Editing Quantum algorithm (section)

===Quantum simulation===
{{main|Hamiltonian 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, yet quantum many-body systems are able to "solve themselves."<ref>
{{Cite journal
 | last1=Feynman | first1=R. P.
 | year=1982
 | title=Simulating physics with computers
 | journal=[[International Journal of Theoretical Physics]]
 | volume=21 | issue=6–7 | pages=467–488
 | bibcode = 1982IJTP...21..467F
 | doi = 10.1007/BF02650179
| citeseerx=10.1.1.45.9310
 | s2cid=124545445
 }}</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 (i.e., polynomial-time) quantum algorithms have been developed for simulating both Bosonic and Fermionic systems,<ref>
{{Cite journal
 | last1=Abrams |first1=D. S.
 | last2=Lloyd | first2=S.
 | year=1997
 | title=Simulation of many-body Fermi systems on a universal quantum computer
 | journal=[[Physical Review Letters]]
 | volume=79 | issue=13 | pages=2586–2589
 | arxiv = quant-ph/9703054
 | bibcode=1997PhRvL..79.2586A
 | doi=10.1103/PhysRevLett.79.2586
|s2cid=18231521
 }}</ref> as well as the simulation of chemical reactions beyond the capabilities of current classical supercomputers using only a few hundred qubits.<ref>
{{Cite journal
 | last1=Kassal | first1=I.
 | last2=Jordan | first2=S. P.
 | last3=Love | first3=P. J.
 | last4=Mohseni | first4=M.
 | last5=Aspuru-Guzik | first5=A.
 | year=2008
 | title=Polynomial-time quantum algorithm for the simulation of chemical dynamics
 | journal=[[Proceedings of the National Academy of Sciences of the United States of America]]
 | volume=105 |issue=48 | pages=18681–86
 | arxiv= 0801.2986
 | bibcode = 2008PNAS..10518681K
 | doi=10.1073/pnas.0808245105
 | pmc=2596249
 | pmid=19033207
| doi-access=free
 }}</ref> Quantum computers can also efficiently simulate topological quantum field theories.<ref>
{{Cite journal
 | last1=Freedman | first1=M.
 | last2=Kitaev | first2=A.
 | last3=Wang | first3=Z.
 | year=2002
 | title=Simulation of Topological Field Theories by Quantum Computers
 | journal=[[Communications in Mathematical Physics]]
 | volume=227 | issue=3 | pages=587–603
 | arxiv = quant-ph/0001071
 | bibcode = 2002CMaPh.227..587F
 | doi=10.1007/s002200200635
| s2cid=449219
 }}</ref> In addition to its intrinsic interest, this result has led to efficient quantum algorithms for estimating [[Quantum invariant|quantum topological invariants]] such as [[Jones polynomial|Jones]]<ref>
{{Cite journal
 | last1=Aharonov | first1=D.
 | last2=Jones | first2=V.
 | last3=Landau | first3=Z.
 | year=2009
 | title=A polynomial quantum algorithm for approximating the Jones polynomial
 | journal=[[Algorithmica]]
 | volume=55 | issue=3 | pages=395–421
 | arxiv=quant-ph/0511096
 | doi=10.1007/s00453-008-9168-0
| s2cid=7058660
 }}</ref> and [[HOMFLY polynomial]]s,<ref>
{{Cite journal
 | last1=Wocjan |first1=P.
 | last2=Yard | first2=J.
 | year=2008
 | title=The Jones polynomial: quantum algorithms and applications in quantum complexity theory
 | journal=[[Quantum Information and Computation]]
 | volume=8 | issue=1 | pages=147–180
 |doi=10.26421/QIC8.1-2-10
 | arxiv=quant-ph/0603069
|bibcode = 2006quant.ph..3069W |s2cid=14494227
 }}</ref> and the [[Turaev-Viro invariant]] of three-dimensional manifolds.<ref>
{{Cite journal
 |last1=Alagic | first1=G.
 |last2=Jordan | first2=S.P.
 |last3=König | first3=R.
 |last4=Reichardt | first4=B. W.
 |year=2010
 |title=Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation
 |journal=[[Physical Review A]]
 |volume=82 |issue=4 |pages=040302
 |arxiv=1003.0923
 |bibcode=2010PhRvA..82d0302A
 |doi=10.1103/PhysRevA.82.040302
| s2cid=28281402
 }}</ref>