10 Search Results for "Clément, Alexandre"

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Research
DOI: 10.4230/TGDK.3.2.2
Distances Between Formal Concept Analysis Structures

Authors: Alexandre Bazin and Giacomo Kahn

Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2

Abstract
In this paper, we study the notion of distance between the most important structures of formal concept analysis: formal contexts, concept lattices, and implication bases. We first define three families of Minkowski-like distances between these three structures. We then present experiments showing that the correlations of these distances are low and depend on the distance between formal contexts.
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Alexandre Bazin and Giacomo Kahn. Distances Between Formal Concept Analysis Structures. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{bazin_et_al:TGDK.3.2.2,
  author =	{Bazin, Alexandre and Kahn, Giacomo},
  title =	{{Distances Between Formal Concept Analysis Structures}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:18},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.2},
  URN =		{urn:nbn:de:0030-drops-248126},
  doi =		{10.4230/TGDK.3.2.2},
  annote =	{Keywords: Formal Concept Analysis, Implication Base, Concept Lattice, Pattern Mining, Ordinal Data Science}
}
Document
DOI: 10.4230/OASIcs.SpaceCHI.2025.26
Movement in Low Gravity (MoLo) – LUNA: Biomechanical Modelling to Mitigate Lunar Surface Operation Risks

Authors: David Andrew Green

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
The Artemis programme seeks to develop and test concepts, hardware and approaches to support long term habitation of the Lunar surface, and future missions to Mars. In preparation for the Artemis missions determination of tasks to be performed, the functional requirements of such tasks and as mission duration extends whether physiological deconditioning becomes functionally significant, compromising the crew member’s ability to perform critical tasks on the surface, and/or upon return to earth [MoLo-LUNA – leveraging the Molo programme (and several other activities) - could become a key supporting activity for LUNA incl. validation of the Puppeteer offloading system itself via creation of a complementary MoLo-LUNA-LAB. Furthermore, the MoLo-LUNA programme could become a key facilitator of simulator suit instrumentation/definition, broader astronaut training activities and mission architecture development – including Artemis mission simulations. By employing a Puppeteer system external to the LUNA chamber hall it will optimise utilisation and cost-effectiveness of LUNA, and as such represents a critical service to future LUNA stakeholders. Furthermore, MoLo-LUNA would generate a unique data set that can be leveraged to predict de-conditioning on the Lunar surface - and thereby optimise functionality, and minimise mission risk – including informing the need for, and prescription of exercise countermeasures on the Lunar Surface and in transit. Thus, MoLo-LUNA offers a unique opportunity to place LUNA, and ESA as a key ongoing provider of evidence to define, optimise and support crew Artemis surface missions.
Cite as

David Andrew Green. Movement in Low Gravity (MoLo) – LUNA: Biomechanical Modelling to Mitigate Lunar Surface Operation Risks. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 26:1-26:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{green:OASIcs.SpaceCHI.2025.26,
  author =	{Green, David Andrew},
  title =	{{Movement in Low Gravity (MoLo) – LUNA: Biomechanical Modelling to Mitigate Lunar Surface Operation Risks}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{26:1--26:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.26},
  URN =		{urn:nbn:de:0030-drops-240166},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.26},
  annote =	{Keywords: Locomotion, hypogravity, modelling, Lunar}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.6
Omega-Regular Verification and Control for Distributional Specifications in MDPs

Authors: S. Akshay, Ouldouz Neysari, and Ðorđe Žikelić

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
A classical approach to studying Markov decision processes (MDPs) is to view them as state transformers. However, MDPs can also be viewed as distribution transformers, where an MDP under a strategy generates a sequence of probability distributions over MDP states. This view arises in several applications, even as the probabilistic model checking problem becomes much harder compared to the classical state transformer counterpart. It is known that even distributional reachability and safety problems become computationally intractable (Skolem- and positivity-hard). To address this challenge, recent works focused on sound but possibly incomplete methods for verification and control of MDPs under the distributional view. However, existing automated methods are applicable only to distributional reachability, safety and reach-avoidance specifications. In this work, we present the first automated method for verification and control of MDPs with respect to distributional omega-regular specifications. To achieve this, we propose a novel notion of distributional certificates, which are sound and complete proof rules for proving that an MDP under a distributionally memoryless strategy satisfies some distributional omega-regular specification. We then use our distributional certificates to design the first fully automated algorithms for verification and control of MDPs with respect to distributional omega-regular specifications. Our algorithms follow a template-based synthesis approach and provide soundness and relative completeness guarantees, while running in PSPACE. Our prototype implementation demonstrates practical applicability of our algorithms to challenging examples collected from the literature.
Cite as

S. Akshay, Ouldouz Neysari, and Ðorđe Žikelić. Omega-Regular Verification and Control for Distributional Specifications in MDPs. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2025.6,
  author =	{Akshay, S. and Neysari, Ouldouz and \v{Z}ikeli\'{c}, Ðor{\d}e},
  title =	{{Omega-Regular Verification and Control for Distributional Specifications in MDPs}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.6},
  URN =		{urn:nbn:de:0030-drops-239562},
  doi =		{10.4230/LIPIcs.CONCUR.2025.6},
  annote =	{Keywords: MDPs, Distributional objectives, \omega-regularity, Certificates}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.31
Higher-Dimensional Automata: Extension to Infinite Tracks

Authors: Luc Passemard, Amazigh Amrane, and Uli Fahrenberg

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
We introduce higher-dimensional automata for infinite interval ipomsets (ω-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by ω-HDAs under Büchi and Muller semantics. We show that Muller acceptance is more expressive than Büchi acceptance and, in contrast to the finite case, both semantics do not yield languages closed under subsumption. Then, we adapt the original rational operations to deal with ω-HDAs and show that while languages of ω-HDAs are ω-rational, not all ω-rational languages can be expressed by ω-HDAs.
Cite as

Luc Passemard, Amazigh Amrane, and Uli Fahrenberg. Higher-Dimensional Automata: Extension to Infinite Tracks. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{passemard_et_al:LIPIcs.FSCD.2025.31,
  author =	{Passemard, Luc and Amrane, Amazigh and Fahrenberg, Uli},
  title =	{{Higher-Dimensional Automata: Extension to Infinite Tracks}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.31},
  URN =		{urn:nbn:de:0030-drops-236466},
  doi =		{10.4230/LIPIcs.FSCD.2025.31},
  annote =	{Keywords: Higher-dimensional automata, concurrency theory, omega pomsets, B\"{u}chi acceptance, Muller acceptance, interval pomsets, pomsets with interfaces}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.38
A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors

Authors: Nicolas Heurtel

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Graphical languages are powerful and useful to represent, rewrite and simplify different kinds of processes. In particular, they have been widely used for quantum processes, improving the state of the art for compilation, simulation and verification. In this work, we focus on one of the main carrier of quantum information and computation: linear optical circuits. We introduce the LO_fi-calculus, the first graphical language to reason on the infinite-dimensional photonic space with circuits only composed of the four core elements of linear optics: the phase shifter, the beam splitter, and auxiliary sources and detectors with bounded photon number. First, we study the subfragment of circuits composed of phase shifters and beam splitters, for which we provide the first minimal equational theory. Next, we introduce a rewriting procedure on those LO_fi-circuits that converge to normal forms. We prove those forms to be unique, establishing both a novel and unique representation of linear optical processes. Finally, we complement the language with an equational theory that we prove to be complete: two LO_fi-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LO_fi-calculus.
Cite as

Nicolas Heurtel. A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 38:1-38:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{heurtel:LIPIcs.CSL.2025.38,
  author =	{Heurtel, Nicolas},
  title =	{{A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{38:1--38:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.38},
  URN =		{urn:nbn:de:0030-drops-227957},
  doi =		{10.4230/LIPIcs.CSL.2025.38},
  annote =	{Keywords: Quantum Computing, Graphical Language, Linear Optical Circuits, Linear Optical Quantum Computing, Completeness, Fock Space}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.20
Quantum Circuit Completeness: Extensions and Simplifications

Authors: Alexandre Clément, Noé Delorme, Simon Perdrix, and Renaud Vilmart

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits can be derived from the equational theory. We improve this completeness result in two ways: (i) We simplify the equational theory by proving that several rules can be derived from the remaining ones. In particular, two out of the three most intricate rules are removed, the third one being slightly simplified. (ii) The complete equational theory can be extended to quantum circuits with ancillae or qubit discarding, to represent respectively quantum computations using an additional workspace, and hybrid quantum computations. We show that the remaining intricate rule can be greatly simplified in these more expressive settings, leading to equational theories where all equations act on a bounded number of qubits. The development of simple and complete equational theories for expressive quantum circuit models opens new avenues for reasoning about quantum circuits. It provides strong formal foundations for various compiling tasks such as circuit optimisation, hardware constraint satisfaction and verification.
Cite as

Alexandre Clément, Noé Delorme, Simon Perdrix, and Renaud Vilmart. Quantum Circuit Completeness: Extensions and Simplifications. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{clement_et_al:LIPIcs.CSL.2024.20,
  author =	{Cl\'{e}ment, Alexandre and Delorme, No\'{e} and Perdrix, Simon and Vilmart, Renaud},
  title =	{{Quantum Circuit Completeness: Extensions and Simplifications}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.20},
  URN =		{urn:nbn:de:0030-drops-196639},
  doi =		{10.4230/LIPIcs.CSL.2024.20},
  annote =	{Keywords: Quantum Circuits, Completeness, Graphical Language}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.35
LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits

Authors: Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, and Benoît Valiron

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We introduce the LO_v-calculus, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs. We present the axiomatics of the language and prove its soundness and completeness: two LO_v-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LO_v-calculus. We give a confluent and terminating rewrite system to rewrite any polarisation-preserving LO_v-circuit into a unique triangular normal form, inspired by the universal decomposition of Reck et al. (1994) for linear optical quantum circuits.
Cite as

Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, and Benoît Valiron. LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{clement_et_al:LIPIcs.MFCS.2022.35,
  author =	{Cl\'{e}ment, Alexandre and Heurtel, Nicolas and Mansfield, Shane and Perdrix, Simon and Valiron, Beno\^{i}t},
  title =	{{LO\underlinev-Calculus: A Graphical Language for Linear Optical Quantum Circuits}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.35},
  URN =		{urn:nbn:de:0030-drops-168334},
  doi =		{10.4230/LIPIcs.MFCS.2022.35},
  annote =	{Keywords: Quantum Computing, Graphical Language, Linear Optical Circuits, Linear Optical Quantum Computing, Completeness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.36
Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-Calculus

Authors: Alexandre Clément and Simon Perdrix

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. For instance, the complexity of implementing the permutation of some given unitary transformations can be strictly decreased by allowing coherent control, rather than using the standard quantum circuit model. In this paper, we address the problem of optimising the resources of coherently controlled quantum computations. We refine the PBS-calculus, a graphical language for coherent control which is inspired by quantum optics. In order to obtain a more resource-sensitive language, it manipulates abstract gates - that can be interpreted as queries to an oracle - and more importantly, it avoids the representation of useless wires by allowing unsaturated polarising beam splitters. Technically the language forms a coloured PROP. The language is equipped with an equational theory that we show to be sound, complete, and minimal. Regarding resource optimisation, we introduce an efficient procedure to minimise the number of oracle queries of a given diagram. We also consider the problem of minimising both the number of oracle queries and the number of polarising beam splitters. We show that this optimisation problem is NP-hard in general, but introduce an efficient heuristic that produces optimal diagrams when at most one query to each oracle is required.
Cite as

Alexandre Clément and Simon Perdrix. Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-Calculus. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 36:1-36:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{clement_et_al:LIPIcs.MFCS.2022.36,
  author =	{Cl\'{e}ment, Alexandre and Perdrix, Simon},
  title =	{{Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-Calculus}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{36:1--36:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.36},
  URN =		{urn:nbn:de:0030-drops-168348},
  doi =		{10.4230/LIPIcs.MFCS.2022.36},
  annote =	{Keywords: Quantum computing, Graphical language, Coherent control, Completeness, Resource optimisation, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.22
Coherent Control and Distinguishability of Quantum Channels via PBS-Diagrams

Authors: Cyril Branciard, Alexandre Clément, Mehdi Mhalla, and Simon Perdrix

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Even though coherent control of quantum operations appears to be achievable in practice, it is still not yet well understood. Among theoretical challenges, standard completely positive trace preserving (CPTP) maps are known not to be appropriate to represent coherently controlled quantum channels. We introduce here a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). We consider different situations of coherent control and disambiguate CPTP maps by considering purified channels, an extension of Stinespring’s dilation. First, we show that in classical control settings, the observational equivalence classes of purified channels correspond to the standard definition of quantum channels (CPTP maps). Then, we propose a refinement of this equivalence class generalising the "half quantum switch" situation, where one is allowed to coherently control which quantum channel is applied; in this case, quantum channel implementations can be distinguished using a so-called transformation matrix. A further refinement characterising observational equivalence with general extended PBS-diagrams as contexts is also obtained. Finally, we propose a refinement that could be used for more general coherent control settings.
Cite as

Cyril Branciard, Alexandre Clément, Mehdi Mhalla, and Simon Perdrix. Coherent Control and Distinguishability of Quantum Channels via PBS-Diagrams. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{branciard_et_al:LIPIcs.MFCS.2021.22,
  author =	{Branciard, Cyril and Cl\'{e}ment, Alexandre and Mhalla, Mehdi and Perdrix, Simon},
  title =	{{Coherent Control and Distinguishability of Quantum Channels via PBS-Diagrams}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.22},
  URN =		{urn:nbn:de:0030-drops-144629},
  doi =		{10.4230/LIPIcs.MFCS.2021.22},
  annote =	{Keywords: Quantum Computing, Diagrammatic Language, Quantum Control, Polarising Beam Splitter, Categorical Quantum Mechanics, Quantum Switch}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.24
PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations

Authors: Alexandre Clément and Simon Perdrix

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. Coherent control, and in particular indefinite causal order, is known to enable multiple computational and communication advantages over classically ordered models like quantum circuits. The PBS-calculus is inspired by quantum optics, in particular the polarising beam splitter (PBS for short). We formalise the syntax and the semantics of the PBS-diagrams, and we equip the language with an equational theory, which is proved to be sound and complete: two diagrams are representing the same quantum evolution if and only if one can be transformed into the other using the rules of the PBS-calculus. Moreover, we show that the equational theory is minimal. Finally, we consider applications like the implementation of controlled permutations and the unrolling of loops.
Cite as

Alexandre Clément and Simon Perdrix. PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{clement_et_al:LIPIcs.MFCS.2020.24,
  author =	{Cl\'{e}ment, Alexandre and Perdrix, Simon},
  title =	{{PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.24},
  URN =		{urn:nbn:de:0030-drops-126921},
  doi =		{10.4230/LIPIcs.MFCS.2020.24},
  annote =	{Keywords: Quantum Computing, Diagrammatic Language, Completeness, Quantum Control, Polarising Beam Splitter, Categorical Quantum Mechanics, Quantum Switch}
}
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