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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.97

Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding

Authors: Amin Shiraz Gilani, Daochen Wang, Pei Wu, and Xingyu Zhou

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks whether there exists a triangle containing a target edge and raises general questions about the hiding of a problem’s input among irrelevant data. The second asks whether there exists a triangle containing a target vertex and raises general questions about the shuffling of a problem’s input. The third asks whether there exists a triangle; this problem bridges the 3-distinctness and 3-sum problems, which have been extensively studied by both cryptographers and complexity theorists. We provide tight or nearly tight results for these problems as well as some first answers to the general questions they raise. Furthermore, given any graph with low maximum degree, such as a typical random sparse graph, we prove that the quantum query complexity of finding a length-k cycle in its length-m edge list is m^{3/4-1/(2^{k+2}-4) ± o(1)}, which matches the best-known upper bound for the quantum query complexity of k-distinctness on length-m inputs up to an m^o(1) factor. We prove the lower bound by developing new techniques within Zhandry’s recording query framework [Zhandry, 2019] as generalized by Hamoudi and Magniez [Hamoudi and Magniez, 2023]. These techniques extend the framework to treat any non-product distribution that results from conditioning a product distribution on the absence of rare events. We prove the upper bound by adapting Belovs’s learning graph algorithm for k-distinctness [Belovs, 2012]. Finally, assuming a plausible conjecture concerning only cycle finding, we show that the lower bound can be lifted to an essentially tight lower bound on the quantum query complexity of k-distinctness, which is a long-standing open question.

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Amin Shiraz Gilani, Daochen Wang, Pei Wu, and Xingyu Zhou. Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 97:1-97:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gilani_et_al:LIPIcs.ICALP.2026.97,
  author =	{Gilani, Amin Shiraz and Wang, Daochen and Wu, Pei and Zhou, Xingyu},
  title =	{{Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{97:1--97:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.97},
  URN =		{urn:nbn:de:0030-drops-264867},
  doi =		{10.4230/LIPIcs.ICALP.2026.97},
  annote =	{Keywords: Quantum query complexity, graph algorithms, edge list model}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.64

Parallel Self-Testing of EPR Pairs Under Computational Assumptions

Authors: Honghao Fu, Daochen Wang, and Qi Zhao

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

Abstract

Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Metger and Vidick, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ε must be poly(N,ε)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution [Metger et al., 2021] under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.

Cite as

Honghao Fu, Daochen Wang, and Qi Zhao. Parallel Self-Testing of EPR Pairs Under Computational Assumptions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2023.64,
  author =	{Fu, Honghao and Wang, Daochen and Zhao, Qi},
  title =	{{Parallel Self-Testing of EPR Pairs Under Computational Assumptions}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{64:1--64:19},
  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.2023.64},
  URN =		{urn:nbn:de:0030-drops-181160},
  doi =		{10.4230/LIPIcs.ICALP.2023.64},
  annote =	{Keywords: Quantum complexity theory, self-testing, LWE}
}

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Documents authored by Wang, Daochen

Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding

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Parallel Self-Testing of EPR Pairs Under Computational Assumptions

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