Ivan H. Deutsch · 1999
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Quantum walks on graphs
Dorit Aharonov, Andris Ambainis, Julia Kempe, and Umesh Vazirani · 2001
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One-dimensional quantum walks
Andris Ambainis, Eric Bach, Ashwin Nayak, Ashvin Vishwanath, and John Watrous · 2001
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Quantum-information processing in bosonic lattices
Radu Ionicioiu and Paolo Zanardi · 2002
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Classical simulation of noninteracting-fermion quantum circuits
Barbara M. Terhal and David P. DiVincenzo · 2002
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Exponential algorithmic speedup by quantum walk
Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A. Spielman · 2003
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Adiabatic quantum state generation and statistical zero knowledge
Dorit Aharonov and Amnon Ta-Shma · 2003
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Quantum walk algorithm for element distinctness
Andris Ambainis · 2004
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Experimental realization of a quantum quincunx by use of linear optical elements
Binh Do, Michael L. Stohler, Sunder Balasubramanian, Daniel S. Elliott, Christopher Eash, Ephraim Fischbach, Michael A. Fischbach, Arthur Mills, and Benjamin Zwickl · 2005
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Quantum walk on a line with two entangled particles
Y. Omar, N. Paunković, L. Sheridan, and S. Bose · 2006
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Efficient quantum algorithms for simulating sparse Hamiltonians
Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders · 2007
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Simple proof of equivalence between adiabatic quantum computation and the circuit model
Ari Mizel, Daniel A. Lidar, and Morgan Mitchell · 2007
Cited alongside, same era.
Quantum random walk of two photons in separable and entangled states
P. K. Pathak and G. S. Agarwal · 2007
Cited alongside, same era.
A quantum algorithm for the Hamiltonian NAND tree
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2008
Cited alongside, same era.
Realization of quantum walks with negligible decoherence in waveguide lattices
Hagai B. Perets, Yoav Lahini, Francesca Pozzi, Marc Sorel, Roberto Morandotti, and Yaron Silberberg · 2008
Cited alongside, same era.
Two-particle states in the Hubbard model
Manuel Valiente and David Petrosyan · 2008
Cited alongside, same era.
Universal computation by quantum walk
Andrew M. Childs · 2009
Cited alongside, same era.
Lattice two-body problem with arbitrary finite-range interactions
Manuel Valiente · 2010
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On the limitations of graph invariants inspired by quantum walks
Jamie Smith · 2011
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Two-photon quantum walks in an elliptical direct-write waveguide array
James O. Owens, Matthew A. Broome, Devon N. Biggerstaff, Michael E. Goggin, Alessandro Fedrizzi, Trond Linjordet, Martin Ams, Graham D. Marshall, Jason Twamley, Michael J. Withford, and Andrew G. White · 2011
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Multi-walker discrete time quantum walks on arbitrary graphs, their properties and their photonic implementation
P. P. Rohde, A. Schreiber, M. Štefaňák, I. Jex, and C. Silberhorn · 2011
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The computational complexity of linear optics
Scott Aaronson and Alex Arkhipov · 2011
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Dispersive photon blockade in a superconducting circuit
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Quantum walk in position space with single optically trapped atoms
Michał Karski, Leonid Förster, Jai-Min Choi, Andreas Steffen, Wolfgang Alt, Dieter Meschede, and Artur Widera · 2009
Cited alongside, same era.
Quantum and classical correlations in waveguide lattices
Yaron Bromberg, Yoav Lahini, Roberto Morandotti, and Yaron Silberberg · 2009
Cited alongside, same era.
A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice
Waseem S. Bakr, Jonathon I. Gillen, Amy Peng, Simon Folling, and Markus Greiner · 2009
Cited alongside, same era.
On the relationship between continuous- and discrete-time quantum walk
Andrew M. Childs · 2010
Cited alongside, same era.
Two-particle quantum walks applied to the graph isomorphism problem
John King Gamble, Mark Friesen, Dong Zhou, Robert Joynt, and S. N. Coppersmith · 2010
Cited alongside, same era.
Quantum walks of correlated particles
Alberto Peruzzo, Mirko Lobino, Jonathan C. F. Matthews, Nobuyuki Matsuda, Alberto Politi, Konstantinos Poulios, Xiao-Qi Zhou, Yoav Lahini, Nur Ismail, Kerstin Wörhoff, Yaron Bromberg, Yaron Silberberg, Mark G. Thompson, and Jeremy L. O’Brien · 2010
Cited alongside, same era.
Anthony J. Hoffman, Srikanth J. Srinivasan, Sebastian Schmidt, Lafe Spietz, José Aumentado, Hakan E. Türeci, and Andrew A. Houck · 2011
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Single-qubit unitary gates by graph scattering
Benjamin A. Blumer, Michael S. Underwood, and David L. Feder · 2011
Later among the works it cites.
Quantum walk of two interacting bosons
Yoav Lahini, Mor Verbin, Sebastian D. Huber, Yaron Bromberg, Rami Pugatch, and Yaron Silberberg · 2012
Closest in time.
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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A 2D Quantum Walk Simulation of Two-Particle Dynamics
A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefaňák, V. Potoček, C. Hamilton, I. Jex, and C. Silberhorn · 2012
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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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Levinson’s theorem for graphs ii
Andrew M. Childs and David Gosset · 2012
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