Abstract structure of unitary oracles for quantum algorithms

William  Zeng; Jamie Vicary

doi:10.4204/EPTCS.172.19

Abstract structure of unitary oracles for quantum algorithms

William Zeng, Jamie Vicary

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.

Original language	English
Title of host publication	Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014)
Editors	Bob Coecke, Ichiro Hasuo, Prakash Panangaden
Publisher	Open Publishing Association
Pages	270-284
DOIs	https://doi.org/10.4204/EPTCS.172.19
Publication status	Published - 28 Dec 2014
Event	11th workshop on Quantum Physics and Logic (QPL 2014) - Kyoto, Japan Duration: 4 Jun 2014 → 6 Jun 2014

Publication series

Name	Electronic Proceedings in Theoretical Computer Science
Publisher	Open Publishing Association
Volume	172
ISSN (Electronic)	2075-2180

Conference

Conference	11th workshop on Quantum Physics and Logic (QPL 2014)
Country/Territory	Japan
City	Kyoto
Period	4/06/14 → 6/06/14

Access to Document

10.4204/EPTCS.172.19Licence: Creative Commons: Attribution (CC BY)

http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPL2014.19.pdfLicence: Creative Commons: Attribution (CC BY)

Cite this

@inproceedings{0ceff5d3b7d442a2bf9cb5b137510453,

title = "Abstract structure of unitary oracles for quantum algorithms",

abstract = "We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.",

author = "William Zeng and Jamie Vicary",

year = "2014",

month = dec,

day = "28",

doi = "10.4204/EPTCS.172.19",

language = "English",

series = "Electronic Proceedings in Theoretical Computer Science",

publisher = "Open Publishing Association",

pages = "270--284",

editor = "{ Coecke}, Bob and Hasuo, {Ichiro } and { Panangaden}, Prakash",

booktitle = "Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014)",

note = "11th workshop on Quantum Physics and Logic (QPL 2014) ; Conference date: 04-06-2014 Through 06-06-2014",

}

Zeng, W & Vicary, J 2014, Abstract structure of unitary oracles for quantum algorithms. in B Coecke, I Hasuo & P Panangaden (eds), Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014). Electronic Proceedings in Theoretical Computer Science, vol. 172, Open Publishing Association, pp. 270-284, 11th workshop on Quantum Physics and Logic (QPL 2014), Kyoto, Japan, 4/06/14. https://doi.org/10.4204/EPTCS.172.19

Abstract structure of unitary oracles for quantum algorithms. / Zeng, William ; Vicary, Jamie.
Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014). ed. / Bob Coecke; Ichiro Hasuo; Prakash Panangaden. Open Publishing Association, 2014. p. 270-284 (Electronic Proceedings in Theoretical Computer Science; Vol. 172).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Abstract structure of unitary oracles for quantum algorithms

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AU - Vicary, Jamie

PY - 2014/12/28

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N2 - We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.

AB - We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.

U2 - 10.4204/EPTCS.172.19

DO - 10.4204/EPTCS.172.19

M3 - Conference contribution

T3 - Electronic Proceedings in Theoretical Computer Science

SP - 270

EP - 284

BT - Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014)

A2 - Coecke, Bob

A2 - Hasuo, Ichiro

A2 - Panangaden, Prakash

PB - Open Publishing Association

T2 - 11th workshop on Quantum Physics and Logic (QPL 2014)

Y2 - 4 June 2014 through 6 June 2014

ER -

Abstract structure of unitary oracles for quantum algorithms

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