imported>Quantling: /* Potential applications */ bold is overkill. The numbering already makes the list stand out.

2025-12-26T22:33:25Z

Potential applications: bold is overkill. The numbering already makes the list stand out.

~2025-32763-74: Link to Shor's algorithm page

2025-11-11T11:27:38Z

Link to Shor's algorithm page

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imported>Frietjes at 17:31, 30 June 2025

2025-06-30T17:31:33Z

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imported>Remsense: Reverted 1 edit by 2409:40F0:1038:BB2E:8000:0:0:0 (talk) to last revision by ShelfSkewed

2025-06-13T14:39:01Z

Reverted 1 edit by 2409:40F0:1038:BB2E:8000:0:0:0 (talk) to last revision by ShelfSkewed

← Previous revision		Revision as of 14:39, 13 June 2025
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	*{{annotated link\|India's quantum computer}}		*{{annotated link\|India's quantum computer}}
	*{{annotated link\|IonQ}}		*{{annotated link\|IonQ}}
	*{{annotated link\|IQM}}
	*{{annotated link\|List of emerging technologies}}		*{{annotated link\|List of emerging technologies}}
	*{{annotated link\|List of quantum processors}}		*{{annotated link\|List of quantum processors}}

imported>MrOllie: Reverted 1 edit by Monirima (talk): Citespammer

2025-05-27T14:14:48Z

Reverted 1 edit by Monirima (talk): Citespammer

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← Previous revision		Revision as of 14:39, 13 June 2025
Line 325:		Line 325:
	*{{annotated link\|India's quantum computer}}		*{{annotated link\|India's quantum computer}}
	*{{annotated link\|IonQ}}		*{{annotated link\|IonQ}}
	*{{annotated link\|IQM}}
	*{{annotated link\|List of emerging technologies}}		*{{annotated link\|List of emerging technologies}}
	*{{annotated link\|List of quantum processors}}		*{{annotated link\|List of quantum processors}}

← Previous revision		Revision as of 22:33, 26 December 2025
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	[[File:Bloch sphere.svg\|thumb\|[[Bloch sphere]] representation of a qubit. The state <math>\| \psi \rangle = \alpha \|0 \rangle + \beta \|1 \rangle</math>is a point on the surface of the sphere, partway between the poles, <math>\|0\rangle</math> and <math>\|1\rangle</math>.]]		[[File:Bloch sphere.svg\|thumb\|[[Bloch sphere]] representation of a qubit. The state <math>\| \psi \rangle = \alpha \|0 \rangle + \beta \|1 \rangle</math>is a point on the surface of the sphere, partway between the poles, <math>\|0\rangle</math> and <math>\|1\rangle</math>.]]

	A '''quantum computer''' is a (real or theoretical) [[computer]] that exploits [[quantum superposition\|superposed]] and [[quantum entanglement\|entangled]] [[quantum state\|states]]~~, and the intrinsically [[non-deterministic]] outcomes of [[quantum measurement]]s, as features of its computation~~. Quantum computers can be viewed as sampling from quantum systems that evolve in ways that may be described as operating on an enormous number of possibilities simultaneously, though still subject to strict computational constraints. By contrast, ordinary ("classical") computers operate according to [[deterministic]] rules. (A [[Computer#Modern computers\|classical computer]] can, in principle, be replicated by a [[Turing machine\|classical mechanical device]], with only a simple multiple of time cost. On the other hand (it is believed), a quantum computer would require [[exponential growth\|exponentially]] more time and energy to be simulated classically.) It is widely believed that a quantum computer could perform ''some'' calculations exponentially faster than any classical computer. For example, a large-scale quantum computer could [[post-quantum cryptography\|break some widely used public-key cryptographic schemes]] and aid physicists in performing [[quantum simulator\|physical simulations]]. However, current hardware implementations of quantum computation are largely experimental and only suitable for specialized tasks.		A '''quantum computer''' is a (real or theoretical) [[computer]] that exploits [[quantum superposition\|superposed]] and [[quantum entanglement\|entangled]] [[quantum state\|states]]. Quantum computers can be viewed as sampling from quantum systems that evolve in ways that may be described as operating on an enormous number of possibilities simultaneously, though still subject to strict computational constraints. By contrast, ordinary ("classical") computers operate according to [[deterministic]] rules. (A [[Computer#Modern computers\|classical computer]] can, in principle, be replicated by a [[Turing machine\|classical mechanical device]], with only a simple multiple of time cost. On the other hand (it is believed), a quantum computer would require [[exponential growth\|exponentially]] more time and energy to be simulated classically.) It is widely believed that a quantum computer could perform ''some'' calculations exponentially faster than any classical computer. For example, a large-scale quantum computer could [[post-quantum cryptography\|break some widely used public-key cryptographic schemes]] and aid physicists in performing [[quantum simulator\|physical simulations]]. However, current hardware implementations of quantum computation are largely experimental and only suitable for specialized tasks.

	<!-- Basic principles of quantum computing-->		<!-- Basic principles of quantum computing-->
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	==== Quantum Turing machine ====		==== 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\|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 \|article-number=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.		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 name="quantum circuits">{{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\|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 \|article-number=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.

	====Noisy intermediate-scale quantum computing====		====Noisy intermediate-scale quantum computing====
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	<!-- Overview of quantum algorithms, particularly abstract routines with no explicit application -->		<!-- Overview of quantum algorithms, particularly abstract routines with no explicit application -->
	Progress in finding [[quantum algorithms]] typically focuses on ~~this~~ quantum circuit model, though exceptions like the [[Adiabatic quantum computation\|quantum adiabatic algorithm]] exist. Quantum algorithms can be roughly categorized by the type of speedup achieved over corresponding classical algorithms.<ref name="zoo">{{cite web \|author=Jordan \|first=Stephen \|date=14 October 2022 \|title=Quantum Algorithm Zoo \|url=http://math.nist.gov/quantum/zoo/ \|url-status=live \|archive-url=https://web.archive.org/web/20180429014516/https://math.nist.gov/quantum/zoo/ \|archive-date=29 April 2018 \|orig-date=22 April 2011}}</ref>		Progress in finding [[quantum algorithms]] typically focuses on the quantum circuit model,<ref name="quantum circuits"/> though exceptions like the [[Adiabatic quantum computation\|quantum adiabatic algorithm]] exist. Quantum algorithms can be roughly categorized by the type of speedup achieved over corresponding classical algorithms.<ref name="zoo">{{cite web \|author=Jordan \|first=Stephen \|date=14 October 2022 \|title=Quantum Algorithm Zoo \|url=http://math.nist.gov/quantum/zoo/ \|url-status=live \|archive-url=https://web.archive.org/web/20180429014516/https://math.nist.gov/quantum/zoo/ \|archive-date=29 April 2018 \|orig-date=22 April 2011}}</ref>

	Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include [[Shor's algorithm]] for factoring and the related quantum algorithms for computing [[discrete logarithm]]s, solving [[Pell's equation]], and, more generally, solving the [[hidden subgroup problem]] for [[Abelian group\|abelian]] finite groups.<ref name="zoo"/> These algorithms depend on the primitive of the [[quantum Fourier transform]]. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, but evidence suggests that this is unlikely.<ref>{{Cite conference \|last1=Aaronson \|first1=Scott \|last2=Arkhipov \|first2=Alex \|date=2011-06-06 \|title=The computational complexity of linear optics \|book-title=Proceedings of the forty-third annual ACM symposium on Theory of computing \|language=en \|location=[[San Jose, California]] \|publisher=[[Association for Computing Machinery]] \|pages=333–342 \|doi=10.1145/1993636.1993682 \|isbn=978-1-4503-0691-1 \|author-link=Scott Aaronson \|arxiv=1011.3245}}</ref> Certain oracle problems like [[Simon's problem]] and the [[Bernstein–Vazirani algorithm\|Bernstein–Vazirani problem]] do give provable speedups, though this is in the [[quantum complexity theory#Quantum query complexity\|quantum query model]], which is a restricted model where lower bounds are much easier to prove and don't necessarily translate to speedups for practical problems.		Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include [[Shor's algorithm]] for factoring and the related quantum algorithms for computing [[discrete logarithm]]s, solving [[Pell's equation]], and, more generally, solving the [[hidden subgroup problem]] for [[Abelian group\|abelian]] finite groups.<ref name="zoo"/> These algorithms depend on the primitive of the [[quantum Fourier transform]]. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, but evidence suggests that this is unlikely.<ref>{{Cite conference \|last1=Aaronson \|first1=Scott \|last2=Arkhipov \|first2=Alex \|date=2011-06-06 \|title=The computational complexity of linear optics \|book-title=Proceedings of the forty-third annual ACM symposium on Theory of computing \|language=en \|location=[[San Jose, California]] \|publisher=[[Association for Computing Machinery]] \|pages=333–342 \|doi=10.1145/1993636.1993682 \|isbn=978-1-4503-0691-1 \|author-link=Scott Aaronson \|arxiv=1011.3245}}</ref> Certain oracle problems like [[Simon's problem]] and the [[Bernstein–Vazirani algorithm\|Bernstein–Vazirani problem]] do give provable speedups, though this is in the [[quantum complexity theory#Quantum query complexity\|quantum query model]], which is a restricted model where lower bounds are much easier to prove and don't necessarily translate to speedups for practical problems.
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	== Potential applications ==		== Potential applications ==

	~~With focus on~~ business management~~'s point of view~~, the potential applications of quantum computing into four ~~major categories are~~ cybersecurity, data analytics and artificial intelligence, optimization and simulation, and data management and ~~searching~~.<ref>{{cite web \|last1=Leong \|first1=Kelvin \|last2=Sung \|first2=Anna \|date= November 2022 \|title= What Business Managers Should Know About Quantum Computing? \|url=http://journalofinterdisciplinarysciences.com/wp-content/uploads/2022/10/3-What-Business-Managers-Should-Know-About-Quantum-Computing.pdf \|access-date=13 August 2023 \|website=[[Journal of Interdisciplinary Sciences]] \|language=en-US}}</ref>		From the perspective of business management, the potential applications of quantum computing are commonly classified into four key domains: (1) cybersecurity; (2) data analytics and artificial intelligence; (3) optimization and simulation; and (4) data management and search.<ref>{{cite web \|last1=Leong \|first1=Kelvin \|last2=Sung \|first2=Anna \|date= November 2022 \|title= What Business Managers Should Know About Quantum Computing? \|url=http://journalofinterdisciplinarysciences.com/wp-content/uploads/2022/10/3-What-Business-Managers-Should-Know-About-Quantum-Computing.pdf \|access-date=13 August 2023 \|website=[[Journal of Interdisciplinary Sciences]] \|language=en-US}}</ref>

	Other applications include healthcare (i.e., drug discovery), financial modeling, and natural language processing.<ref>{{Cite web \|title=10 Quantum Computing Applications & Examples to Know \|url=https://builtin.com/hardware/quantum-computing-applications \|access-date=2025-06-21 \|website=Built In \|language=en}}</ref>		Other applications include healthcare (i.e., drug discovery), financial modeling, and natural language processing.<ref>{{Cite web \|title=10 Quantum Computing Applications & Examples to Know \|url=https://builtin.com/hardware/quantum-computing-applications \|access-date=2025-06-21 \|website=Built In \|language=en}}</ref>
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	*{{annotated link\|Electronic quantum holography}}		*{{annotated link\|Electronic quantum holography}}
	*{{annotated link\|Glossary of quantum computing}}		*{{annotated link\|Glossary of quantum computing}}
	*{{annotated link\|~~IARPA~~}}		*{{annotated link\|Intelligence Advanced Research Projects Activity}}
	*{{annotated link\|India's quantum computer}}		*{{annotated link\|India's quantum computer}}
			**{{annotated link\|QpiAI-Indus}}
	*{{annotated link\|IonQ}}		*{{annotated link\|IonQ}}
	*{{annotated link\|List of emerging technologies}}		*{{annotated link\|List of emerging technologies}}

Quantum computing - Revision history

imported>Quantling: /* Potential applications */ bold is overkill. The numbering already makes the list stand out.

~2025-32763-74: Link to Shor's algorithm page

imported>Frietjes at 17:31, 30 June 2025

imported>Remsense: Reverted 1 edit by 2409:40F0:1038:BB2E:8000:0:0:0 (talk) to last revision by ShelfSkewed

imported>MrOllie: Reverted 1 edit by Monirima (talk): Citespammer