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===Quantum Simulation===
The idea that quantum computers might be more powerful than classical computers originated in Richard Feynman's observation that classical computers seem to require exponential time to simulate many-particle quantum systems.<ref>{{Cite journal | last1=Feynman | first1=Richard P. | author1-link=Richard Feynman | title=Simulating physics with computers | year=1982 | journal=International Journal of Theoretical Physics | volume=21 | page=467 | postscript=<!--None-->|bibcode = 1982IJTP...21..467F |doi = 10.1007/BF02650179 }}</ref> Since then, the idea that quantum computers can simulate quantum physical processes exponentially faster than classical computers has been greatly fleshed out and elaborated. Efficient (that is, polynomial-time) quantum algorithms have been developed for simulating both Bosonic and Fermionic systems<ref>{{Cite journal | doi=10.1103/PhysRevLett.79.2586 | last1=Abrams | first1=D.S. | last2=Lloyd | first2=Seth | author2-link=Seth Lloyd | title=Simulation of many-body Fermi systems on a universal quantum computer | publisher=APS | year=1997 | journal=[[Physical Review Letters]] | volume=79 | issue=13 | pages=2586–2589 | postscript=<!--None--> | bibcode=1997PhRvL..79.2586A|arxiv = quant-ph/9703054 }}. {{arXiv|quant-ph/9703054}}</ref> and in particular, the simulation chemical reactions beyond the capabilities of current classical supercomputers requires only a few hundred qubits.<ref>{{Cite journal | doi=10.1073/pnas.0808245105 | last1=Kassal | first1=I. | last2=Jordan | first2=S.P. | last3=Love | first3=P.J. | last4=Mohseni | first4=M. | last5=Aspuru-Guzik | first5=A. | title=Polynomial-time quantum algorithm for the simulation of chemical dynamics | year=2008 | journal=[[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | volume=105 | issue=48 | pages=18681–18686 | pmid=19033207 | pmc=2596249 | postscript=<!--None-->|bibcode = 2008PNAS..10518681K }}. {{arXiv|0801.2986}}</ref> Quantum computers can also efficiently simulate topological quantum field theories.<ref>{{Cite journal | doi=10.1007/s002200200635 | last1=Freedman | first1=Michael | last2=Kitaev | first2=Alexei | last3=Wang | first3=Zhenghan | title=Simulation of Topological Field Theories by Quantum Computers | publisher=[[Springer-Verlag]] | ___location=Berlin, New York | year=2002 | journal=Communications in Mathematical Physics | volume=227 | issue=3 | pages=587–603 | postscript=<!--None-->|arxiv = quant-ph/0001071 |bibcode = 2002CMaPh.227..587F }}</ref> In addition to its intrinsic interest, this result has let to efficient quantum algorithms for estimating "quantum" topological invariants such as Jones<ref>{{Cite journal | doi=10.1007/s00453-008-9168-0 | last1=Aharonov | first1=Dorit | last2=Jones | first2=V. | last3=Landau | first3=Z. | title=A polynomial quantum algorithm for approximating the Jones polynomial | publisher=[[Springer-Verlag]] | ___location=Berlin, New York | year=2009 | journal=Algorithmica | volume=55 | issue=3 | pages=395–421 | postscript=<!--None-->}}. {{arXiv|quant-ph/0511096}}</ref> and HOMFLY<ref>{{Cite journal | last1=Wocjan | first1=P. | last2=Yard | first2=J. | title=The Jones polynomial: quantum algorithms and applications in quantum complexity theory | year=2008 | journal=Quantum Information and Computation | volume=8 | issue=1 | pages=147–180 | postscript=<!--None-->}}. {{arXiv|quant-ph/0603069}}</ref> polynomials, and the Turaev-Viro invariant of three-dimensional manifolds.<ref>{{Cite journal | last1=Alagic | first1=G. | last2=Jordan | first2=S.P. | last3=Koenig | first3=R. | last4=Reichardt | first4=Ben W. | title=Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation | year=2010 | postscript=<!--None-->}}. {{arXiv|1003.0923}}</ref>
==References==
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