Editing Quantum computing (section)

==== Quantum Turing machine ====

A [[quantum Turing machine]] is the quantum analog of a [[Turing machine]].<ref name="The computer as a physical system"/> All of these models of computation—quantum circuits,<ref>{{Cite book|last=Chi-Chih Yao|first=A.|title=Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science |chapter=Quantum circuit complexity |year=1993|chapter-url=https://ieeexplore.ieee.org/document/366852|pages=352–361|doi=10.1109/SFCS.1993.366852|isbn=0-8186-4370-6|s2cid=195866146}}</ref> [[One-way quantum computer|one-way quantum computation]],<ref>{{Cite journal |last1=Raussendorf |first1=Robert |last2=Browne |first2=Daniel E. |last3=Briegel |first3=Hans J. |date=2003-08-25 |title=Measurement-based quantum computation on cluster states |journal=Physical Review A |volume=68 |issue=2 |pages=022312 |doi=10.1103/PhysRevA.68.022312 |arxiv=quant-ph/0301052 |bibcode=2003PhRvA..68b2312R |s2cid=6197709}}</ref> adiabatic quantum computation,<ref>{{Cite journal |last1=Aharonov |first1=Dorit |last2=van Dam |first2=Wim |last3=Kempe |first3=Julia |last4=Landau |first4=Zeph |last5=Lloyd |first5=Seth |last6=Regev |first6=Oded |date=2008-01-01 |title=Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation |journal=SIAM Review |volume=50 |issue=4 |pages=755–787 |doi=10.1137/080734479 |arxiv=quant-ph/0405098 |bibcode=2008SIAMR..50..755A |s2cid=1503123 |issn=0036-1445}}</ref> and topological quantum computation<ref name="FLW02">{{Cite journal |last1=Freedman |first1=Michael H. |last2=Larsen |first2=Michael |last3=Wang |first3=Zhenghan |date=2002-06-01 |title=A Modular Functor Which is Universal for Quantum Computation |journal=Communications in Mathematical Physics |volume=227 |issue=3 |pages=605–622 |doi=10.1007/s002200200645 |issn=0010-3616 |arxiv=quant-ph/0001108 |bibcode=2002CMaPh.227..605F |s2cid=8990600}}</ref>—have been shown to be equivalent to the quantum Turing machine; given a perfect implementation of one such quantum computer, it can simulate all the others with no more than polynomial overhead. This equivalence need not hold for practical quantum computers, since the overhead of simulation may be too large to be practical.