Domains of Commutative C-Subalgebras

C. Heunen; B. Lindenhovius

doi:10.1109/LICS.2015.49

Domains of Commutative C-Subalgebras

C. Heunen, B. Lindenhovius

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

Abstract

Operator algebras provide uniform semantics for deterministic, reversible, probabilistic, and quantum computing, where intermediate results of partial computations are given by commutative sub algebras. We study this setting using domain theory, and show that a given operator algebra is scattered if and only if its associated partial order is, equivalently: continuous (a domain), algebraic, atomistic, quasi-continuous, or quasialgebraic. In that case, conversely, we prove that the Lawson topology, modelling information approximation, allows one to associate an operator algebra to the domain.

Original language	English
Title of host publication	Logic in Computer Science (LICS), 2015 30th Annual ACM/IEEE Symposium on
Publisher	Institute of Electrical and Electronics Engineers
Pages	450-461
Number of pages	12
DOIs	https://doi.org/10.1109/LICS.2015.49
Publication status	Published - 1 Jul 2015

Keywords / Materials (for Non-textual outputs)

algebra
approximation theory
quantum computing
Lawson topology
commutative C*-subalgebras
deterministic computing
domain theory
modelling information approximation
operator algebras
probabilistic computing
reversible computing
uniform semantics
Algebra
Approximation methods
Computational modeling
Probabilistic logic
Quantum computing
Semantics
Topology
C-algebra
Domain

Access to Document

10.1109/LICS.2015.49

domainsAccepted author manuscript, 242 KB

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7174903

Combining Viewpoints in Quantum Theory
Heunen, C.
EPSRC
2/10/15 → 1/01/19
Project: Research

Cite this

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title = "Domains of Commutative C-Subalgebras",

abstract = "Operator algebras provide uniform semantics for deterministic, reversible, probabilistic, and quantum computing, where intermediate results of partial computations are given by commutative sub algebras. We study this setting using domain theory, and show that a given operator algebra is scattered if and only if its associated partial order is, equivalently: continuous (a domain), algebraic, atomistic, quasi-continuous, or quasialgebraic. In that case, conversely, we prove that the Lawson topology, modelling information approximation, allows one to associate an operator algebra to the domain.",

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doi = "10.1109/LICS.2015.49",

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AU - Lindenhovius, B.

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N2 - Operator algebras provide uniform semantics for deterministic, reversible, probabilistic, and quantum computing, where intermediate results of partial computations are given by commutative sub algebras. We study this setting using domain theory, and show that a given operator algebra is scattered if and only if its associated partial order is, equivalently: continuous (a domain), algebraic, atomistic, quasi-continuous, or quasialgebraic. In that case, conversely, we prove that the Lawson topology, modelling information approximation, allows one to associate an operator algebra to the domain.

AB - Operator algebras provide uniform semantics for deterministic, reversible, probabilistic, and quantum computing, where intermediate results of partial computations are given by commutative sub algebras. We study this setting using domain theory, and show that a given operator algebra is scattered if and only if its associated partial order is, equivalently: continuous (a domain), algebraic, atomistic, quasi-continuous, or quasialgebraic. In that case, conversely, we prove that the Lawson topology, modelling information approximation, allows one to associate an operator algebra to the domain.

KW - algebra

KW - approximation theory

KW - quantum computing

KW - Lawson topology

KW - commutative C-subalgebras

KW - deterministic computing

KW - domain theory

KW - modelling information approximation

KW - operator algebras

KW - probabilistic computing

KW - reversible computing

KW - uniform semantics

KW - Algebra

KW - Approximation methods

KW - Computational modeling

KW - Probabilistic logic

KW - Quantum computing

KW - Semantics

KW - Topology

KW - C-algebra

KW - Domain

U2 - 10.1109/LICS.2015.49

DO - 10.1109/LICS.2015.49

M3 - Conference contribution

SP - 450

EP - 461

BT - Logic in Computer Science (LICS), 2015 30th Annual ACM/IEEE Symposium on

PB - Institute of Electrical and Electronics Engineers

ER -

Domains of Commutative C-Subalgebras

Abstract

Keywords / Materials (for Non-textual outputs)

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Projects

Combining Viewpoints in Quantum Theory

Cite this