Editing Hypercomputation (section)

===Quantum models===
Some scholars conjecture that a [[Quantum mechanics|quantum mechanical]] system which somehow uses an infinite superposition of states could compute a non-[[computable function]].<ref>There have been some claims to this effect; see {{cite journal | author = Tien Kieu | title = Quantum Algorithm for the Hilbert's Tenth Problem | journal = Int. J. Theor. Phys. | year = 2003 | volume = 42 | arxiv = quant-ph/0110136 | pages = 1461–1478 | doi = 10.1023/A:1025780028846 | issue = 7| title-link = Hilbert problems | s2cid = 6634980 }} or {{cite journal | author = M. Ziegler | title = Computational Power of Infinite Quantum Parallelism | year = 2005 | journal = [[International Journal of Theoretical Physics]] | volume = 44 | issue = 11 | pages = 2059–2071 | doi = 10.1007/s10773-005-8984-0| arxiv = quant-ph/0410141 | bibcode = 2005IJTP...44.2059Z | s2cid = 9879859 }} and the ensuing literature. For a retort see  {{cite journal | author = Warren D. Smith | doi = 10.1016/j.amc.2005.09.078 | title = Three counterexamples refuting Kieu's plan for "quantum adiabatic hypercomputation"; and some uncomputable quantum mechanical tasks | journal = Applied Mathematics and Computation | volume = 178 | issue = 1 | pages = 184–193| year = 2006 }}.
</ref> This is not possible using the standard [[qubit]]-model [[quantum computer]], because it is proven that a regular quantum computer is [[PSPACE]]-[[Reduction (complexity)|reducible]] (a quantum computer running in [[polynomial time]] can be simulated by a classical computer running in [[polynomial space]]).<ref>{{cite journal |url=http://www.cs.berkeley.edu/~vazirani/bv.ps |doi=10.1137/S0097539796300921|title=Quantum Complexity Theory|year=1997|last1=Bernstein|first1=Ethan|last2=Vazirani|first2=Umesh|journal=SIAM Journal on Computing|volume=26|issue=5|pages=1411–1473}}</ref>