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Documents authored by Savin, Valentin

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DOI: 10.4230/DagRep.14.5.173
Classical-Quantum Synergies in the Theory and Practice of Quantum Error Correction (Dagstuhl Seminar 24212)

Authors: Carmen G. Almudéver, Leonid Pryadko, Valentin Savin, and Bane Vasic

Published in: Dagstuhl Reports, Volume 14, Issue 5 (2024)

Abstract
The Dagstuhl Seminar 24212 "Classical-Quantum Synergies in the Theory and Practice of Quantum Error Correction" was held on May 20-23, 2024, and brought together 30 participants from 13 countries. The seminar served as an interaction forum for senior and talented junior researchers, crossing boundaries between classical and quantum coding theory, and related areas of quantum technology and engineering problems. The topics covered by the seminar ranged from models of quantum noise to the theory and practice of quantum codes, including fault-tolerant error correction and fault-tolerant quantum computation, quantum error correction for specific technology constraints or noise models, decoding aspects of topological and quantum LDPC codes, and quantum error correction for scalable modular quantum computing architectures. The two and a half day program of the seminar consisted of 14 invited talks, and five breakout sessions, aimed at fostering an exchange of knowledge and viewpoints on challenges faced by quantum error correction. This report briefly presents the background, the motivation, and the topics covered by the seminar, and provides an overview of the invited talks and of three of the breakout sessions that brought together a large number of participants.
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Carmen G. Almudéver, Leonid Pryadko, Valentin Savin, and Bane Vasic. Classical-Quantum Synergies in the Theory and Practice of Quantum Error Correction (Dagstuhl Seminar 24212). In Dagstuhl Reports, Volume 14, Issue 5, pp. 173-190, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{almudever_et_al:DagRep.14.5.173,
  author =	{Almud\'{e}ver, Carmen G. and Pryadko, Leonid and Savin, Valentin and Vasic, Bane},
  title =	{{Classical-Quantum Synergies in the Theory and Practice of Quantum Error Correction (Dagstuhl Seminar 24212)}},
  pages =	{173--190},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{14},
  number =	{5},
  editor =	{Almud\'{e}ver, Carmen G. and Pryadko, Leonid and Savin, Valentin and Vasic, Bane},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.5.173},
  URN =		{urn:nbn:de:0030-drops-222647},
  doi =		{10.4230/DagRep.14.5.173},
  annote =	{Keywords: Fault-tolerant quantum computing, Quantum computing architectures, Quantum error correction, quantum information, Quantum LDPC codes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.36
Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems

Authors: Maxime Cautrès, Nathan Claudet, Mehdi Mhalla, Simon Perdrix, Valentin Savin, and Stéphan Thomassé

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study the notion of k-stabilizer universal quantum state, that is, an n-qubit quantum state, such that it is possible to induce any stabilizer state on any k qubits, by using only local operations and classical communications. These states generalize the notion of k-pairable states introduced by Bravyi et al., and can be studied from a combinatorial perspective using graph states and k-vertex-minor universal graphs. First, we demonstrate the existence of k-stabilizer universal graph states that are optimal in size with n = Θ(k²) qubits. We also provide parameters for which a random graph state on Θ(k²) qubits is k-stabilizer universal with high probability. Our second contribution consists of two explicit constructions of k-stabilizer universal graph states on n = O(k⁴) qubits. Both rely upon the incidence graph of the projective plane over a finite field 𝔽_q. This provides a major improvement over the previously known explicit construction of k-pairable graph states with n = O(2^{3k}), bringing forth a new and potentially powerful family of multipartite quantum resources.
Cite as

Maxime Cautrès, Nathan Claudet, Mehdi Mhalla, Simon Perdrix, Valentin Savin, and Stéphan Thomassé. Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cautres_et_al:LIPIcs.ICALP.2024.36,
  author =	{Cautr\`{e}s, Maxime and Claudet, Nathan and Mhalla, Mehdi and Perdrix, Simon and Savin, Valentin and Thomass\'{e}, St\'{e}phan},
  title =	{{Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.36},
  URN =		{urn:nbn:de:0030-drops-201796},
  doi =		{10.4230/LIPIcs.ICALP.2024.36},
  annote =	{Keywords: Quantum networks, graph states, vertex-minors, k-pairability}
}
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