A 2-Categorical Approach to Composing Quantum Structures

David Reutter; Jamie Vicary

doi:10.4230/LIPIcs.CALCO.2017.20

A 2-Categorical Approach to Composing Quantum Structures

David Reutter, Jamie Vicary

Computer Science

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

Abstract

We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. They
have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.

Original language	English
Title of host publication	7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Editors	Filippo Bonchi , Barbara König
Publisher	Schloss Dagstuhl
Pages	20:1-20:20
Number of pages	20
ISBN (Electronic)	9783959770330
DOIs	https://doi.org/10.4230/LIPIcs.CALCO.2017.20
Publication status	Published - 2 Nov 2017
Event	7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) - Ljubljana, Slovenia Duration: 13 Jun 2017 → 16 Jun 2017

Publication series

Name	Leibniz International Proceedings in Informatics (LIPIcs)
Publisher	Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Volume	72
ISSN (Electronic)	1868-8969

Conference

Conference	7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Country/Territory	Slovenia
City	Ljubljana
Period	13/06/17 → 16/06/17

Keywords

quantum constructions
2-category
graphical calculus
planar algebra

Access to Document

10.4230/LIPIcs.CALCO.2017.20Licence: Creative Commons: Attribution (CC BY)

Cite this

@inproceedings{8d71a98289ea4f74b5be4c6c10a58437,

title = "A 2-Categorical Approach to Composing Quantum Structures",

abstract = "We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. Theyhave an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.",

keywords = "quantum constructions, 2-category, graphical calculus, planar algebra",

author = "David Reutter and Jamie Vicary",

year = "2017",

month = nov,

day = "2",

doi = "10.4230/LIPIcs.CALCO.2017.20",

language = "English",

series = "Leibniz International Proceedings in Informatics (LIPIcs)",

publisher = "Schloss Dagstuhl",

pages = "20:1--20:20",

editor = "{Bonchi }, {Filippo } and K{\"o}nig, {Barbara }",

booktitle = "7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)",

address = "Germany",

note = "7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) ; Conference date: 13-06-2017 Through 16-06-2017",

}

Reutter, D & Vicary, J 2017, A 2-Categorical Approach to Composing Quantum Structures. in F Bonchi & B König (eds), 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), vol. 72, Schloss Dagstuhl, pp. 20:1-20:20, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017), Ljubljana, Slovenia, 13/06/17. https://doi.org/10.4230/LIPIcs.CALCO.2017.20

A 2-Categorical Approach to Composing Quantum Structures. / Reutter, David; Vicary, Jamie.
7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). ed. / Filippo Bonchi ; Barbara König. Schloss Dagstuhl, 2017. p. 20:1-20:20 (Leibniz International Proceedings in Informatics (LIPIcs); Vol. 72).

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

TY - GEN

T1 - A 2-Categorical Approach to Composing Quantum Structures

AU - Reutter, David

AU - Vicary, Jamie

PY - 2017/11/2

Y1 - 2017/11/2

N2 - We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. Theyhave an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.

AB - We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. Theyhave an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.

KW - quantum constructions

KW - 2-category

KW - graphical calculus

KW - planar algebra

U2 - 10.4230/LIPIcs.CALCO.2017.20

DO - 10.4230/LIPIcs.CALCO.2017.20

M3 - Conference contribution

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

SP - 20:1-20:20

BT - 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

A2 - Bonchi , Filippo

A2 - König, Barbara

PB - Schloss Dagstuhl

T2 - 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

Y2 - 13 June 2017 through 16 June 2017

ER -

A 2-Categorical Approach to Composing Quantum Structures

Abstract

Publication series

Conference

Keywords

Access to Document

Fingerprint

Cite this