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Added more references on using (nonabelian) geometric phases due to adiabatic parameter movement as quantum gates:
Paolo Zanardi, Mario Rasetti, Holonomic Quantum Computation, Phys. Lett. A 264 (1999) 94-99 [doi:10.1016/S0375-9601%2899%2900803-8, arXiv:quant-ph/9904011 ]
Jonathan A. Jones, Vlatko Vedral, Artur Ekert, Giuseppe Castagnoli, Geometric quantum computation using nuclear magnetic resonance, Nature 403 (2000) 869–871 [doi:10.1038/35002528]
Giuseppe Falci, Rosario Fazio, G. Massimo Palma, Jens Siewert & Vlatko Vedral, Detection of geometric phases in superconducting nanocircuits, Nature 407 355–358 (2000) [doi:10.1038/35030052]
L. M. Duan, J. I. Cirac, P. Zoller, Geometric Manipulation of Trapped Ions for Quantum Computation, Science 292 (2001) 1695 [arXiv:quant-ph/0111086, doi:10.1126/science.1058835]
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added another reference which makes the adiabatic nature of topological quantum computation nicely explicit:
Jiannis K. Pachos, Introduction to Topological Quantum Computation, Cambridge University Press (2012) [doi:10.1017/CBO9780511792908]
[p. 50]: “topological quantum computation resembles an adiabatic quantum computation with constant energy gap, where the quasiparticle coordinates provide the control parameters of the Hamiltonian.”
[p. 52]: “Holonomic quantum computation resembles the adiabatic scheme […] topological quantum computation can be considered as holonomic computation where the employed adiabatic evolutions have topological characteristics.”
added more and more original references, such as these:
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Michael Sipser, Quantum Computation by Adiabatic Evolution [arXiv:quant-ph/0001106]
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, Daniel Preda, A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem, Science 292 5516 (2001) 472-475 [doi:10.1126/science.1057726]
Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, Oded Regev, Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation, SIAM Journal of Computing 37 1 (2007) 166-194 [arXiv:quant-ph/0405098, jstor:20454175, doi:10.1109/FOCS.2004.8, doi:10.1137/080734479]
and this one:
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added more of the original references on holonomic quantum computation:
Jiannis Pachos, Paolo Zanardi, Mario Rasetti, Non-Abelian Berry connections for quantum computation, Phys. Rev. A 61 (2000) 010305 [arXiv:quant-ph/9907103, doi:10.1103/PhysRevA.61.010305]
Jiannis Pachos, Paolo Zanardi, Quantum Holonomies for Quantum Computing, Int. J. Mod. Phys. B 15 (2001) 1257-1286 [arXiv:quant-ph/0007110, doi:10.1142/S0217979201004836]
as well as this recent preprint:
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