Volume
LIPIcs, Volume 158
15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)
Event
TQC 2020, June 9-12, 2020, Riga, LatviaEditor
Publication Details
- published at: 2020-06-08
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-146-7
- DBLP: db/conf/tqc/tqc2020
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Complete Volume
LIPIcs, Volume 158, TQC 2020, Complete Volume
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
Front Matter, Table of Contents, Preface, Conference Organization
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
Exponential Quantum Communication Reductions from Generalizations of the Boolean Hidden Matching Problem
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
Improved Approximate Degree Bounds for k-Distinctness
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
Building Trust for Continuous Variable Quantum States
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}
}
Document
Uncloneable Quantum Encryption via Oracles
Abstract
Quantum information is well known to achieve cryptographic feats that are unattainable using classical information alone. Here, we add to this repertoire by introducing a new cryptographic functionality called uncloneable encryption. This functionality allows the encryption of a classical message such that two collaborating but isolated adversaries are prevented from simultaneously recovering the message, even when the encryption key is revealed. Clearly, such functionality is unattainable using classical information alone.
We formally define uncloneable encryption, and show how to achieve it using Wiesner’s conjugate coding, combined with a quantum-secure pseudorandom function (qPRF). Modelling the qPRF as an oracle, we show security by adapting techniques from the quantum one-way-to-hiding lemma, as well as using bounds from quantum monogamy-of-entanglement games.
Cite as
Anne Broadbent and Sébastien Lord. Uncloneable Quantum Encryption via Oracles. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{broadbent_et_al:LIPIcs.TQC.2020.4,
author = {Broadbent, Anne and Lord, S\'{e}bastien},
title = {{Uncloneable Quantum Encryption via Oracles}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {4:1--4:22},
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.2020.4},
URN = {urn:nbn:de:0030-drops-120639},
doi = {10.4230/LIPIcs.TQC.2020.4},
annote = {Keywords: Quantum Cryptography, Symmetric Key, Monogamy-of-Entanglement}
}
Document
Quasirandom Quantum Channels
Abstract
Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of sparse vertex transitive graphs using the famous Grothendieck inequality.
Here we generalize these results to the non-commutative, or "quantum", case, where a transition matrix becomes a quantum channel. In particular, we show that for irreducibly covariant quantum channels, expansion is equivalent to a natural analog of uniformity for graphs, generalizing the result of Conlon and Zhao. Moreover, we show that in these results, the non-commutative and commutative (resp.) Grothendieck inequalities yield the best-possible constants.
Cite as
Tom Bannink, Jop Briët, Farrokh Labib, and Hans Maassen. Quasirandom Quantum Channels. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{bannink_et_al:LIPIcs.TQC.2020.5,
author = {Bannink, Tom and Bri\"{e}t, Jop and Labib, Farrokh and Maassen, Hans},
title = {{Quasirandom Quantum Channels}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {5:1--5:20},
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.2020.5},
URN = {urn:nbn:de:0030-drops-120642},
doi = {10.4230/LIPIcs.TQC.2020.5},
annote = {Keywords: Quantum channels, quantum expanders, quasirandomness}
}
Document
Towards Quantum One-Time Memories from Stateless Hardware
Abstract
A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver, against a linear number of adaptive queries to the token, in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also show our scheme is "tight" according to two scenarios.
Cite as
Anne Broadbent, Sevag Gharibian, and Hong-Sheng Zhou. Towards Quantum One-Time Memories from Stateless Hardware. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{broadbent_et_al:LIPIcs.TQC.2020.6,
author = {Broadbent, Anne and Gharibian, Sevag and Zhou, Hong-Sheng},
title = {{Towards Quantum One-Time Memories from Stateless Hardware}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {6:1--6:25},
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.2020.6},
URN = {urn:nbn:de:0030-drops-120654},
doi = {10.4230/LIPIcs.TQC.2020.6},
annote = {Keywords: quantum cryptography, one-time memories, semi-definite programming}
}
Document
Beyond Product State Approximations for a Quantum Analogue of Max Cut
Abstract
We consider a computational problem where the goal is to approximate the maximum eigenvalue of a two-local Hamiltonian that describes Heisenberg interactions between qubits located at the vertices of a graph. Previous work has shed light on this problem’s approximability by product states. For any instance of this problem the maximum energy attained by a product state is lower bounded by the Max Cut of the graph and upper bounded by the standard Goemans-Williamson semidefinite programming relaxation of it. Gharibian and Parekh described an efficient classical approximation algorithm for this problem which outputs a product state with energy at least 0.498 times the maximum eigenvalue in the worst case, and observe that there exist instances where the best product state has energy 1/2 of optimal. We investigate approximation algorithms with performance exceeding this limitation which are based on optimizing over tensor products of few-qubit states and shallow quantum circuits. We provide an efficient classical algorithm which achieves an approximation ratio of at least 0.53 in the worst case. We also show that for any instance defined by a 3 or 4-regular graph, there is an efficiently computable shallow quantum circuit that prepares a state with energy larger than the best product state (larger even than its semidefinite programming relaxation).
Cite as
Anurag Anshu, David Gosset, and Karen Morenz. Beyond Product State Approximations for a Quantum Analogue of Max Cut. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{anshu_et_al:LIPIcs.TQC.2020.7,
author = {Anshu, Anurag and Gosset, David and Morenz, Karen},
title = {{Beyond Product State Approximations for a Quantum Analogue of Max Cut}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {7:1--7:15},
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.2020.7},
URN = {urn:nbn:de:0030-drops-120660},
doi = {10.4230/LIPIcs.TQC.2020.7},
annote = {Keywords: Approximation algorithms, Quantum many-body systems}
}
Document
Simpler Proofs of Quantumness
Abstract
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the first step towards constructing a useful quantum computer.
There are currently three approaches for exhibiting proofs of quantumness: (i) Inverting a classically-hard one-way function (e.g. using Shor’s algorithm). This seems technologically out of reach. (ii) Sampling from a classically-hard-to-sample distribution (e.g. BosonSampling). This may be within reach of near-term experiments, but for all such tasks known verification requires exponential time. (iii) Interactive protocols based on cryptographic assumptions. The use of a trapdoor scheme allows for efficient verification, and implementation seems to require much less resources than (i), yet still more than (ii).
In this work we propose a significant simplification to approach (iii) by employing the random oracle heuristic. (We note that we do not apply the Fiat-Shamir paradigm.)
We give a two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function. In contrast to earlier proposals we do not need an adaptive hard-core bit property. This allows the use of smaller security parameters and more diverse computational assumptions (such as Ring Learning with Errors), significantly reducing the quantum computational effort required for a successful demonstration.
Cite as
Zvika Brakerski, Venkata Koppula, Umesh Vazirani, and Thomas Vidick. Simpler Proofs of Quantumness. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{brakerski_et_al:LIPIcs.TQC.2020.8,
author = {Brakerski, Zvika and Koppula, Venkata and Vazirani, Umesh and Vidick, Thomas},
title = {{Simpler Proofs of Quantumness}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {8:1--8:14},
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.2020.8},
URN = {urn:nbn:de:0030-drops-120677},
doi = {10.4230/LIPIcs.TQC.2020.8},
annote = {Keywords: Proof of Quantumness, Random Oracle, Learning with Errors}
}
Document
Quantum Algorithms for Computational Geometry Problems
Abstract
We study quantum algorithms for problems in computational geometry, such as Point-On-3-Lines problem. In this problem, we are given a set of lines and we are asked to find a point that lies on at least 3 of these lines. Point-On-3-Lines and many other computational geometry problems are known to be 3Sum-Hard. That is, solving them classically requires time Ω(n^{2-o(1)}), unless there is faster algorithm for the well known 3Sum problem (in which we are given a set S of n integers and have to determine if there are a, b, c ∈ S such that a + b + c = 0). Quantumly, 3Sum can be solved in time O(n log n) using Grover’s quantum search algorithm. This leads to a question: can we solve Point-On-3-Lines and other 3Sum-Hard problems in O(n^c) time quantumly, for c<2? We answer this question affirmatively, by constructing a quantum algorithm that solves Point-On-3-Lines in time O(n^{1 + o(1)}). The algorithm combines recursive use of amplitude amplification with geometrical ideas. We show that the same ideas give O(n^{1 + o(1)}) time algorithm for many 3Sum-Hard geometrical problems.
Cite as
Andris Ambainis and Nikita Larka. Quantum Algorithms for Computational Geometry Problems. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 9:1-9:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{ambainis_et_al:LIPIcs.TQC.2020.9,
author = {Ambainis, Andris and Larka, Nikita},
title = {{Quantum Algorithms for Computational Geometry Problems}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {9:1--9:10},
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.2020.9},
URN = {urn:nbn:de:0030-drops-120687},
doi = {10.4230/LIPIcs.TQC.2020.9},
annote = {Keywords: Quantum algorithms, quantum search, computational geometry, 3Sum problem, amplitude amplification}
}
Document
Quantum Coupon Collector
Abstract
We study how efficiently a k-element set S⊆[n] can be learned from a uniform superposition |S> of its elements. One can think of |S>=∑_{i∈S}|i>/√|S| as the quantum version of a uniformly random sample over S, as in the classical analysis of the "coupon collector problem." We show that if k is close to n, then we can learn S using asymptotically fewer quantum samples than random samples. In particular, if there are n-k=O(1) missing elements then O(k) copies of |S> suffice, in contrast to the Θ(k log k) random samples needed by a classical coupon collector. On the other hand, if n-k=Ω(k), then Ω(k log k) quantum samples are necessary.
More generally, we give tight bounds on the number of quantum samples needed for every k and n, and we give efficient quantum learning algorithms. We also give tight bounds in the model where we can additionally reflect through |S>. Finally, we relate coupon collection to a known example separating proper and improper PAC learning that turns out to show no separation in the quantum case.
Cite as
Srinivasan Arunachalam, Aleksandrs Belovs, Andrew M. Childs, Robin Kothari, Ansis Rosmanis, and Ronald de Wolf. Quantum Coupon Collector. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{arunachalam_et_al:LIPIcs.TQC.2020.10,
author = {Arunachalam, Srinivasan and Belovs, Aleksandrs and Childs, Andrew M. and Kothari, Robin and Rosmanis, Ansis and de Wolf, Ronald},
title = {{Quantum Coupon Collector}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {10:1--10:17},
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.2020.10},
URN = {urn:nbn:de:0030-drops-120692},
doi = {10.4230/LIPIcs.TQC.2020.10},
annote = {Keywords: Quantum algorithms, Adversary method, Coupon collector, Quantum learning theory}
}
Document
Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities
Abstract
In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to say a circuit of CNOT, Hadamard, and π/2-phase rotations, together with T operations (π/4-phase rotations). For many error correcting codes, fault-tolerant realisations of Clifford operations are significantly less resource-intensive than those of T gates, which motivates finding ways to realise the same transformation involving T-count (the number of T gates involved) which is as low as possible. Investigations into this problem [Matthew Amy et al., 2013; Gosset et al., 2014; Matthew Amy et al., 2014; Matthew Amy et al., 2018; Earl T. Campbell and Mark Howard, 2017; Matthew Amy and Michele Mosca, 2019] has led to observations that this problem is closely related to NP-hard tensor decomposition problems [Luke E. Heyfron and Earl T. Campbell, 2018] and is tantamount to the difficult problem of decoding exponentially long Reed-Muller codes [Matthew Amy and Michele Mosca, 2019]. This problem then presents itself as one for which must be content in practise with approximate optimisation, in which one develops an array of tactics to be deployed through some pragmatic strategy. In this vein, we describe techniques to reduce the T-count, based on the effective application of "spider nest identities": easily recognised products of parity-phase operations which are equivalent to the identity operation. We demonstrate the effectiveness of such techniques by obtaining improvements in the T-counts of a number of circuits, in run-times which are typically less than the time required to make a fresh cup of coffee.
Cite as
Niel de Beaudrap, Xiaoning Bian, and Quanlong Wang. Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
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@InProceedings{debeaudrap_et_al:LIPIcs.TQC.2020.11,
author = {de Beaudrap, Niel and Bian, Xiaoning and Wang, Quanlong},
title = {{Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities}},
booktitle = {15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
pages = {11:1--11:23},
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.2020.11},
URN = {urn:nbn:de:0030-drops-120705},
doi = {10.4230/LIPIcs.TQC.2020.11},
annote = {Keywords: T-count, Parity-phase operations, Phase gadgets, Clifford hierarchy, ZX calculus}
}
Document
A Device-Independent Protocol for XOR Oblivious Transfer
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}
}