Quantum algorithm: Difference between revisions

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tweak phrasing in paragraph 3 to be consistent with the "might be able to" phrasing of paragraph 2, as noted on the Talk page
 
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Problems that are [[Undecidable problem|undecidable]] using classical computers remain undecidable using quantum computers.<ref name=nielchuan>{{cite book|title=Quantum Computation and Quantum Information|last1=Nielsen|first1=Michael A.|last2=Chuang|first2=Isaac L.|publisher=Cambridge University Press|year=2010|isbn=978-1-107-00217-3|edition=2nd|___location=Cambridge|author-link=Michael A. Nielsen|author-link2=Isaac Chuang|url=https://books.google.com/books?id=-s4DEy7o-a0C}}</ref>{{rp|127}} What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms because the quantum superposition and quantum entanglement that quantum algorithms exploit generally cannot be efficiently simulated on classical computers (see [[Quantum supremacy]]).
 
The best-known algorithms are [[Shor's algorithm]] for factoring and [[Grover's algorithm]] for searching an unstructured database or an unordered list. Shor's algorithm runswould, if implemented, run much (almost exponentially) faster than the most efficient known classical algorithm for factoring, the [[general number field sieve]].<ref>{{Cite web|url=https://quantum-computing.ibm.com/docs/iqx/guide/shors-algorithm|title=Shor's algorithm|access-date=21 October 2020|archive-date=12 January 2023|archive-url=https://web.archive.org/web/20230112064753/https://quantum-computing.ibm.com/docs/iqx/guide/shors-algorithm|url-status=dead}}</ref> Likewise, Grover's algorithm runswould run quadratically faster than the best possible classical algorithm for the same task,<ref>{{cite web |url=https://quantum-computing.ibm.com/composer/docs/iqx/guide/grovers-algorithm |title=IBM quantum composer user guide: Grover's algorithm |access-date=7 June 2022 |website=quantum-computing.ibm.com |archive-date=27 September 2022 |archive-url=https://web.archive.org/web/20220927192200/https://quantum-computing.ibm.com/composer/docs/iqx/guide/grovers-algorithm |url-status=dead }}</ref> a [[linear search]].
 
==Overview==