Volume

LIPIcs, Volume 22

8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)



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Event

TQC 2013, May 21-23, 2013, Guelph, Canada

Editors

Simone Severini
Fernando Brandao

Publication Details

  • published at: 2013-11-13
  • Publisher: Schloss-Dagstuhl - Leibniz Zentrum für Informatik
  • ISBN: 978-3-939897-55-2
  • DBLP: db/conf/tqc/tqc2013

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Document
Complete Volume
LIPIcs, Volume 22, TQC'13, Complete Volume

Authors: Simone Severini and Fernando Brandao


Abstract
LIPIcs, Volume 22, TQC'13, Complete Volume

Cite as

Simone Severini and Fernando Brandao. LIPIcs, Volume 22, TQC'13, Complete Volume. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@Proceedings{severini_et_al:LIPIcs.TQC.2013,
  title =	{{LIPIcs, Volume 22, TQC'13, Complete Volume}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013},
  URN =		{urn:nbn:de:0030-drops-43480},
  doi =		{10.4230/LIPIcs.TQC.2013},
  annote =	{Keywords: Data Encryption, Coding and Information Theory, Theory of Computation}
}
Document
Front Matter
Frontmatter, Table of Contents, Preface, Conference Organization

Authors: Simone Severini and Fernando Brandao


Abstract
Frontmatter, Table of Contents, Preface, Conference Organization

Cite as

Simone Severini and Fernando Brandao. Frontmatter, Table of Contents, Preface, Conference Organization. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. i-x, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{severini_et_al:LIPIcs.TQC.2013.i,
  author =	{Severini, Simone and Brandao, Fernando},
  title =	{{Frontmatter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{i--x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.i},
  URN =		{urn:nbn:de:0030-drops-43081},
  doi =		{10.4230/LIPIcs.TQC.2013.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Conference Organization}
}
Document
Ancilla Driven Quantum Computation with Arbitrary Entangling Strength

Authors: Kerem Halil Shah and Daniel K.L. Oi


Abstract
We extend the model of Ancilla Driven Quantum Computation (ADQC) by considering gates with arbitrary entangling power. By giving up stepwise determinism, universal QC can still be achieved through a variable length sequence of single qubit gates and probabilistic "repeat-until-succes" entangling operations. This opens up a new range of possible physical implementations as well as shedding light on the sets of resources sufficient for universal QC.

Cite as

Kerem Halil Shah and Daniel K.L. Oi. Ancilla Driven Quantum Computation with Arbitrary Entangling Strength. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 1-19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{halilshah_et_al:LIPIcs.TQC.2013.1,
  author =	{Halil Shah, Kerem and Oi, Daniel K.L.},
  title =	{{Ancilla Driven Quantum Computation with Arbitrary Entangling Strength}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{1--19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.1},
  URN =		{urn:nbn:de:0030-drops-43094},
  doi =		{10.4230/LIPIcs.TQC.2013.1},
  annote =	{Keywords: Ancilla, weak measurement, quantum computation, entanglement, random walks}
}
Document
Another Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem

Authors: Greg Kuperberg


Abstract
We give an algorithm for the hidden subgroup problem for the dihedral group D_N, or equivalently the cyclic hidden shift problem, that supersedes our first algorithm and is suggested by Regev's algorithm. It runs in exp(O(sqrt(log N))) quantum time and uses exp(O(sqrt(log N))) classical space, but only O(log N) quantum space. The algorithm also runs faster with quantumly addressable classical space than with fully classical space. In the hidden shift form, which is more natural for this algorithm regardless, it can also make use of multiple hidden shifts. It can also be extended with two parameters that trade classical space and classical time for quantum time. At the extreme space-saving end, the algorithm becomes Regev's algorithm. At the other end, if the algorithm is allowed classical memory with quantum random access, then many trade-offs between classical and quantum time are possible.

Cite as

Greg Kuperberg. Another Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 20-34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{kuperberg:LIPIcs.TQC.2013.20,
  author =	{Kuperberg, Greg},
  title =	{{Another Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{20--34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.20},
  URN =		{urn:nbn:de:0030-drops-43213},
  doi =		{10.4230/LIPIcs.TQC.2013.20},
  annote =	{Keywords: quantum algorithm, hidden subgroup problem, sieve, subexponential time}
}
Document
Universal Entanglers for Bosonic and Fermionic Systems

Authors: Joel Klassen, Jianxin Chen, and Bei Zeng


Abstract
A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles 1,2 with a Hilbert space C^{d_1} otimes C^{d_2}, a UE exists when min(d_1,d_2) >= 3 and (d_1,d_2) != (3,3). It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of C^d otimes C^d. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of C^d otimes C^d if and only if d >= 3 (resp. d >= 8). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indistinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems.

Cite as

Joel Klassen, Jianxin Chen, and Bei Zeng. Universal Entanglers for Bosonic and Fermionic Systems. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 35-49, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{klassen_et_al:LIPIcs.TQC.2013.35,
  author =	{Klassen, Joel and Chen, Jianxin and Zeng, Bei},
  title =	{{Universal Entanglers for Bosonic and Fermionic Systems}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{35--49},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.35},
  URN =		{urn:nbn:de:0030-drops-43223},
  doi =		{10.4230/LIPIcs.TQC.2013.35},
  annote =	{Keywords: Universal Entangler, Bosonic States, Fermionic States}
}
Document
Easy and Hard Functions for the Boolean Hidden Shift Problem

Authors: Andrew M. Childs, Robin Kothari, Maris Ozols, and Martin Roetteler


Abstract
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem.

Cite as

Andrew M. Childs, Robin Kothari, Maris Ozols, and Martin Roetteler. Easy and Hard Functions for the Boolean Hidden Shift Problem. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 50-79, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{childs_et_al:LIPIcs.TQC.2013.50,
  author =	{Childs, Andrew M. and Kothari, Robin and Ozols, Maris and Roetteler, Martin},
  title =	{{Easy and Hard Functions for the Boolean Hidden Shift Problem}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{50--79},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.50},
  URN =		{urn:nbn:de:0030-drops-43203},
  doi =		{10.4230/LIPIcs.TQC.2013.50},
  annote =	{Keywords: Boolean hidden shift problem, quantum algorithms, query complexity, Fourier transform, bent functions}
}
Document
Dequantizing Read-once Quantum Formulas

Authors: Alessandro Cosentino, Robin Kothari, and Adam Paetznick


Abstract
Quantum formulas, defined by Yao [FOCS'93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all single-qubit gates is equivalent to a read-once classical formula of the same size and depth over an analogous classical gate set. For example, any read-once quantum formula over Toffoli and single-qubit gates is equivalent to a read-once classical formula over Toffoli and NOT gates. We then show that the equivalence does not hold if the read-once restriction is removed. To show the power of quantum formulas without the read-once restriction, we define a new model of computation called the one-qubit model and show that it can compute all boolean functions. This model may also be of independent interest.

Cite as

Alessandro Cosentino, Robin Kothari, and Adam Paetznick. Dequantizing Read-once Quantum Formulas. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 80-92, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{cosentino_et_al:LIPIcs.TQC.2013.80,
  author =	{Cosentino, Alessandro and Kothari, Robin and Paetznick, Adam},
  title =	{{Dequantizing Read-once Quantum Formulas}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{80--92},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.80},
  URN =		{urn:nbn:de:0030-drops-43197},
  doi =		{10.4230/LIPIcs.TQC.2013.80},
  annote =	{Keywords: formulas, dequantization, circuit complexity}
}
Document
The Minimum Size of Qubit Unextendible Product Bases

Authors: Nathaniel Johnston


Abstract
We investigate the problem of constructing unextendible product bases in the qubit case - that is, when each local dimension equals 2. The cardinality of the smallest unextendible product basis is known in all qubit cases except when the number of parties is a multiple of 4 greater than 4 itself. We construct small unextendible product bases in all of the remaining open cases, and we use graph theory techniques to produce a computer-assisted proof that our constructions are indeed the smallest possible.

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Nathaniel Johnston. The Minimum Size of Qubit Unextendible Product Bases. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 93-105, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{johnston:LIPIcs.TQC.2013.93,
  author =	{Johnston, Nathaniel},
  title =	{{The Minimum Size of Qubit Unextendible Product Bases}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{93--105},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.93},
  URN =		{urn:nbn:de:0030-drops-43173},
  doi =		{10.4230/LIPIcs.TQC.2013.93},
  annote =	{Keywords: unextendible product basis; quantum entanglement; graph factorization}
}
Document
Robust Online Hamiltonian Learning

Authors: Christopher E. Granade, Christopher Ferrie, Nathan Wiebe, and D. G. Cory


Abstract
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance. We further illustrate the practicality of our algorithm by applying it to two test problems: (1) learning an unknown frequency and the decoherence time for a single-qubit quantum system and (2) learning couplings in a many-qubit Ising model Hamiltonian with no external magnetic field.

Cite as

Christopher E. Granade, Christopher Ferrie, Nathan Wiebe, and D. G. Cory. Robust Online Hamiltonian Learning. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 106-125, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{granade_et_al:LIPIcs.TQC.2013.106,
  author =	{Granade, Christopher E. and Ferrie, Christopher and Wiebe, Nathan and Cory, D. G.},
  title =	{{Robust Online Hamiltonian Learning}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{106--125},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.106},
  URN =		{urn:nbn:de:0030-drops-43185},
  doi =		{10.4230/LIPIcs.TQC.2013.106},
  annote =	{Keywords: Quantum information, sequential Monte Carlo, Bayesian, experiment design, parameter estimation}
}
Document
Classical and Quantum Algorithms for Testing Equivalence of Group Extensions

Authors: Kevin C. Zatloukal


Abstract
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special type of central extension, is widely believed to contain the essential hard cases. However, looking specifically at central extensions, the natural formulation of being "the same" is not isomorphism but rather "equivalence," which requires an isomorphism to preserves the structure of the extension. In this paper, we show that equivalence of central extensions can be computed efficiently on a classical computer when the groups are small enough to be given by their multiplication tables. However, in the model of black box groups, which allows the groups to be much larger, we show that equivalence can be computed efficiently on a quantum computer but not a classical one (under common complexity assumptions). Our quantum algorithm demonstrates a new application of the hidden subgroup problem for general abelian groups.

Cite as

Kevin C. Zatloukal. Classical and Quantum Algorithms for Testing Equivalence of Group Extensions. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 126-145, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{zatloukal:LIPIcs.TQC.2013.126,
  author =	{Zatloukal, Kevin C.},
  title =	{{Classical and Quantum Algorithms for Testing Equivalence of Group Extensions}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{126--145},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.126},
  URN =		{urn:nbn:de:0030-drops-43164},
  doi =		{10.4230/LIPIcs.TQC.2013.126},
  annote =	{Keywords: quantum computing, algorithms, computational group theory}
}
Document
Provable Advantage for Quantum Strategies in Random Symmetric XOR Games

Authors: Andris Ambainis and Janis Iraids


Abstract
Non-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of n players with 0-1 valued questions. For this class of games, each player receives an input bit and responds with an output bit without communicating to the other players. The winning condition only depends on XOR of output bits and is constant w.r.t. permutation of players. We prove that for almost any n-player symmetric XOR game the entangled value of the game is Theta((sqrt(ln(n)))/(n^{1/4})) adapting an old result by Salem and Zygmund on the asymptotics of random trigonometric polynomials. Consequently, we show that the classical-quantum gap is Theta(sqrt(ln(n))) for almost any symmetric XOR game.

Cite as

Andris Ambainis and Janis Iraids. Provable Advantage for Quantum Strategies in Random Symmetric XOR Games. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 146-156, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{ambainis_et_al:LIPIcs.TQC.2013.146,
  author =	{Ambainis, Andris and Iraids, Janis},
  title =	{{Provable Advantage for Quantum Strategies in Random Symmetric XOR Games}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{146--156},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.146},
  URN =		{urn:nbn:de:0030-drops-43156},
  doi =		{10.4230/LIPIcs.TQC.2013.146},
  annote =	{Keywords: Random Symmetric XOR games, Entanglement}
}
Document
Towards Efficient Decoding of Classical-Quantum Polar Codes

Authors: Mark M. Wilde, Olivier Landon-Cardinal, and Patrick Hayden


Abstract
Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a fully collective strategy is not necessary in order to recover all of the information bits. In fact, when coding for a large number N uses of a cq channel W, N*I(W_{acc}) of the bits can be recovered by a non-collective strategy which amounts to coherent quantum processing of the results of product measurements, where I(W_{acc}) is the accessible information of the channel W. In order to decode the other N(I(W)-I(W_{acc})) bits, where I(W) is the Holevo rate, our conclusion is that the receiver should employ collective measurements. We also present two other results: 1) collective Fuchs-Caves measurements (quantum likelihood ratio measurements) can be used at the receiver to achieve the Holevo rate and 2) we give an explicit form of the Helstrom measurements used in small-size polar codes. The main approach used to demonstrate these results is a quantum extension of Arikan's polar codes.

Cite as

Mark M. Wilde, Olivier Landon-Cardinal, and Patrick Hayden. Towards Efficient Decoding of Classical-Quantum Polar Codes. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 157-177, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{wilde_et_al:LIPIcs.TQC.2013.157,
  author =	{Wilde, Mark M. and Landon-Cardinal, Olivier and Hayden, Patrick},
  title =	{{Towards Efficient Decoding of Classical-Quantum Polar Codes}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{157--177},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.157},
  URN =		{urn:nbn:de:0030-drops-43141},
  doi =		{10.4230/LIPIcs.TQC.2013.157},
  annote =	{Keywords: classical-quantum channel, classical-quantum polar codes, quantum likelihood ratio, quantum successive cancellation decoder}
}
Document
On the Query Complexity of Perfect Gate Discrimination

Authors: Giulio Chiribella, Giacomo Mauro D'Ariano, and Martin Roetteler


Abstract
We investigate the problem of finding the minimum number of queries needed to perfectly identify an unknown quantum gate within a finite set of alternatives, considering both deterministic strategies. For unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, we prove that parallel strategies are sufficient to identify the unknown gate with minimum number of queries and we use this fact to provide upper and lower bounds on the query complexity. In addition, we introduce the notion of generalized $t$-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized $t$-design we prove that there is no difference between perfect probabilistic and perfect deterministic gate discrimination. Hence, evaluating of the query complexity of perfect discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination.

Cite as

Giulio Chiribella, Giacomo Mauro D'Ariano, and Martin Roetteler. On the Query Complexity of Perfect Gate Discrimination. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 178-191, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{chiribella_et_al:LIPIcs.TQC.2013.178,
  author =	{Chiribella, Giulio and D'Ariano, Giacomo Mauro and Roetteler, Martin},
  title =	{{On the Query Complexity of Perfect Gate Discrimination}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{178--191},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.178},
  URN =		{urn:nbn:de:0030-drops-43133},
  doi =		{10.4230/LIPIcs.TQC.2013.178},
  annote =	{Keywords: quantum gate identification, unambiguous discrimination, minimum error discrimination, query complexity}
}
Document
Symmetries of Codeword Stabilized Quantum Codes

Authors: Salman Beigi, Jianxin Chen, Markus Grassl, Zhengfeng Ji, Qiang Wang, and Bei Zeng


Abstract
Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant.

Cite as

Salman Beigi, Jianxin Chen, Markus Grassl, Zhengfeng Ji, Qiang Wang, and Bei Zeng. Symmetries of Codeword Stabilized Quantum Codes. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 192-206, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{beigi_et_al:LIPIcs.TQC.2013.192,
  author =	{Beigi, Salman and Chen, Jianxin and Grassl, Markus and Ji, Zhengfeng and Wang, Qiang and Zeng, Bei},
  title =	{{Symmetries of Codeword Stabilized Quantum Codes}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{192--206},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.192},
  URN =		{urn:nbn:de:0030-drops-43129},
  doi =		{10.4230/LIPIcs.TQC.2013.192},
  annote =	{Keywords: CWS Codes, Union Stabilizer Codes, Permutation Symmetry, Toric Code}
}
Document
Certifying the Absence of Apparent Randomness under Minimal Assumptions

Authors: Gonzalo de la Torre, Chirag Dhara, and Antonio Acin


Abstract
Contrary to classical physics, the predictions of quantum theory for measurement outcomes are of a probabilistic nature. Questions about the completeness of such predictions lie at the core of quantum physics and can be traced back to the foundations of the field. Recently, the completeness of quantum probabilistic predictions could be established based on the assumption of freedom of choice. Here we ask when can events be established to be as unpredictable as we observe them to be relying only on minimal assumptions, ie. distrusting even the free choice assumption but assuming the existence of an arbitrarily weak (but non-zero) source of randomness. We answer the latter by identifying a sufficient condition weaker than the monogamy of correlations which allow us to provide a family of finite scenarios based on GHZ paradoxes where quantum probabilistic predictions are as accurate as they can possibly be. Our results can be used for a protocol of full randomness amplification, without the need of privacy amplification, in which the final bit approaches a perfect random bit exponentially fast on the number of parties.

Cite as

Gonzalo de la Torre, Chirag Dhara, and Antonio Acin. Certifying the Absence of Apparent Randomness under Minimal Assumptions. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 207-219, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{delatorre_et_al:LIPIcs.TQC.2013.207,
  author =	{de la Torre, Gonzalo and Dhara, Chirag and Acin, Antonio},
  title =	{{Certifying the Absence of Apparent Randomness under Minimal Assumptions}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{207--219},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.207},
  URN =		{urn:nbn:de:0030-drops-43112},
  doi =		{10.4230/LIPIcs.TQC.2013.207},
  annote =	{Keywords: randomness, Bell nonlocality, free choice}
}
Document
Is Global Asymptotic Cloning State Estimation?

Authors: Yuxiang Yang and Giulio Chiribella


Abstract
We investigate the asymptotic relationship between quantum cloning and quantum estimation from the global point of view where all the copies produced by the cloner are considered jointly. For an N-to-M cloner, we consider the overall fidelity between the state of the M output systems and the state of M ideal copies, and we ask whether the optimal fidelity is attained by a measure and-prepare protocol in the limit M -> \infty. In order to gain intuition into the general problem, we analyze two concrete examples: i) cloning qubit states on the equator of the Bloch sphere and ii) cloning two-qubit maximally entangled states. In the first case, we show that the optimal measure-and-prepare fidelity converges to the fidelity of the optimal cloner in the limit M -> \infty. In the second case, we restrict our attention to economical covariant cloners, and again, we exhibit a measure-and-prepare protocol that achieves asymptotically the optimal fidelity. Quite counterintuitively, in both cases the optimal states that have to be prepared in order to maximize the overall fidelity are not product states corresponding to M identical copies, but instead suitable M-partite entangled states.

Cite as

Yuxiang Yang and Giulio Chiribella. Is Global Asymptotic Cloning State Estimation?. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 220-234, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{yang_et_al:LIPIcs.TQC.2013.220,
  author =	{Yang, Yuxiang and Chiribella, Giulio},
  title =	{{Is Global Asymptotic Cloning State Estimation?}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{220--234},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.220},
  URN =		{urn:nbn:de:0030-drops-43100},
  doi =		{10.4230/LIPIcs.TQC.2013.220},
  annote =	{Keywords: quantum cloning, quantum estimation}
}
Document
Distillation of Non-Stabilizer States for Universal Quantum Computation

Authors: Guillaume Duclos-Cianci and Krysta M. Svore


Abstract
Magic state distillation is a fundamental technique for realizing fault-tolerant universal quantum computing, and produces high-fidelity Clifford eigenstates, called magic states, which can be used to implement the non-Clifford pi/8 gate. We propose an efficient protocol for distilling other non-stabilizer states that requires only Clifford operations, measurement, and magic states. One critical application of our protocol is efficiently and fault tolerantly implementing arbitrary, non-Clifford, single-qubit rotations in average constant online circuit depth and polylogarithmic (in precision) offline resource cost, resulting in significant improvements over state-of-the-art decomposition techniques. Finally, we show that our protocol is robust to noise in the resource states.

Cite as

Guillaume Duclos-Cianci and Krysta M. Svore. Distillation of Non-Stabilizer States for Universal Quantum Computation. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 235-243, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{ducloscianci_et_al:LIPIcs.TQC.2013.235,
  author =	{Duclos-Cianci, Guillaume and Svore, Krysta M.},
  title =	{{Distillation of Non-Stabilizer States for Universal Quantum Computation}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{235--243},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.235},
  URN =		{urn:nbn:de:0030-drops-43233},
  doi =		{10.4230/LIPIcs.TQC.2013.235},
  annote =	{Keywords: quantum computing, resource estimation, magic state distillation}
}
Document
Realistic Cost for the Model of Coherent Computing

Authors: Akira SaiToh


Abstract
For the model of so-called coherent computing recently proposed by Yamamoto et al. [Y. Yamamoto et al., New Gen. Comput. 30 (2012) 327-355], a theoretical analysis of the success probability is given. Although it was claimed as their prospect that the Ising spin configuration problem would be efficiently solvable in the model, here it is shown that the probability of finding a desired spin configuration decreases exponentially in the number of spins for certain hard instances. The model is thus physically unfeasible for solving the problem within a polynomial cost.

Cite as

Akira SaiToh. Realistic Cost for the Model of Coherent Computing. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 244-253, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{saitoh:LIPIcs.TQC.2013.244,
  author =	{SaiToh, Akira},
  title =	{{Realistic Cost for the Model of Coherent Computing}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{244--253},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.244},
  URN =		{urn:nbn:de:0030-drops-43249},
  doi =		{10.4230/LIPIcs.TQC.2013.244},
  annote =	{Keywords: Reliability, Laser-network computing, Computational complexity}
}
Document
Optimal Robust Self-Testing by Binary Nonlocal XOR Games

Authors: Carl A. Miller and Yaoyun Shi


Abstract
Self-testing a quantum apparatus means verifying the existence of a certain quantum state as well as the effect of the associated measuring devices based only on the statistics of the measurement outcomes. Robust (i.e., error-tolerant) self-testing quantum apparatuses are critical building blocks for quantum cryptographic protocols that rely on imperfect or untrusted devices. We devise a general scheme for proving optimal robust self-testing properties for tests based on nonlocal binary XOR games. We offer some simplified proofs of known results on self-testing, and also prove some new results.

Cite as

Carl A. Miller and Yaoyun Shi. Optimal Robust Self-Testing by Binary Nonlocal XOR Games. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 254-262, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{miller_et_al:LIPIcs.TQC.2013.254,
  author =	{Miller, Carl A. and Shi, Yaoyun},
  title =	{{Optimal Robust Self-Testing by Binary Nonlocal XOR Games}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{254--262},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.254},
  URN =		{urn:nbn:de:0030-drops-43253},
  doi =		{10.4230/LIPIcs.TQC.2013.254},
  annote =	{Keywords: self-testing, quantum cryptography, random number generation, nonlocal games}
}
Document
Exact Quantum Query Complexity of EXACT and THRESHOLD

Authors: Andris Ambainis, Janis Iraids, and Juris Smotrovs


Abstract
A quantum algorithm is exact if it always produces the correct answer, on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. In this paper, we present two new exact quantum algorithms for natural problems: - for the problem EXACT_k^n in which we have to determine whether the sequence of input bits x_1, ..., x_n contains exactly k values x_i=1; - for the problem THRESHOLD_k^n in which we have to determine if at least k of n input bits are equal to 1.

Cite as

Andris Ambainis, Janis Iraids, and Juris Smotrovs. Exact Quantum Query Complexity of EXACT and THRESHOLD. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 263-269, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{ambainis_et_al:LIPIcs.TQC.2013.263,
  author =	{Ambainis, Andris and Iraids, Janis and Smotrovs, Juris},
  title =	{{Exact Quantum Query Complexity of EXACT and THRESHOLD}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{263--269},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.263},
  URN =		{urn:nbn:de:0030-drops-43261},
  doi =		{10.4230/LIPIcs.TQC.2013.263},
  annote =	{Keywords: Quantum query algorithms, Complexity of Boolean functions}
}
Document
The Quantum Entropy Cone of Stabiliser States

Authors: Noah Linden, Frantisek Matus, Mary Beth Ruskai, and Andreas Winter


Abstract
We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the classic inequalities, a type of linear rank inequalities associated with the combinatorial structure of normal subgroups of certain matrix groups. In the 4-party case, there is only one such inequality, the so-called Ingleton inequality. For these systems we show that strong subadditivity, weak monotonicity and Ingleton inequality exactly characterize the entropy cone for stabiliser states.

Cite as

Noah Linden, Frantisek Matus, Mary Beth Ruskai, and Andreas Winter. The Quantum Entropy Cone of Stabiliser States. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 270-284, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{linden_et_al:LIPIcs.TQC.2013.270,
  author =	{Linden, Noah and Matus, Frantisek and Ruskai, Mary Beth and Winter, Andreas},
  title =	{{The Quantum Entropy Cone of Stabiliser States}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{270--284},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.270},
  URN =		{urn:nbn:de:0030-drops-43278},
  doi =		{10.4230/LIPIcs.TQC.2013.270},
  annote =	{Keywords: Entropy inequalities, Stabiliser states, Ingleton inequality}
}
Document
Kitaev's Z_d-Codes Threshold Estimates

Authors: Guillaume Duclos-Cianci and David Poulin


Abstract
We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group method we previously introduced in [Duclos-Cianci/Poulin,arXiv:0911.0581,2009; Duclos-Cianci/Poulin,ITW'10,2010] for Z_2 topological codes.

Cite as

Guillaume Duclos-Cianci and David Poulin. Kitaev's Z_d-Codes Threshold Estimates. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 285-293, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{ducloscianci_et_al:LIPIcs.TQC.2013.285,
  author =	{Duclos-Cianci, Guillaume and Poulin, David},
  title =	{{Kitaev's Z\underlined-Codes Threshold Estimates}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{285--293},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.285},
  URN =		{urn:nbn:de:0030-drops-43280},
  doi =		{10.4230/LIPIcs.TQC.2013.285},
  annote =	{Keywords: Quantum error-correction threshold, Topological stabilizer codes, Qudit stabilizer codes}
}
Document
Optimal Quantum Circuits for Nearest-Neighbor Architectures

Authors: David J. Rosenbaum


Abstract
We show that the depth of quantum circuits in the realistic architecture where a classical controller determines which local interactions to apply on the kD grid Z^k where k >= 2 is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed. This allows minimum-depth circuits (up to a constant factor) for the nearest-neighbor architecture to be obtained from minimum-depth circuits in the standard abstract model. Our work therefore justifies the standard assumption that interactions can be performed between arbitrary pairs of qubits. In particular, our results imply that Shor's algorithm, controlled operations and fanouts can be implemented in constant depth, polynomial size and polynomial width in this architecture. We also present optimal non-adaptive quantum circuits for controlled operations and fanouts on a kD grid. These circuits have depth Theta(sqrt[k](n)), size Theta(n) and width Theta(n). Our lower bound also applies to a more general class of operations.

Cite as

David J. Rosenbaum. Optimal Quantum Circuits for Nearest-Neighbor Architectures. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 294-307, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{rosenbaum:LIPIcs.TQC.2013.294,
  author =	{Rosenbaum, David J.},
  title =	{{Optimal Quantum Circuits for Nearest-Neighbor Architectures}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{294--307},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.294},
  URN =		{urn:nbn:de:0030-drops-43290},
  doi =		{10.4230/LIPIcs.TQC.2013.294},
  annote =	{Keywords: 2D, Nearest Neighbor, Quantum Architecture, Quantum Complexity, Quantum Computation}
}
Document
Access Structure in Graphs in High Dimension and Application to Secret Sharing

Authors: Anne Marin, Damian Markham, and Simon Perdrix


Abstract
We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension q, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on $k$ for the existence of a ((k,n))_q scheme and prove, using probabilistic methods, that there exists alpha such that a random multigraph has an accessing parameter k => alpha*n with high probability.

Cite as

Anne Marin, Damian Markham, and Simon Perdrix. Access Structure in Graphs in High Dimension and Application to Secret Sharing. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 308-324, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{marin_et_al:LIPIcs.TQC.2013.308,
  author =	{Marin, Anne and Markham, Damian and Perdrix, Simon},
  title =	{{Access Structure in Graphs in High Dimension and Application to Secret Sharing}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{308--324},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.308},
  URN =		{urn:nbn:de:0030-drops-43306},
  doi =		{10.4230/LIPIcs.TQC.2013.308},
  annote =	{Keywords: Quantum Secret Sharing, Graph State, Multigraph, Access structure}
}

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