11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)

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Complete Volume

DOI: 10.4230/LIPIcs.TQC.2016

LIPIcs, Volume 61, TQC'16, Complete Volume

Authors: Anne Broadbent

Abstract

LIPIcs, Volume 61, TQC'16, Complete Volume

Cite as

11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Proceedings{broadbent:LIPIcs.TQC.2016,
  title =	{{LIPIcs, Volume 61, TQC'16, Complete Volume}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016},
  URN =		{urn:nbn:de:0030-drops-66984},
  doi =		{10.4230/LIPIcs.TQC.2016},
  annote =	{Keywords: Data Encryption, Coding and Information Theory, Theory of Computation}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.TQC.2016.0

Front Matter, Table of Contents, Preface, List of Contributed Talks, Conference Organization

Authors: Anne Broadbent

Abstract

Front Matter, Table of Contents, Preface, List of Contributed Talks, Conference Organization

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11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{broadbent:LIPIcs.TQC.2016.0,
  author =	{Broadbent, Anne},
  title =	{{Front Matter, Table of Contents, Preface, List of Contributed Talks, Conference Organization}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.0},
  URN =		{urn:nbn:de:0030-drops-66816},
  doi =		{10.4230/LIPIcs.TQC.2016.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, List of Contributed Talks, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.1

On the Power of Quantum Fourier Sampling

Authors: Bill Fefferman and Christopher Umans

Abstract

A line of work initiated by Terhal and DiVincenzo [Terhal/DiVincenzo, arXiv, 2002] and Bremner, Jozsa, and Shepherd [Bremner/Jozsa/Sheperd, Proc. Royal Soc. A, 2010], shows that restricted classes of quantum computation can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov [Aaronson/Arkhipov, J. Theory of Comp., 2013] take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled exactly by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson-Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, as well as many other familiar #P-hard polynomials. Since our distribution likely requires the full power of universal quantum computation, while the Aaronson-Arkhipov distribution uses only linear optical quantum computation with noninteracting bosons, why is our result interesting? We can think of at least three reasons: 1. Since the conjectures required in [Aaronson/Arkhipov, J. Theory of Comp., 2013] have not yet been proven, it seems worthwhile to weaken them as much as possible. We do this in two ways, by weakening both conjectures to apply to any "Efficiently Specifiable" polynomial, and by weakening the so-called Anti-Concentration conjecture so that it need only hold for one distribution in a broad class of distributions. 2. Our construction can be understood without any knowledge of linear optics. While this may be a disadvantage for experimentalists, in our opinion it results in a very clean and simple exposition that may be more immediately accessible to computer scientists. 3. It is extremely common for quantum computations to employ “Quantum Fourier Sampling” in the following way: first apply a classically efficient function to a uniform superposition of inputs, then apply a Quantum Fourier Transform followed by a measurement. Our distributions are obtained in exactly this way, where the classically efficient function is related to a (presumed) hard polynomial. Establishing rigorously a robust sense in which the central primitive of Quantum Fourier Sampling is classically hard seems a worthwhile goal in itself.

Cite as

Bill Fefferman and Christopher Umans. On the Power of Quantum Fourier Sampling. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fefferman_et_al:LIPIcs.TQC.2016.1,
  author =	{Fefferman, Bill and Umans, Christopher},
  title =	{{On the Power of Quantum Fourier Sampling}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.1},
  URN =		{urn:nbn:de:0030-drops-66829},
  doi =		{10.4230/LIPIcs.TQC.2016.1},
  annote =	{Keywords: Quantum Complexity Theory, Sampling Complexity}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.2

Quantum-Proof Multi-Source Randomness Extractors in the Markov Model

Authors: Rotem Arnon-Friedman, Christopher Portmann, and Volkher B. Scholz

Abstract

Randomness extractors, widely used in classical and quantum cryptography and other fields of computer science, e.g., derandomization, are functions which generate almost uniform randomness from weak sources of randomness. In the quantum setting one must take into account the quantum side information held by an adversary which might be used to break the security of the extractor. In the case of seeded extractors the presence of quantum side information has been extensively studied. For multi-source extractors one can easily see that high conditional min-entropy is not sufficient to guarantee security against arbitrary side information, even in the classical case. Hence, the interesting question is under which models of (both quantum and classical) side information multi-source extractors remain secure. In this work we suggest a natural model of side information, which we call the Markov model, and prove that any multi-source extractor remains secure in the presence of quantum side information of this type (albeit with weaker parameters). This improves on previous results in which more restricted models were considered or the security of only some types of extractors was shown.

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Rotem Arnon-Friedman, Christopher Portmann, and Volkher B. Scholz. Quantum-Proof Multi-Source Randomness Extractors in the Markov Model. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 2:1-2:34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{arnonfriedman_et_al:LIPIcs.TQC.2016.2,
  author =	{Arnon-Friedman, Rotem and Portmann, Christopher and Scholz, Volkher B.},
  title =	{{Quantum-Proof Multi-Source Randomness Extractors in the Markov Model}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{2:1--2:34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.2},
  URN =		{urn:nbn:de:0030-drops-66830},
  doi =		{10.4230/LIPIcs.TQC.2016.2},
  annote =	{Keywords: Quantum proof randomness extractors, multisource extractors, device independent quantum cryptography}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.3

Lower Bound on Expected Communication Cost of Quantum Huffman Coding

Authors: Anurag Anshu, Ankit Garg, Aram W. Harrow, and Penghui Yao

Abstract

Data compression is a fundamental problem in quantum and classical information theory. A typical version of the problem is that the sender Alice receives a (classical or quantum) state from some known ensemble and needs to transmit them to the receiver Bob with average error below some specified bound. We consider the case in which the message can have a variable length and the goal is to minimize its expected length. For classical messages this problem has a well-known solution given by Huffman coding. In this scheme, the expected length of the message is equal to the Shannon entropy of the source (with a constant additive factor) and the scheme succeeds with zero error. This is a single-shot result which implies the asymptotic result, viz. Shannon's source coding theorem, by encoding each state sequentially. For the quantum case, the asymptotic compression rate is given by the von-Neumann entropy. However, we show that there is no one-shot scheme which is able to match this rate, even if interactive communication is allowed. This is a relatively rare case in quantum information theory when the cost of a quantum task is significantly different than the classical analogue. Our result has implications for direct sum theorems in quantum communication complexity and one-shot formulations of Quantum Reverse Shannon theorem.

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Anurag Anshu, Ankit Garg, Aram W. Harrow, and Penghui Yao. Lower Bound on Expected Communication Cost of Quantum Huffman Coding. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{anshu_et_al:LIPIcs.TQC.2016.3,
  author =	{Anshu, Anurag and Garg, Ankit and Harrow, Aram W. and Yao, Penghui},
  title =	{{Lower Bound on Expected Communication Cost of Quantum Huffman Coding}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.3},
  URN =		{urn:nbn:de:0030-drops-66843},
  doi =		{10.4230/LIPIcs.TQC.2016.3},
  annote =	{Keywords: Quantum information, quantum communication, expected communica- tion cost, huffman coding}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.4

Simple, Near-Optimal Quantum Protocols for Die-Rolling

Authors: Jamie Sikora

Abstract

Die-rolling is the cryptographic task where two mistrustful, remote parties wish to generate a random D-sided die-roll over a communication channel. Optimal quantum protocols for this task have been given by Aharon and Silman (New Journal of Physics, 2010) but are based on optimal weak coin-flipping protocols which are currently very complicated and not very well understood. In this paper, we first present very simple classical protocols for die-rolling which have decent (and sometimes optimal) security which is in stark contrast to coin-flipping, bit-commitment, oblivious transfer, and many other two-party cryptographic primitives. We also present quantum protocols based on the idea of integer-commitment, a generalization of bit-commitment, where one wishes to commit to an integer. We analyze these protocols using semidefinite programming and finally give protocols which are very close to Kitaev's lower bound for any D >= 3.

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Jamie Sikora. Simple, Near-Optimal Quantum Protocols for Die-Rolling. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{sikora:LIPIcs.TQC.2016.4,
  author =	{Sikora, Jamie},
  title =	{{Simple, Near-Optimal Quantum Protocols for Die-Rolling}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.4},
  URN =		{urn:nbn:de:0030-drops-66851},
  doi =		{10.4230/LIPIcs.TQC.2016.4},
  annote =	{Keywords: Quantum Cryptography, Semidefinite Programming, Die-Rolling, Integer-Commitment}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.5

Robust Bell Inequalities from Communication Complexity

Authors: Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno

Abstract

The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities.

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Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno. Robust Bell Inequalities from Communication Complexity. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{laplante_et_al:LIPIcs.TQC.2016.5,
  author =	{Laplante, Sophie and Lauri\`{e}re, Mathieu and Nolin, Alexandre and Roland, J\'{e}r\'{e}mie and Senno, Gabriel},
  title =	{{Robust Bell Inequalities from Communication Complexity}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.5},
  URN =		{urn:nbn:de:0030-drops-66867},
  doi =		{10.4230/LIPIcs.TQC.2016.5},
  annote =	{Keywords: Communication complexity, Bell inequalities, nonlocality, detector efficiency}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.6

How Hard Is Deciding Trivial Versus Nontrivial in the Dihedral Coset Problem?

Authors: Nai-Hui Chia and Sean Hallgren

Abstract

We study the hardness of the dihedral hidden subgroup problem. It is known that lattice problems reduce to it, and that it reduces to random subset sum with density > 1 and also to quantum sampling subset sum solutions. We examine a decision version of the problem where the question asks whether the hidden subgroup is trivial or order two. The decision problem essentially asks if a given vector is in the span of all coset states. We approach this by first computing an explicit basis for the coset space and the perpendicular space. We then look at the consequences of having efficient unitaries that use this basis. We show that if a unitary maps the basis to the standard basis in any way, then that unitary can be used to solve random subset sum with constant density >1. We also show that if a unitary can exactly decide membership in the coset subspace, then the collision problem for subset sum can be solved for density >1 but approaching 1 as the problem size increases. This strengthens the previous hardness result that implementing the optimal POVM in a specific way is as hard as quantum sampling subset sum solutions.

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Nai-Hui Chia and Sean Hallgren. How Hard Is Deciding Trivial Versus Nontrivial in the Dihedral Coset Problem?. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chia_et_al:LIPIcs.TQC.2016.6,
  author =	{Chia, Nai-Hui and Hallgren, Sean},
  title =	{{How Hard Is Deciding Trivial Versus Nontrivial in the Dihedral Coset Problem?}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.6},
  URN =		{urn:nbn:de:0030-drops-66877},
  doi =		{10.4230/LIPIcs.TQC.2016.6},
  annote =	{Keywords: Quantum algorithms, hidden subgroup problem, random subset sum problem}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.7

The Structure of Promises in Quantum Speedups

Authors: Shalev Ben-David

Abstract

In 1998, Beals, Buhrman, Cleve, Mosca, and de Wolf showed that no super-polynomial quantum speedup is possible in the query complexity setting unless there is a promise on the input. We examine several types of "unstructured" promises, and show that they also are not compatible with super-polynomial quantum speedups. We conclude that such speedups are only possible when the input is known to have some structure. Specifically, we show that there is a polynomial relationship of degree 18 between D(f) and Q(f) for any Boolean function f defined on permutations (elements of [n]^n in which each alphabet element occurs exactly once). More generally, this holds for all f defined on orbits of the symmetric group action (which acts on an element of [M]^n by permuting its entries). We also show that any Boolean function f defined on a "symmetric" subset of the Boolean hypercube has a polynomial relationship between R(f) and Q(f) - although in that setting, D(f) may be exponentially larger.

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Shalev Ben-David. The Structure of Promises in Quantum Speedups. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bendavid:LIPIcs.TQC.2016.7,
  author =	{Ben-David, Shalev},
  title =	{{The Structure of Promises in Quantum Speedups}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.7},
  URN =		{urn:nbn:de:0030-drops-66882},
  doi =		{10.4230/LIPIcs.TQC.2016.7},
  annote =	{Keywords: Quantum computing, quantum query complexity, decision tree complexity, lower bounds, quantum adversary method}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.8

Quantum Algorithms for Abelian Difference Sets and Applications to Dihedral Hidden Subgroups

Authors: Martin Roetteler

Abstract

Difference sets are basic combinatorial structures that have applications in signal processing, coding theory, and cryptography. We consider the problem of identifying a shifted version of the characteristic function of a (known) difference set and present a general algorithm that can be used to tackle any hidden shift problem for any difference set in any abelian group. We discuss special cases of this framework which include a) Paley difference sets based on quadratic residues in finite fields which allow to recover the shifted Legendre function quantum algorithm, b) Hadamard difference sets which allow to recover the shifted bent function quantum algorithm, and c) Singer difference sets which allow us to define instances of the dihedral hidden subgroup problem which can be efficiently solved on a quantum computer.

Cite as

Martin Roetteler. Quantum Algorithms for Abelian Difference Sets and Applications to Dihedral Hidden Subgroups. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{roetteler:LIPIcs.TQC.2016.8,
  author =	{Roetteler, Martin},
  title =	{{Quantum Algorithms for Abelian Difference Sets and Applications to Dihedral Hidden Subgroups}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.8},
  URN =		{urn:nbn:de:0030-drops-66896},
  doi =		{10.4230/LIPIcs.TQC.2016.8},
  annote =	{Keywords: Quantum algorithms, hidden shift problem, hidden subgroup problem, difference sets, Fourier transforms}
}

Document

DOI: 10.4230/LIPIcs.TQC.2016.9

Instantaneous Non-Local Computation of Low T-Depth Quantum Circuits

Authors: Florian Speelman

Abstract

Instantaneous non-local quantum computation requires multiple parties to jointly perform a quantum operation, using pre-shared entanglement and a single round of simultaneous communication. We study this task for its close connection to position-based quantum cryptography, but it also has natural applications in the context of foundations of quantum physics and in distributed computing. The best known general construction for instantaneous non-local quantum computation requires a pre-shared state which is exponentially large in the number of qubits involved in the operation, while efficient constructions are known for very specific cases only. We partially close this gap by presenting new schemes for efficient instantaneous non-local computation of several classes of quantum circuits, using the Clifford+T gate set. Our main result is a protocol which uses entanglement exponential in the T-depth of a quantum circuit, able to perform non-local computation of quantum circuits with a (poly-)logarithmic number of layers of T gates with quasi-polynomial entanglement. Our proofs combine ideas from blind and delegated quantum computation with the garden-hose model, a combinatorial model of communication complexity which was recently introduced as a tool for studying certain schemes for quantum position verification. As an application of our results, we also present an efficient attack on a recently-proposed scheme for position verification by Chakraborty and Leverrier.

Cite as

Florian Speelman. Instantaneous Non-Local Computation of Low T-Depth Quantum Circuits. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 9:1-9:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{speelman:LIPIcs.TQC.2016.9,
  author =	{Speelman, Florian},
  title =	{{Instantaneous Non-Local Computation of Low T-Depth Quantum Circuits}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{9:1--9:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.9},
  URN =		{urn:nbn:de:0030-drops-66909},
  doi =		{10.4230/LIPIcs.TQC.2016.9},
  annote =	{Keywords: Quantum Cryptography, Quantum Communication}
}

LIPIcs, Volume 61

11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)

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