4 Search Results for "Leverrier, Anthony"


Document
Robust Quantum Entanglement at (Nearly) Room Temperature

Authors: Lior Eldar

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)


Abstract
We formulate an average-case analog of the NLTS conjecture of Freedman and Hastings (QIC 2014) by asking whether there exist topologically ordered systems with corresponding local Hamiltonians for which the thermal Gibbs state for constant temperature cannot even be approximated by shallow quantum circuits. We then prove this conjecture for nearly optimal parameters: we construct a quantum error correcting code whose corresponding (log) local Hamiltonian has the following property: for nearly constant temperature (temperature decays as 1/log²log(n)) the thermal Gibbs state of that Hamiltonian cannot be approximated by any circuit of depth less than log(n), and it is highly entangled in a well-defined way. This implies that appropriately chosen local Hamiltonians can give rise to ground-state long-range entanglement which can survive without active error correction at temperatures which are nearly independent of the system size: thereby improving exponentially upon previously known bounds.

Cite as

Lior Eldar. Robust Quantum Entanglement at (Nearly) Room Temperature. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 49:1-49:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{eldar:LIPIcs.ITCS.2021.49,
  author =	{Eldar, Lior},
  title =	{{Robust Quantum Entanglement at (Nearly) Room Temperature}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{49:1--49:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.49},
  URN =		{urn:nbn:de:0030-drops-135886},
  doi =		{10.4230/LIPIcs.ITCS.2021.49},
  annote =	{Keywords: Quantum error-correcting codes, Quantum Entanglement, Quantum Locally-Testable Codes, Local Hamiltonians, quantum PCP, NLTS}
}
Document
Towards Local Testability for Quantum Coding

Authors: Anthony Leverrier, Vivien Londe, and Gilles Zémor

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)


Abstract
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n > p) and stabilizer constraints with faces of dimension (p ± 1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into N = 2^{n-p-1} binom(n,p) physical qubits and displays local testability with a soundness of Ω(1/log(N)) beating the current state-of-the-art of 1/log²(N) due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors. We then extend this code family by considering the quotient of the n-cube by arbitrary linear classical codes of length n. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be constant, similarly to the ordinary n-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension.

Cite as

Anthony Leverrier, Vivien Londe, and Gilles Zémor. Towards Local Testability for Quantum Coding. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 65:1-65:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{leverrier_et_al:LIPIcs.ITCS.2021.65,
  author =	{Leverrier, Anthony and Londe, Vivien and Z\'{e}mor, Gilles},
  title =	{{Towards Local Testability for Quantum Coding}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{65:1--65:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.65},
  URN =		{urn:nbn:de:0030-drops-136049},
  doi =		{10.4230/LIPIcs.ITCS.2021.65},
  annote =	{Keywords: Quantum error correcting code}
}
Document
Quantum Walk Sampling by Growing Seed Sets

Authors: Simon Apers

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)


Abstract
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as O~(m^(1/3) delta^(-1/3)), with m the number of edges and delta the random walk spectral gap. This improves on existing strategies by initially growing a classical seed set in the graph, from which a quantum walk is then run. The algorithm leads to a number of improvements: (i) it provides a new bound on the setup cost of quantum walk search algorithms, (ii) it yields a new algorithm for st-connectivity, and (iii) it allows to create a superposition over the isomorphisms of an n-node graph in time O~(2^(n/3)), surpassing the Omega(2^(n/2)) barrier set by index erasure.

Cite as

Simon Apers. Quantum Walk Sampling by Growing Seed Sets. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{apers:LIPIcs.ESA.2019.9,
  author =	{Apers, Simon},
  title =	{{Quantum Walk Sampling by Growing Seed Sets}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{9:1--9:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.9},
  URN =		{urn:nbn:de:0030-drops-111300},
  doi =		{10.4230/LIPIcs.ESA.2019.9},
  annote =	{Keywords: Quantum algorithms, Quantum walks, Connectivity, Graph theory}
}
Document
Quantum key distribution and cryptography: a survey

Authors: Romain Alléaume, Norbert Lütkenhaus, Renato Renner, Philippe Grangier, Thierry Debuisschert, Gregoire Ribordy, Nicolas Gisin, Philippe Painchault, Thomas Pornin, Louis Slavail, Michel Riguidel, Andrew Shilds, Thomas Länger, Momtchil Peev, Mehrdad Dianati, Anthony Leverrier, Andreas Poppe, Jan Bouda, Cyril Branciard, Mark Godfrey, John Rarity, Harald Weinfurter, Anton Zeilinger, and Christian Monyk

Published in: Dagstuhl Seminar Proceedings, Volume 9311, Classical and Quantum Information Assurance Foundations and Practice (2010)


Abstract
I will try to partially answer, based on a review on recent work, the following question: Can QKD and more generally quantum information be useful to cover some practical security requirements in current (and future) IT infrastructures ? I will in particular cover the following topics - practical performances of QKD - QKD network deployment - SECOQC project - Capabilities of QKD as a cryptographic primitive - comparative advantage with other solution, in order to cover practical security requirements - Quantum information and Side-channels - QKD security assurance - Thoughts about "real" Post-Quantum Cryptography

Cite as

Romain Alléaume, Norbert Lütkenhaus, Renato Renner, Philippe Grangier, Thierry Debuisschert, Gregoire Ribordy, Nicolas Gisin, Philippe Painchault, Thomas Pornin, Louis Slavail, Michel Riguidel, Andrew Shilds, Thomas Länger, Momtchil Peev, Mehrdad Dianati, Anthony Leverrier, Andreas Poppe, Jan Bouda, Cyril Branciard, Mark Godfrey, John Rarity, Harald Weinfurter, Anton Zeilinger, and Christian Monyk. Quantum key distribution and cryptography: a survey. In Classical and Quantum Information Assurance Foundations and Practice. Dagstuhl Seminar Proceedings, Volume 9311, pp. 1-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


Copy BibTex To Clipboard

@InProceedings{alleaume_et_al:DagSemProc.09311.3,
  author =	{All\'{e}aume, Romain and L\"{u}tkenhaus, Norbert and Renner, Renato and Grangier, Philippe and Debuisschert, Thierry and Ribordy, Gregoire and Gisin, Nicolas and Painchault, Philippe and Pornin, Thomas and Slavail, Louis and Riguidel, Michel and Shilds, Andrew and L\"{a}nger, Thomas and Peev, Momtchil and Dianati, Mehrdad and Leverrier, Anthony and Poppe, Andreas and Bouda, Jan and Branciard, Cyril and Godfrey, Mark and Rarity, John and Weinfurter, Harald and Zeilinger, Anton and Monyk, Christian},
  title =	{{Quantum key distribution and cryptography: a survey}},
  booktitle =	{Classical and Quantum Information Assurance Foundations and Practice},
  pages =	{1--29},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9311},
  editor =	{Samual L. Braunstein and Hoi-Kwong Lo and Kenny Paterson and Peter Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09311.3},
  URN =		{urn:nbn:de:0030-drops-23618},
  doi =		{10.4230/DagSemProc.09311.3},
  annote =	{Keywords: QKD, QKD networks, Security assurance, Post-Quantum Cryptography}
}
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