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of 13
pro vyhledávání: '"Renaud Vilmart"'
Autor:
Renaud Vilmart
Publikováno v:
Logical Methods in Computer Science, Vol Volume 20, Issue 1 (2024)
The "Sum-Over-Paths" formalism is a way to symbolically manipulate linear maps that describe quantum systems, and is a tool that is used in formal verification of such systems. We give here a new set of rewrite rules for the formalism, and show that
Externí odkaz:
https://doaj.org/article/ed737bebdaf8418cb6399a7f2788c4d4
Autor:
Renaud Vilmart
Publikováno v:
Electronic Proceedings in Theoretical Computer Science, Vol 287, Iss Proc. QPL 2018, Pp 313-344 (2019)
We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. We precisely show the form of the matrices it represents, and we provide an axiomatisation which m
Externí odkaz:
https://doaj.org/article/621ba5ed6f124b14bf330b60e45d8d19
Publikováno v:
Logical Methods in Computer Science, Vol Volume 16, Issue 2 (2020)
The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics and quantum information theory. It comes equipped with an equational presentation. We focus here on a very important property of the language: completeness, which
Externí odkaz:
https://doaj.org/article/a0194c260e1d49a39594d6eef27f4d21
Publikováno v:
Electronic Proceedings in Theoretical Computer Science, Vol 266, Iss Proc. QPL 2017, Pp 23-57 (2018)
We introduce a ZX-like diagrammatic language devoted to manipulating real matrices – and rebits –, with its own set of axioms. We prove the necessity of some non trivial axioms of these. We show that some restriction of the language is complete.
Externí odkaz:
https://doaj.org/article/8c471c89d31a42b5b1d989038d1cd261
Publikováno v:
ACM Transactions on Quantum Computing
ACM Transactions on Quantum Computing, 2021, 2 (4), pp.1-28. ⟨10.1145/3464693⟩
ACM Transactions on Quantum Computing, 2021, 2 (4), pp.1-28. ⟨10.1145/3464693⟩
There exist several graphical languages for quantum information processing, like quantum circuits, ZX-calculus, ZW-calculus, and so on. Each of these languages forms a †-symmetric monoidal category (†-SMC) and comes with an interpretation functor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81e8a9e9d4b59a33ea216f8e72b61bb2
https://doi.org/10.1145/3464693
https://doi.org/10.1145/3464693
Autor:
Renaud Vilmart
Publikováno v:
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785765⟩
LICS
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785765⟩
LICS
Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for an approximately universal restriction of the language, and then for the whole language. The main drawbacks were that the axioms that were added to achieve com
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e4367d2e45c8cc5845a8f49e67ca445f
https://hal.archives-ouvertes.fr/hal-01963426/document
https://hal.archives-ouvertes.fr/hal-01963426/document
Publikováno v:
The 33rd Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2018
The 33rd Annual Symposium on Logic in Computer Science, 2018, Jul 2018, Oxford, United Kingdom. pp.559--568, ⟨10.1145/3209108.3209131⟩
The 33rd Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2018, Jul 2018, Oxford, United Kingdom. pp.559--568, ⟨10.1145/3209108.3209131⟩
LICS
The 33rd Annual Symposium on Logic in Computer Science, 2018, Jul 2018, Oxford, United Kingdom. pp.559--568, ⟨10.1145/3209108.3209131⟩
The 33rd Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2018, Jul 2018, Oxford, United Kingdom. pp.559--568, ⟨10.1145/3209108.3209131⟩
LICS
We introduce the first complete and approximately universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum mechanics by addi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d77a9c6b759119a2613e8c9843e98bec
https://hal.archives-ouvertes.fr/hal-01529623v2/document
https://hal.archives-ouvertes.fr/hal-01529623v2/document
Autor:
Renaud Vilmart
Publikováno v:
QPL 2018
QPL 2018, Jun 2018, Halifax, Canada. pp.313-344, ⟨10.4204/EPTCS.287.18⟩
QPL
Electronic Proceedings in Theoretical Computer Science, Vol 287, Iss Proc. QPL 2018, Pp 313-344 (2019)
QPL 2018, Jun 2018, Halifax, Canada. pp.313-344, ⟨10.4204/EPTCS.287.18⟩
QPL
Electronic Proceedings in Theoretical Computer Science, Vol 287, Iss Proc. QPL 2018, Pp 313-344 (2019)
We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. We precisely show the form of the matrices it represents, and we provide an axiomatisation which m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c692db3dd3d603f97904474d99f6610
https://hal.science/hal-01762264
https://hal.science/hal-01762264
Publikováno v:
LICS
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785754⟩
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science
LICS 2019-34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785754⟩
Recent completeness results on the ZX-calculus used a third-party language, namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly non-constructive. We address this issue in the following. To do so, we first describe a generic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b6554b6c322dc0e960cd703e7b525f3c
http://arxiv.org/abs/1805.05296
http://arxiv.org/abs/1805.05296