Semantics for a Quantum Programming Language by Operator Algebras

Cho, Kenta

doi:10.1007/s00354-016-0204-3

Cited by 20 publications

(35 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3.10 of [11]). 3 Addition and scalar multiplication are computed coordinate-wise in B a (X); multiplication is given by composition, and involution is the adjoint.…”

mentioning

confidence: 99%

Paschke Dilations

Westerbaan

2017

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

show abstract

“…3.10 of [11]). 3 Addition and scalar multiplication are computed coordinate-wise in B a (X); multiplication is given by composition, and involution is the adjoint.…”

mentioning

confidence: 99%

Paschke Dilations

Westerbaan

2017

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

show abstract

“…Recently there are several works using C * -algebras [11,19], which led the author to the present work. The use of W * -algebras in this context appeared independently and coincidentally in Rennela's thesis [35] and the present work (or the author's thesis [6]). In [35, Theorem 3.8], he also observed that the category Wstar PSU of W * -algebras and normal positive subunital maps are Dcppo-enriched, which is almost the same result as Theorem 5.3 in the present paper.…”

mentioning

confidence: 61%

“…Section 10 concludes the paper with future work. This paper is based on the author's master thesis [6], in which one may find further details.…”

mentioning

confidence: 99%

Semantics for a Quantum Programming Language by Operator Algebras

Cho

2014

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of the category of W*-algebras and normal completely positive subunital maps is an elementary quantum flow chart category in the sense of Selinger. As a consequence, it gives a denotational semantics for Selinger's first-order functional quantum programming language QPL. The use of operator algebras allows us to accommodate infinite structures and to handle classical and quantum computations in a unified way.Comment: In Proceedings QPL 2014, arXiv:1412.810

show abstract

“…Equipped with this order, our category C is DCPO ⊥! -enriched[2, Theorem 4.3]. The least element in C(A, B)is also a zero morphism and is given by the map 0 : A → B, defined by 0(x) = 0.…”

mentioning

confidence: 99%

Quantum Programming with Inductive Datatypes: Causality and Affine Type Theory

Péchoux

Perdrix

Rennela

et al. 2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL. We construct a sound categorical model for the language and by doing so we provide the first detailed semantic treatment of user-defined inductive datatypes in quantum programming. We also show our denotational interpretation is invariant with respect to big-step reduction, thereby establishing another novel result for quantum programming. Compared to classical programming, this property is considerably more difficult to prove and we demonstrate its usefulness by showing how it immediately implies computational adequacy at all types. To further cement our results, our semantics is entirely based on a physically natural model of von Neumann algebras, which are mathematical structures used by physicists to study quantum mechanics.

show abstract

Semantics for a Quantum Programming Language by Operator Algebras

Cited by 20 publications

References 47 publications

Paschke Dilations

Paschke Dilations

Semantics for a Quantum Programming Language by Operator Algebras

Quantum Programming with Inductive Datatypes: Causality and Affine Type Theory

Contact Info

Product

Resources

About