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DOI: 10.4230/LIPIcs.TQC.2013.235

Distillation of Non-Stabilizer States for Universal Quantum Computation

Authors: Guillaume Duclos-Cianci and Krysta M. Svore

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

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.

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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}
}

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DOI: 10.4230/LIPIcs.TQC.2013.285

Kitaev's Z_d-Codes Threshold Estimates

Authors: Guillaume Duclos-Cianci and David Poulin

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

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.

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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}
}

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Documents authored by Duclos-Cianci, Guillaume

Distillation of Non-Stabilizer States for Universal Quantum Computation

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Kitaev's Z_d-Codes Threshold Estimates

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