33 Search Results for "Le Gall, François"


Volume

LIPIcs, Volume 232

17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)

TQC 2022, July 11-15, 2022, Urbana Champaign, Illinois, USA

Editors: François Le Gall and Tomoyuki Morimae

Document
Invited Talk
Quantum Distributed Computing: Potential and Limitations (Invited Talk)

Authors: François Le Gall

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)


Abstract
The subject of this talk is quantum distributed computing, i.e., distributed computing where the processors of the network can exchange quantum messages. In the first part of the talk I survey recent results [Taisuke Izumi and François Le Gall, 2019; Taisuke Izumi et al., 2020; François Le Gall and Frédéric Magniez, 2018; François Le Gall et al., 2019; Xudong Wu and Penghui Yao, 2022] and some older results [Michael Ben-Or and Avinatan Hassidim, 2005; Seiichiro Tani et al., 2012] that show the potential of quantum distributed algorithms. In the second part I present our recent work [Xavier Coiteux-Roy et al., 2023] showing the limitations of quantum distributed algorithms for approximate graph coloring. Finally, I mention interesting and important open questions in quantum distributed computing.

Cite as

François Le Gall. Quantum Distributed Computing: Potential and Limitations (Invited Talk). In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{legall:LIPIcs.OPODIS.2023.2,
  author =	{Le Gall, Fran\c{c}ois},
  title =	{{Quantum Distributed Computing: Potential and Limitations}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.2},
  URN =		{urn:nbn:de:0030-drops-194925},
  doi =		{10.4230/LIPIcs.OPODIS.2023.2},
  annote =	{Keywords: Quantum computing, distributed algorithms, CONGEST model, LOCAL model}
}
Document
Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications

Authors: François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022], Rosenthal and Yuen [ITCS 2022], Metger and Yuen [QIP 2023] under the term state synthesis. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state U|ψ⟩ at the rightmost node of the line, where |ψ⟩ is a quantum state given at the leftmost node and U is a unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020], and complement our protocol by showing classical lower bounds for this problem. Our second contribution is a dQMA protocol, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this dQMA protocol, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.

Cite as

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{legall_et_al:LIPIcs.MFCS.2023.63,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki and Nishimura, Harumichi},
  title =	{{Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{63:1--63:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.63},
  URN =		{urn:nbn:de:0030-drops-185975},
  doi =		{10.4230/LIPIcs.MFCS.2023.63},
  annote =	{Keywords: distributed quantum Merlin-Arthur, distributed verification, quantum computation}
}
Document
Local Hamiltonians with No Low-Energy Stabilizer States

Authors: Nolan J. Coble, Matthew Coudron, Jon Nelson, and Seyed Sajjad Nezhadi

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)


Abstract
The recently-defined No Low-energy Sampleable States (NLSS) conjecture of Gharibian and Le Gall [Sevag Gharibian and François {Le Gall}, 2022] posits the existence of a family of local Hamiltonians where all states of low-enough constant energy do not have succinct representations allowing perfect sampling access. States that can be prepared using only Clifford gates (i.e. stabilizer states) are an example of sampleable states, so the NLSS conjecture implies the existence of local Hamiltonians whose low-energy space contains no stabilizer states. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [Anshu et al., 2022], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states. We hope that our techniques will eventually be helpful for constructing Hamiltonians which simultaneously satisfy NLSS and NLTS.

Cite as

Nolan J. Coble, Matthew Coudron, Jon Nelson, and Seyed Sajjad Nezhadi. Local Hamiltonians with No Low-Energy Stabilizer States. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{coble_et_al:LIPIcs.TQC.2023.14,
  author =	{Coble, Nolan J. and Coudron, Matthew and Nelson, Jon and Nezhadi, Seyed Sajjad},
  title =	{{Local Hamiltonians with No Low-Energy Stabilizer States}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.14},
  URN =		{urn:nbn:de:0030-drops-183243},
  doi =		{10.4230/LIPIcs.TQC.2023.14},
  annote =	{Keywords: Hamiltonian complexity, Stabilizer codes, Low-energy states}
}
Document
Track A: Algorithms, Complexity and Games
Improved Hardness Results for the Guided Local Hamiltonian Problem

Authors: Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, and Jordi Weggemans

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding state has fidelity (inverse-polynomially) close to 1/2 with a ground state. In this paper, we optimally improve both the locality and the fidelity parameter: we show that the BQP-completeness persists even with 2-local Hamiltonians, and even when the guiding state has fidelity (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. Beyond the hardness of estimating the ground state energy, we also show BQP-hardness persists when considering estimating energies of excited states of these Hamiltonians instead. Those make further steps towards establishing practical quantum advantage in quantum chemistry.

Cite as

Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, and Jordi Weggemans. Improved Hardness Results for the Guided Local Hamiltonian Problem. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cade_et_al:LIPIcs.ICALP.2023.32,
  author =	{Cade, Chris and Folkertsma, Marten and Gharibian, Sevag and Hayakawa, Ryu and Le Gall, Fran\c{c}ois and Morimae, Tomoyuki and Weggemans, Jordi},
  title =	{{Improved Hardness Results for the Guided Local Hamiltonian Problem}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.32},
  URN =		{urn:nbn:de:0030-drops-180840},
  doi =		{10.4230/LIPIcs.ICALP.2023.32},
  annote =	{Keywords: Quantum computing, Quantum advantage, Quantum Chemistry, Guided Local Hamiltonian Problem}
}
Document
Distributed Quantum Interactive Proofs

Authors: François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In distributed interactive proofs, the nodes of an n-node network G can exchange short messages (called certificates) with a powerful prover. The goal is to decide if the input (including G itself) belongs to some language, with as few turns of interaction and as few bits exchanged between nodes and the prover as possible. There are several results showing that the size of certificates can be reduced drastically with a constant number of interactions compared to non-interactive distributed proofs. In this paper, we introduce the quantum counterpart of distributed interactive proofs: certificates can now be quantum bits, and the nodes of the network can perform quantum computation. The first result of this paper shows that by using distributed quantum interactive proofs, the number of interactions can be significantly reduced. More precisely, our result shows that for any constant k, the class of languages that can be decided by a k-turn classical (i.e., non-quantum) distributed interactive protocol with f(n)-bit certificate size is contained in the class of languages that can be decided by a 5-turn distributed quantum interactive protocol with O(f(n))-bit certificate size. We also show that if we allow to use shared randomness, the number of turns can be reduced to three. Since no similar turn-reduction classical technique is currently known, our result gives evidence of the power of quantum computation in the setting of distributed interactive proofs as well. As a corollary of our results, we show that there exist 5-turn/3-turn distributed quantum interactive protocols with small certificate size for problems that have been considered in prior works on distributed interactive proofs such as [Kol, Oshman, and Saxena PODC 2018, Naor, Parter, and Yogev SODA 2020]. We then utilize the framework of the distributed quantum interactive proofs to test closeness of two quantum states each of which is distributed over the entire network.

Cite as

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Distributed Quantum Interactive Proofs. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{legall_et_al:LIPIcs.STACS.2023.42,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki and Nishimura, Harumichi},
  title =	{{Distributed Quantum Interactive Proofs}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{42:1--42:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.42},
  URN =		{urn:nbn:de:0030-drops-176949},
  doi =		{10.4230/LIPIcs.STACS.2023.42},
  annote =	{Keywords: distributed interactive proofs, distributed verification, quantum computation}
}
Document
An Optimal Oracle Separation of Classical and Quantum Hybrid Schemes

Authors: Atsuya Hasegawa and François Le Gall

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)


Abstract
Recently, Chia, Chung and Lai (STOC 2020) and Coudron and Menda (STOC 2020) have shown that there exists an oracle 𝒪 such that BQP^𝒪 ≠ (BPP^BQNC)^𝒪 ∪ (BQNC^BPP)^𝒪. In fact, Chia et al. proved a stronger statement: for any depth parameter d, there exists an oracle that separates quantum depth d and 2d+1, when polynomial-time classical computation is allowed. This implies that relative to an oracle, doubling quantum depth gives classical and quantum hybrid schemes more computational power. In this paper, we show that for any depth parameter d, there exists an oracle that separates quantum depth d and d+1, when polynomial-time classical computation is allowed. This gives an optimal oracle separation of classical and quantum hybrid schemes. To prove our result, we consider d-Bijective Shuffling Simon’s Problem (which is a variant of d-Shuffling Simon’s Problem considered by Chia et al.) and an oracle inspired by an "in-place" permutation oracle.

Cite as

Atsuya Hasegawa and François Le Gall. An Optimal Oracle Separation of Classical and Quantum Hybrid Schemes. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{hasegawa_et_al:LIPIcs.ISAAC.2022.6,
  author =	{Hasegawa, Atsuya and Le Gall, Fran\c{c}ois},
  title =	{{An Optimal Oracle Separation of Classical and Quantum Hybrid Schemes}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.6},
  URN =		{urn:nbn:de:0030-drops-172918},
  doi =		{10.4230/LIPIcs.ISAAC.2022.6},
  annote =	{Keywords: small-depth quantum circuit, hybrid quantum computer, oracle separation}
}
Document
Brief Announcement
Brief Announcement: Distributed Quantum Interactive Proofs

Authors: François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)


Abstract
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In distributed interactive proofs, the nodes of an n-node network G can exchange short messages (called certificates) with a powerful prover. The goal is to decide if the input (including G itself) belongs to some language, with as few turns of interaction and as few bits exchanged between nodes and the prover as possible. There are several results showing that the size of certificates can be reduced drastically with a constant number of interactions compared to non-interactive distributed proofs. In this brief announcement, we introduce the quantum counterpart of distributed interactive proofs: certificates can now be quantum bits, and the nodes of the network can perform quantum computation. The main result of this paper shows that by using quantum distributed interactive proofs, the number of interactions can be significantly reduced. More precisely, our main result shows that for any constant k, the class of languages that can be decided by a k-turn classical (i.e., non-quantum) distributed interactive protocol with f(n)-bit certificate size is contained in the class of languages that can be decided by a 5-turn distributed quantum interactive protocol with O(f(n))-bit certificate size. We also show that if we allow to use shared randomness, the number of turns can be reduced to 3-turn. Since no similar turn-reduction classical technique is currently known, our result gives evidence of the power of quantum computation in the setting of distributed interactive proofs as well.

Cite as

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Brief Announcement: Distributed Quantum Interactive Proofs. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 48:1-48:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{legall_et_al:LIPIcs.DISC.2022.48,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki and Nishimura, Harumichi},
  title =	{{Brief Announcement: Distributed Quantum Interactive Proofs}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{48:1--48:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.48},
  URN =		{urn:nbn:de:0030-drops-172396},
  doi =		{10.4230/LIPIcs.DISC.2022.48},
  annote =	{Keywords: distributed interactive proofs, distributed verification, quantum computation}
}
Document
Complete Volume
LIPIcs, Volume 232, TQC 2022, Complete Volume

Authors: François Le Gall and Tomoyuki Morimae

Published in: LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)


Abstract
LIPIcs, Volume 232, TQC 2022, Complete Volume

Cite as

17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 1-218, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Proceedings{legall_et_al:LIPIcs.TQC.2022,
  title =	{{LIPIcs, Volume 232, TQC 2022, Complete Volume}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{1--218},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-237-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{232},
  editor =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022},
  URN =		{urn:nbn:de:0030-drops-165067},
  doi =		{10.4230/LIPIcs.TQC.2022},
  annote =	{Keywords: LIPIcs, Volume 232, TQC 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: François Le Gall and Tomoyuki Morimae

Published in: LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{legall_et_al:LIPIcs.TQC.2022.0,
  author =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-237-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{232},
  editor =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.0},
  URN =		{urn:nbn:de:0030-drops-165071},
  doi =		{10.4230/LIPIcs.TQC.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Centralized, Parallel, and Distributed Multi-Source Shortest Paths via Hopsets and Rectangular Matrix Multiplication

Authors: Michael Elkin and Ofer Neiman

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)


Abstract
Consider an undirected weighted graph G = (V,E,w). We study the problem of computing (1+ε)-approximate shortest paths for S × V, for a subset S ⊆ V of |S| = n^r sources, for some 0 < r ≤ 1. We devise a significantly improved algorithm for this problem in the entire range of parameter r, in both the classical centralized and the parallel (PRAM) models of computation, and in a wide range of r in the distributed (Congested Clique) model. Specifically, our centralized algorithm for this problem requires time Õ(|E| ⋅ n^{o(1)} + n^{ω(r)}), where n^{ω(r)} is the time required to multiply an n^r × n matrix by an n × n one. Our PRAM algorithm has polylogarithmic time (log n)^{O(1/ρ)}, and its work complexity is Õ(|E| ⋅ n^ρ + n^{ω(r)}), for any arbitrarily small constant ρ > 0. In particular, for r ≤ 0.313…, our centralized algorithm computes S × V (1+ε)-approximate shortest paths in n^{2 + o(1)} time. Our PRAM polylogarithmic-time algorithm has work complexity O(|E| ⋅ n^ρ + n^{2+o(1)}), for any arbitrarily small constant ρ > 0. Previously existing solutions either require centralized time/parallel work of O(|E| ⋅ |S|) or provide much weaker approximation guarantees. In the Congested Clique model, our algorithm solves the problem in polylogarithmic time for |S| = n^r sources, for r ≤ 0.655, while previous state-of-the-art algorithms did so only for r ≤ 1/2. Moreover, it improves previous bounds for all r > 1/2. For unweighted graphs, the running time is improved further to poly(log log n) for r ≤ 0.655. Previously this running time was known for r ≤ 1/2.

Cite as

Michael Elkin and Ofer Neiman. Centralized, Parallel, and Distributed Multi-Source Shortest Paths via Hopsets and Rectangular Matrix Multiplication. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 27:1-27:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{elkin_et_al:LIPIcs.STACS.2022.27,
  author =	{Elkin, Michael and Neiman, Ofer},
  title =	{{Centralized, Parallel, and Distributed Multi-Source Shortest Paths via Hopsets and Rectangular Matrix Multiplication}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{27:1--27:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.27},
  URN =		{urn:nbn:de:0030-drops-158379},
  doi =		{10.4230/LIPIcs.STACS.2022.27},
  annote =	{Keywords: Shortest paths, matrix multiplication, hopsets}
}
Document
Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters

Authors: Amir Nikabadi and Janne H. Korhonen

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)


Abstract
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph: - On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique. - On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard. - On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting. In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems.

Cite as

Amir Nikabadi and Janne H. Korhonen. Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{nikabadi_et_al:LIPIcs.OPODIS.2021.15,
  author =	{Nikabadi, Amir and Korhonen, Janne H.},
  title =	{{Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.15},
  URN =		{urn:nbn:de:0030-drops-157902},
  doi =		{10.4230/LIPIcs.OPODIS.2021.15},
  annote =	{Keywords: distributed algorithms, parameterized distributed complexity, CONGEST model, induced subgraph detection, graph parameters, lower bounds}
}
Document
Quantum Distributed Algorithms for Detection of Cliques

Authors: Keren Censor-Hillel, Orr Fischer, François Le Gall, Dean Leitersdorf, and Rotem Oshman

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
The possibilities offered by quantum computing have drawn attention in the distributed computing community recently, with several breakthrough results showing quantum distributed algorithms that run faster than the fastest known classical counterparts, and even separations between the two models. A prime example is the result by Izumi, Le Gall, and Magniez [STACS 2020], who showed that triangle detection by quantum distributed algorithms is easier than triangle listing, while an analogous result is not known in the classical case. In this paper we present a framework for fast quantum distributed clique detection. This improves upon the state-of-the-art for the triangle case, and is also more general, applying to larger clique sizes. Our main technical contribution is a new approach for detecting cliques by encapsulating this as a search task for nodes that can be added to smaller cliques. To extract the best complexities out of our approach, we develop a framework for nested distributed quantum searches, which employ checking procedures that are quantum themselves. Moreover, we show a circuit-complexity barrier on proving a lower bound of the form Ω(n^{3/5+ε}) for K_p-detection for any p ≥ 4, even in the classical (non-quantum) distributed CONGEST setting.

Cite as

Keren Censor-Hillel, Orr Fischer, François Le Gall, Dean Leitersdorf, and Rotem Oshman. Quantum Distributed Algorithms for Detection of Cliques. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 35:1-35:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{censorhillel_et_al:LIPIcs.ITCS.2022.35,
  author =	{Censor-Hillel, Keren and Fischer, Orr and Le Gall, Fran\c{c}ois and Leitersdorf, Dean and Oshman, Rotem},
  title =	{{Quantum Distributed Algorithms for Detection of Cliques}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{35:1--35:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.35},
  URN =		{urn:nbn:de:0030-drops-156319},
  doi =		{10.4230/LIPIcs.ITCS.2022.35},
  annote =	{Keywords: distributed graph algorithms, quantum algorithms, cycles, cliques, Congested Clique, CONGEST}
}
Document
Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems

Authors: François Le Gall and Saeed Seddighin

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms for these problems along with quantum lower bounds. Our results shed light on a very surprising fact: Although the classic solutions for LCS and LPS are almost identical (via suffix trees), their quantum computational complexities are different. While we give an exact Õ(√n) time algorithm for LPS, we prove that LCS needs at least time ̃ Ω(n^{2/3}) even for 0/1 strings.

Cite as

François Le Gall and Saeed Seddighin. Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 97:1-97:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{legall_et_al:LIPIcs.ITCS.2022.97,
  author =	{Le Gall, Fran\c{c}ois and Seddighin, Saeed},
  title =	{{Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{97:1--97:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.97},
  URN =		{urn:nbn:de:0030-drops-156934},
  doi =		{10.4230/LIPIcs.ITCS.2022.97},
  annote =	{Keywords: Longest common substring, Longest palindrome substring, Quantum algorithms, Sublinear algorithms}
}
Document
Lower Bounds for Induced Cycle Detection in Distributed Computing

Authors: François Le Gall and Masayuki Miyamoto

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)


Abstract
The distributed subgraph detection asks, for a fixed graph H, whether the n-node input graph contains H as a subgraph or not. In the standard CONGEST model of distributed computing, the complexity of clique/cycle detection and listing has received a lot of attention recently. In this paper we consider the induced variant of subgraph detection, where the goal is to decide whether the n-node input graph contains H as an induced subgraph or not. We first show a Ω̃(n) lower bound for detecting the existence of an induced k-cycle for any k ≥ 4 in the CONGEST model. This lower bound is tight for k = 4, and shows that the induced variant of k-cycle detection is much harder than the non-induced version. This lower bound is proved via a reduction from two-party communication complexity. We complement this result by showing that for 5 ≤ k ≤ 7, this Ω̃(n) lower bound cannot be improved via the two-party communication framework. We then show how to prove stronger lower bounds for larger values of k. More precisely, we show that detecting an induced k-cycle for any k ≥ 8 requires Ω̃(n^{2-Θ{(1/k)}}) rounds in the CONGEST model, nearly matching the known upper bound Õ(n^{2-Θ{(1/k)}}) of the general k-node subgraph detection (which also applies to the induced version) by Eden, Fiat, Fischer, Kuhn, and Oshman [DISC 2019]. Finally, we investigate the case where H is the diamond (the diamond is obtained by adding an edge to a 4-cycle, or equivalently removing an edge from a 4-clique), and show non-trivial upper and lower bounds on the complexity of the induced version of diamond detecting and listing.

Cite as

François Le Gall and Masayuki Miyamoto. Lower Bounds for Induced Cycle Detection in Distributed Computing. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 58:1-58:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{legall_et_al:LIPIcs.ISAAC.2021.58,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki},
  title =	{{Lower Bounds for Induced Cycle Detection in Distributed Computing}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{58:1--58:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.58},
  URN =		{urn:nbn:de:0030-drops-154919},
  doi =		{10.4230/LIPIcs.ISAAC.2021.58},
  annote =	{Keywords: Distributed computing, Lower bounds, Subgraph detection}
}
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