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Documents authored by van Dam, Wim

Document
Complete Volume
DOI: 10.4230/LIPIcs.TQC.2019
LIPIcs, Volume 135, TQC'19, Complete Volume

Authors: Wim van Dam and Laura Mančinska

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract
LIPIcs, Volume 135, TQC'19, Complete Volume
Cite as

14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{vandam_et_al:LIPIcs.TQC.2019,
  title =	{{LIPIcs, Volume 135, TQC'19, Complete Volume}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019},
  URN =		{urn:nbn:de:0030-drops-105052},
  doi =		{10.4230/LIPIcs.TQC.2019},
  annote =	{Keywords: Theory of computation, Quantum computation theory, Quantum complexity theory, Quantum communication complexity}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TQC.2019.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Wim van Dam and Laura Mančinska

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 0:i-0:xiii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{vandam_et_al:LIPIcs.TQC.2019.0,
  author =	{van Dam, Wim and Man\v{c}inska, Laura},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{0:i--0:xiii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.0},
  URN =		{urn:nbn:de:0030-drops-103920},
  doi =		{10.4230/LIPIcs.TQC.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.TQC.2018.7
Two-qubit Stabilizer Circuits with Recovery I: Existence

Authors: Wim van Dam and Raymond Wong

Published in: LIPIcs, Volume 111, 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)

Abstract
In this paper, we further investigate the many ways of using stabilizer operations to generate a single qubit output from a two-qubit state. In particular, by restricting the input to certain product states, we discover probabilistic operations capable of transforming stabilizer circuit outputs back into stabilizer circuit inputs. These secondary operations are ideally suited for recovery purposes and require only one extra resource input to proceed. As a result of reusing qubits in this manner, we present an alternative to the original state preparation process that can lower the overall costs of executing a two-qubit stabilizer procedure involving non-stabilizer resources.
Cite as

Wim van Dam and Raymond Wong. Two-qubit Stabilizer Circuits with Recovery I: Existence. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 111, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vandam_et_al:LIPIcs.TQC.2018.7,
  author =	{van Dam, Wim and Wong, Raymond},
  title =	{{Two-qubit Stabilizer Circuits with Recovery I: Existence}},
  booktitle =	{13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-080-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{111},
  editor =	{Jeffery, Stacey},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2018.7},
  URN =		{urn:nbn:de:0030-drops-92540},
  doi =		{10.4230/LIPIcs.TQC.2018.7},
  annote =	{Keywords: stabilizer circuit, recovery circuit, magic state}
}
Document
DOI: 10.4230/LIPIcs.TQC.2018.8
Two-qubit Stabilizer Circuits with Recovery II: Analysis

Authors: Wim van Dam and Raymond Wong

Published in: LIPIcs, Volume 111, 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)

Abstract
We study stabilizer circuits that use non-stabilizer qubits and Z-measurements to produce other non-stabilizer qubits. These productions are successful when the correct measurement outcome occurs, but when the opposite outcome is observed, the non-stabilizer input qubit is potentially destroyed. In preceding work [arXiv:1803.06081 (2018)] we introduced protocols able to recreate the expensive non-stabilizer input qubit when the two-qubit stabilizer circuit has an unsuccessful measurement outcome. Such protocols potentially allow a deep computation to recover from such failed measurements without the need to repeat the whole prior computation. Possible complications arise when the recovery protocol itself suffers from a failed measurement. To deal with this, we need to use nested recovery protocols. Here we give a precise analysis of the potential advantage of such recovery protocols as we examine its optimal nesting depth. We show that if the expensive input qubit has cost d, then typically a depth O(log d) recovery protocol is optimal, while a certain special case has optimal depth O(sqrt{d}). We also show that the recovery protocol can achieve a cost reduction by a factor of at most two over circuits that do not use recovery.
Cite as

Wim van Dam and Raymond Wong. Two-qubit Stabilizer Circuits with Recovery II: Analysis. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 111, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vandam_et_al:LIPIcs.TQC.2018.8,
  author =	{van Dam, Wim and Wong, Raymond},
  title =	{{Two-qubit Stabilizer Circuits with Recovery II: Analysis}},
  booktitle =	{13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-080-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{111},
  editor =	{Jeffery, Stacey},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2018.8},
  URN =		{urn:nbn:de:0030-drops-92551},
  doi =		{10.4230/LIPIcs.TQC.2018.8},
  annote =	{Keywords: stabilizer circuit, recovery circuit, magic state}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.16
Optimal Quantum Algorithm for Polynomial Interpolation

Authors: Andrew M. Childs, Wim van Dam, Shih-Han Hung, and Igor E. Shparlinski

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over F_q. A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2 + 1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2 + 1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2 + 1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm’s success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log(q)) with negligible decrease in the success probability. We end with a conjecture about the quantum query complexity of multivariate polynomial interpolation.
Cite as

Andrew M. Childs, Wim van Dam, Shih-Han Hung, and Igor E. Shparlinski. Optimal Quantum Algorithm for Polynomial Interpolation. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{childs_et_al:LIPIcs.ICALP.2016.16,
  author =	{Childs, Andrew M. and van Dam, Wim and Hung, Shih-Han and Shparlinski, Igor E.},
  title =	{{Optimal Quantum Algorithm for Polynomial Interpolation}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{16:1--16:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.16},
  URN =		{urn:nbn:de:0030-drops-62985},
  doi =		{10.4230/LIPIcs.ICALP.2016.16},
  annote =	{Keywords: Quantum algorithms, query complexity, polynomial interpolation, finite fields}
}
Document
DOI: 10.4230/LIPIcs.TQC.2014.110
Hidden Subgroup Quantum Algorithms for a Class of Semi-Direct Product Groups

Authors: Wim van Dam and Siladitya Dey

Published in: LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Abstract
A quantum algorithm for the Hidden Subgroup Problem over the group Z/p^{r}Z \rtimes Z/q^{s}Z is presented. This algorithm, which for certain parameters of the group qualifies as 'efficient', generalizes prior work on related semi-direct product groups.
Cite as

Wim van Dam and Siladitya Dey. Hidden Subgroup Quantum Algorithms for a Class of Semi-Direct Product Groups. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 110-117, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{vandam_et_al:LIPIcs.TQC.2014.110,
  author =	{van Dam, Wim and Dey, Siladitya},
  title =	{{Hidden Subgroup Quantum Algorithms for a Class of Semi-Direct Product Groups}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{110--117},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Flammia, Steven T. and Harrow, Aram W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.110},
  URN =		{urn:nbn:de:0030-drops-48117},
  doi =		{10.4230/LIPIcs.TQC.2014.110},
  annote =	{Keywords: quantum algorithms, quantum complexity theory, computational group theory}
}
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