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In BQP part of the table, I changed rejects to accepts and used equations to make it more concise. |
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<u>This introduction is very clear and insightful, but it could use some citations. I also love the inclusion of the wikilinks. Notice how most wiki articles begin with a summary of the subject and then jump into the background and more details. A quick summary will let readers know right away if your article is the info they're interested in</u>
One of the reasons quantum complexity theory is studied are the implications of quantum computing for the modern [[Church–Turing thesis|Church-Turing thesis]]. In short the modern Church-Turing thesis states that any computational model can be simulated in polynomial time with a [[probabilistic Turing machine]].<ref name=":0">{{Cite journal|last=Vazirani|first=Umesh V.|date=2002|title=A survey of quantum complexity theory|url=http://dx.doi.org/10.1090/psapm/058/1922899|journal=Proceedings of Symposia in Applied Mathematics|pages=193–217|doi=10.1090/psapm/058/1922899|issn=2324-7088}}</ref><ref>{{Cite book|last=Nielsen, Michael A., 1974-|url=https://www.worldcat.org/oclc/665137861|title=Quantum computation and quantum information|date=2010|publisher=Cambridge University Press|others=Chuang, Isaac L., 1968-|isbn=978-1-107-00217-3|edition=10th anniversary ed|___location=Cambridge|oclc=665137861}}</ref> However, questions around the Church-Turing thesis arise in the context of quantum computing. It is unclear whether the Church-Turing thesis holds for the quantum computation model. There is much evidence that the thesis does not hold. It may not be possible for a probabilistic Turing machine to simulate quantum computation models in polynomial time.<ref name=":0" />
<u>The last sentence of this paragraph is rather long and complex. I think it would be clearer if you broke it down into 3-4 short sentences, even if you feel it sounds redenudant, sometimes redundancy improves clarity</u>
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