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Volume

LIPIcs, Volume 158

15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

TQC 2020, June 9-12, 2020, Riga, Latvia

Editors: Steven T. Flammia

Volume

LIPIcs, Volume 27

9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

TQC 2014, May 21-23, 2014, Singapore

Editors: Steven T. Flammia and Aram W. Harrow

Document

DOI: 10.4230/LIPIcs.TQC.2024.5

Revocable Quantum Digital Signatures

Authors: Tomoyuki Morimae, Alexander Poremba, and Takashi Yamakawa

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract

We study digital signatures with revocation capabilities and show two results. First, we define and construct digital signatures with revocable signing keys from the LWE assumption. In this primitive, the signing key is a quantum state which enables a user to sign many messages and yet, the quantum key is also revocable, i.e., it can be collapsed into a classical certificate which can later be verified. Once the key is successfully revoked, we require that the initial recipient of the key loses the ability to sign. We construct digital signatures with revocable signing keys from a newly introduced primitive which we call two-tier one-shot signatures, which may be of independent interest. This is a variant of one-shot signatures, where the verification of a signature for the message "0" is done publicly, whereas the verification for the message "1" is done in private. We give a construction of two-tier one-shot signatures from the LWE assumption. As a complementary result, we also construct digital signatures with quantum revocation from group actions, where the quantum signing key is simply "returned" and then verified as part of revocation. Second, we define and construct digital signatures with revocable signatures from OWFs. In this primitive, the signer can produce quantum signatures which can later be revoked. Here, the security property requires that, once revocation is successful, the initial recipient of the signature loses the ability to find accepting inputs to the signature verification algorithm. We construct this primitive using a newly introduced two-tier variant of tokenized signatures. For the construction, we show a new lemma which we call the adaptive hardcore bit property for OWFs, which may enable further applications.

Cite as

Tomoyuki Morimae, Alexander Poremba, and Takashi Yamakawa. Revocable Quantum Digital Signatures. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{morimae_et_al:LIPIcs.TQC.2024.5,
  author =	{Morimae, Tomoyuki and Poremba, Alexander and Yamakawa, Takashi},
  title =	{{Revocable Quantum Digital Signatures}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.5},
  URN =		{urn:nbn:de:0030-drops-206757},
  doi =		{10.4230/LIPIcs.TQC.2024.5},
  annote =	{Keywords: Quantum cryptography, digital signatures, revocable cryptography}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2024.9

Quantum Algorithms for Hopcroft’s Problem

Authors: Vladimirs Andrejevs, Aleksandrs Belovs, and Jevgēnijs Vihrovs

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

In this work we study quantum algorithms for Hopcroft’s problem which is a fundamental problem in computational geometry. Given n points and n lines in the plane, the task is to determine whether there is a point-line incidence. The classical complexity of this problem is well-studied, with the best known algorithm running in O(n^{4/3}) time, with matching lower bounds in some restricted settings. Our results are two different quantum algorithms with time complexity Õ(n^{5/6}). The first algorithm is based on partition trees and the quantum backtracking algorithm. The second algorithm uses a quantum walk together with a history-independent dynamic data structure for storing line arrangement which supports efficient point location queries. In the setting where the number of points and lines differ, the quantum walk-based algorithm is asymptotically faster. The quantum speedups for the aforementioned data structures may be useful for other geometric problems.

Cite as

Vladimirs Andrejevs, Aleksandrs Belovs, and Jevgēnijs Vihrovs. Quantum Algorithms for Hopcroft’s Problem. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{andrejevs_et_al:LIPIcs.MFCS.2024.9,
  author =	{Andrejevs, Vladimirs and Belovs, Aleksandrs and Vihrovs, Jevg\={e}nijs},
  title =	{{Quantum Algorithms for Hopcroft’s Problem}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.9},
  URN =		{urn:nbn:de:0030-drops-205653},
  doi =		{10.4230/LIPIcs.MFCS.2024.9},
  annote =	{Keywords: Quantum algorithms, Quantum walks, Computational Geometry}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.21

Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure

Authors: Adam Bouland, Bill Fefferman, Soumik Ghosh, Tony Metger, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

Given a local Hamiltonian, how difficult is it to determine the entanglement structure of its ground state? We show that this problem is computationally intractable even if one is only trying to decide if the ground state is volume-law vs near area-law entangled. We prove this by constructing strong forms of pseudoentanglement in a public-key setting, where the circuits used to prepare the states are public knowledge. In particular, we construct two families of quantum circuits which produce volume-law vs near area-law entangled states, but nonetheless the classical descriptions of the circuits are indistinguishable under the Learning with Errors (LWE) assumption. Indistinguishability of the circuits then allows us to translate our construction to Hamiltonians. Our work opens new directions in Hamiltonian complexity, for example whether it is difficult to learn certain phases of matter.

Cite as

Adam Bouland, Bill Fefferman, Soumik Ghosh, Tony Metger, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou. Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bouland_et_al:LIPIcs.CCC.2024.21,
  author =	{Bouland, Adam and Fefferman, Bill and Ghosh, Soumik and Metger, Tony and Vazirani, Umesh and Zhang, Chenyi and Zhou, Zixin},
  title =	{{Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.21},
  URN =		{urn:nbn:de:0030-drops-204175},
  doi =		{10.4230/LIPIcs.CCC.2024.21},
  annote =	{Keywords: Quantum computing, Quantum complexity theory, entanglement}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.13

Learning Low-Degree Quantum Objects

Authors: Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, and Carlos Palazuelos

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

Abstract

We consider the problem of learning low-degree quantum objects up to ε-error in 𝓁₂-distance. We show the following results: (i) unknown n-qubit degree-d (in the Pauli basis) quantum channels and unitaries can be learned using O(1/ε^d) queries (which is independent of n), (ii) polynomials p:{-1,1}ⁿ → [-1,1] arising from d-query quantum algorithms can be learned from O((1/ε)^d ⋅ log n) many random examples (x,p(x)) (which implies learnability even for d = O(log n)), and (iii) degree-d polynomials p:{-1,1}ⁿ → [-1,1] can be learned through O(1/ε^d) queries to a quantum unitary U_p that block-encodes p. Our main technical contributions are new Bohnenblust-Hille inequalities for quantum channels and completely bounded polynomials.

Cite as

Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, and Carlos Palazuelos. Learning Low-Degree Quantum Objects. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{arunachalam_et_al:LIPIcs.ICALP.2024.13,
  author =	{Arunachalam, Srinivasan and Dutt, Arkopal and Escudero Guti\'{e}rrez, Francisco and Palazuelos, Carlos},
  title =	{{Learning Low-Degree Quantum Objects}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{13:1--13:19},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-201563},
  doi =		{10.4230/LIPIcs.ICALP.2024.13},
  annote =	{Keywords: Tomography}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.105

An Improved Quantum Max Cut Approximation via Maximum Matching

Authors: Eunou Lee and Ojas Parekh

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

Abstract

Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.595, outperforming the previous best algorithms of Lee [Eunou Lee, 2022] (0.562, generic input graph) and King [King, 2023] (0.582, triangle-free input graph). The algorithm is based on finding the maximum weighted matching of an input graph and outputs a product of at most 2-qubit states, which is simpler than the fully entangled output states of the previous best algorithms.

Cite as

Eunou Lee and Ojas Parekh. An Improved Quantum Max Cut Approximation via Maximum Matching. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 105:1-105:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lee_et_al:LIPIcs.ICALP.2024.105,
  author =	{Lee, Eunou and Parekh, Ojas},
  title =	{{An Improved Quantum Max Cut Approximation via Maximum Matching}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{105:1--105:11},
  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.2024.105},
  URN =		{urn:nbn:de:0030-drops-202482},
  doi =		{10.4230/LIPIcs.ICALP.2024.105},
  annote =	{Keywords: approximation, optimization, local Hamiltonian, rounding, SDP, matching}
}

Document

DOI: 10.4230/LIPIcs.TQC.2022.4

Averaged Circuit Eigenvalue Sampling

Authors: Steven T. Flammia

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

Abstract

We introduce ACES, a method for scalable noise metrology of quantum circuits that stands for Averaged Circuit Eigenvalue Sampling. It simultaneously estimates the individual error rates of all the gates in collections of quantum circuits, and can even account for space and time correlations between these gates. ACES strictly generalizes randomized benchmarking (RB), interleaved RB, simultaneous RB, and several other related techniques. However, ACES provides much more information and provably works under strictly weaker assumptions than these techniques. Finally, ACES is extremely scalable: we demonstrate with numerical simulations that it simultaneously and precisely estimates all the Pauli error rates on every gate and measurement in a 100 qubit quantum device using fewer than 20 relatively shallow Clifford circuits and an experimentally feasible number of samples. By learning the detailed gate errors for large quantum devices, ACES opens new possibilities for error mitigation, bespoke quantum error correcting codes and decoders, customized compilers, and more.

Cite as

Steven T. Flammia. Averaged Circuit Eigenvalue Sampling. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 4:1-4:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{flammia:LIPIcs.TQC.2022.4,
  author =	{Flammia, Steven T.},
  title =	{{Averaged Circuit Eigenvalue Sampling}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{4:1--4:10},
  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.2022.4},
  URN =		{urn:nbn:de:0030-drops-165114},
  doi =		{10.4230/LIPIcs.TQC.2022.4},
  annote =	{Keywords: Quantum noise estimation, quantum benchmarking, QCVV}
}

Document

DOI: 10.4230/LIPIcs.TQC.2021.8

Pauli Error Estimation via Population Recovery

Authors: Steven T. Flammia and Ryan O'Donnell

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract

Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an n-qubit channel to precision ε in 𝓁_∞ using just O(1/ε²) log(n/ε) applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an O(1/ε) factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability ≤ 1/4. We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability 1-η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1 ± ε (i.e., additive precision εη) using just O(1/(ε²η)) log(n/ε) applications of the channel.

Cite as

Steven T. Flammia and Ryan O'Donnell. Pauli Error Estimation via Population Recovery. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{flammia_et_al:LIPIcs.TQC.2021.8,
  author =	{Flammia, Steven T. and O'Donnell, Ryan},
  title =	{{Pauli Error Estimation via Population Recovery}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.8},
  URN =		{urn:nbn:de:0030-drops-140034},
  doi =		{10.4230/LIPIcs.TQC.2021.8},
  annote =	{Keywords: Pauli channels, population recovery, Goldreich-Levin, sparse recovery, quantum channel tomography}
}

Document

DOI: 10.4230/LIPIcs.TQC.2020.12

A Device-Independent Protocol for XOR Oblivious Transfer

Authors: Srijita Kundu, Jamie Sikora, and Ernest Y.-Z. Tan

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract

Oblivious transfer is a cryptographic primitive where Alice has two bits and Bob wishes to learn some function of them. Ideally, Alice should not learn Bob’s desired function choice and Bob should not learn any more than logically implied by the function value. While decent quantum protocols for this task are known, many quickly become insecure if an adversary were to control the quantum devices used in the implementation of the protocol. Here we present how some existing protocols fail in this device-independent framework, and give a fully-device independent quantum protocol for XOR oblivious transfer which is provably more secure than any classical protocol.

Cite as

Srijita Kundu, Jamie Sikora, and Ernest Y.-Z. Tan. A Device-Independent Protocol for XOR Oblivious Transfer. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kundu_et_al:LIPIcs.TQC.2020.12,
  author =	{Kundu, Srijita and Sikora, Jamie and Tan, Ernest Y.-Z.},
  title =	{{A Device-Independent Protocol for XOR Oblivious Transfer}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.12},
  URN =		{urn:nbn:de:0030-drops-127579},
  doi =		{10.4230/LIPIcs.TQC.2020.12},
  annote =	{Keywords: Quantum cryptography, device independence, oblivious transfer, semidefinite programming, security analysis}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.TQC.2020

LIPIcs, Volume 158, TQC 2020, Complete Volume

Authors: Steven T. Flammia

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract

LIPIcs, Volume 158, TQC 2020, Complete Volume

Cite as

15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 1-230, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{flammia:LIPIcs.TQC.2020,
  title =	{{LIPIcs, Volume 158, TQC 2020, Complete Volume}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{1--230},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020},
  URN =		{urn:nbn:de:0030-drops-120583},
  doi =		{10.4230/LIPIcs.TQC.2020},
  annote =	{Keywords: LIPIcs, Volume 158, TQC 2020, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.TQC.2020.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Steven T. Flammia

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{flammia:LIPIcs.TQC.2020.0,
  author =	{Flammia, Steven T.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{0:i--0:x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.0},
  URN =		{urn:nbn:de:0030-drops-120598},
  doi =		{10.4230/LIPIcs.TQC.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.TQC.2020.1

Exponential Quantum Communication Reductions from Generalizations of the Boolean Hidden Matching Problem

Authors: João F. Doriguello and Ashley Montanaro

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract

In this work we revisit the Boolean Hidden Matching communication problem, which was the first communication problem in the one-way model to demonstrate an exponential classical-quantum communication separation. In this problem, Alice’s bits are matched into pairs according to a partition that Bob holds. These pairs are compressed using a Parity function and it is promised that the final bit-string is equal either to another bit-string Bob holds, or its complement. The problem is to decide which case is the correct one. Here we generalize the Boolean Hidden Matching problem by replacing the parity function with an arbitrary function f. Efficient communication protocols are presented depending on the sign-degree of f. If its sign-degree is less than or equal to 1, we show an efficient classical protocol. If its sign-degree is less than or equal to 2, we show an efficient quantum protocol. We then completely characterize the classical hardness of all symmetric functions f of sign-degree greater than or equal to 2, except for one family of specific cases. We also prove, via Fourier analysis, a classical lower bound for any function f whose pure high degree is greater than or equal to 2. Similarly, we prove, also via Fourier analysis, a quantum lower bound for any function f whose pure high degree is greater than or equal to 3. These results give a large family of new exponential classical-quantum communication separations.

Cite as

João F. Doriguello and Ashley Montanaro. Exponential Quantum Communication Reductions from Generalizations of the Boolean Hidden Matching Problem. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{doriguello_et_al:LIPIcs.TQC.2020.1,
  author =	{Doriguello, Jo\~{a}o F. and Montanaro, Ashley},
  title =	{{Exponential Quantum Communication Reductions from Generalizations of the Boolean Hidden Matching Problem}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{1:1--1:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.1},
  URN =		{urn:nbn:de:0030-drops-120601},
  doi =		{10.4230/LIPIcs.TQC.2020.1},
  annote =	{Keywords: Communication Complexity, Quantum Communication Complexity, Boolean Hidden Matching Problem}
}

Document

DOI: 10.4230/LIPIcs.TQC.2020.2

Improved Approximate Degree Bounds for k-Distinctness

Authors: Nikhil S. Mande, Justin Thaler, and Shuchen Zhu

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract

An open problem that is widely regarded as one of the most important in quantum query complexity is to resolve the quantum query complexity of the k-distinctness function on inputs of size N. While the case of k=2 (also called Element Distinctness) is well-understood, there is a polynomial gap between the known upper and lower bounds for all constants k>2. Specifically, the best known upper bound is O (N^{(3/4)-1/(2^{k+2}-4)}) (Belovs, FOCS 2012), while the best known lower bound for k≥ 2 is Ω̃(N^{2/3} + N^{(3/4)-1/(2k)}) (Aaronson and Shi, J. ACM 2004; Bun, Kothari, and Thaler, STOC 2018). For any constant k ≥ 4, we improve the lower bound to Ω̃(N^{(3/4)-1/(4k)}). This yields, for example, the first proof that 4-distinctness is strictly harder than Element Distinctness. Our lower bound applies more generally to approximate degree. As a secondary result, we give a simple construction of an approximating polynomial of degree Õ(N^{3/4}) that applies whenever k ≤ polylog(N).

Cite as

Nikhil S. Mande, Justin Thaler, and Shuchen Zhu. Improved Approximate Degree Bounds for k-Distinctness. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mande_et_al:LIPIcs.TQC.2020.2,
  author =	{Mande, Nikhil S. and Thaler, Justin and Zhu, Shuchen},
  title =	{{Improved Approximate Degree Bounds for k-Distinctness}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{2:1--2:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.2},
  URN =		{urn:nbn:de:0030-drops-120613},
  doi =		{10.4230/LIPIcs.TQC.2020.2},
  annote =	{Keywords: Quantum Query Complexity, Approximate Degree, Dual Polynomials, k-distinctness}
}

Document

DOI: 10.4230/LIPIcs.TQC.2020.3

Building Trust for Continuous Variable Quantum States

Authors: Ulysse Chabaud, Tom Douce, Frédéric Grosshans, Elham Kashefi, and Damian Markham

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract

In this work we develop new methods for the characterisation of continuous variable quantum states using heterodyne measurement in both the trusted and untrusted settings. First, building on quantum state tomography with heterodyne detection, we introduce a reliable method for continuous variable quantum state certification, which directly yields the elements of the density matrix of the state considered with analytical confidence intervals. This method neither needs mathematical reconstruction of the data nor discrete binning of the sample space and uses a single Gaussian measurement setting. Second, beyond quantum state tomography and without its identical copies assumption, we promote our reliable tomography method to a general efficient protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries, i.e., making no assumptions whatsoever on the state generated by the adversary. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over the Fock basis, computed with samples from heterodyne detection of the state.

Cite as

Ulysse Chabaud, Tom Douce, Frédéric Grosshans, Elham Kashefi, and Damian Markham. Building Trust for Continuous Variable Quantum States. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chabaud_et_al:LIPIcs.TQC.2020.3,
  author =	{Chabaud, Ulysse and Douce, Tom and Grosshans, Fr\'{e}d\'{e}ric and Kashefi, Elham and Markham, Damian},
  title =	{{Building Trust for Continuous Variable Quantum States}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.3},
  URN =		{urn:nbn:de:0030-drops-120623},
  doi =		{10.4230/LIPIcs.TQC.2020.3},
  annote =	{Keywords: Continuous variable quantum information, reliable state tomography, certification, verification}
}

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