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DOI: 10.4230/LIPIcs.TQC.2014.141

Circuit Obfuscation Using Braids

Authors: Gorjan Alagic, Stacey Jeffery, and Stephen Jordan

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

Abstract

An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.

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Gorjan Alagic, Stacey Jeffery, and Stephen Jordan. Circuit Obfuscation Using Braids. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 141-160, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{alagic_et_al:LIPIcs.TQC.2014.141,
  author =	{Alagic, Gorjan and Jeffery, Stacey and Jordan, Stephen},
  title =	{{Circuit Obfuscation Using Braids}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{141--160},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.141},
  URN =		{urn:nbn:de:0030-drops-48135},
  doi =		{10.4230/LIPIcs.TQC.2014.141},
  annote =	{Keywords: obfuscation, cryptography, universality, quantum}
}

Document

DOI: 10.4230/LIPIcs.TQC.2014.161

Classical Simulation of Yang-Baxter Gates

Authors: Gorjan Alagic, Aniruddha Bapat, and Stephen Jordan

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

Abstract

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B_n for every n >= 2. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., d = 2) solutions, and some simple families that include solutions for arbitrary d >= 2. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting.

Cite as

Gorjan Alagic, Aniruddha Bapat, and Stephen Jordan. Classical Simulation of Yang-Baxter Gates. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 161-175, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

Copy BibTex To Clipboard

@InProceedings{alagic_et_al:LIPIcs.TQC.2014.161,
  author =	{Alagic, Gorjan and Bapat, Aniruddha and Jordan, Stephen},
  title =	{{Classical Simulation of Yang-Baxter Gates}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{161--175},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.161},
  URN =		{urn:nbn:de:0030-drops-48143},
  doi =		{10.4230/LIPIcs.TQC.2014.161},
  annote =	{Keywords: Quantum, Yang-Baxter, Braid, Anyon}
}

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Circuit Obfuscation Using Braids

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Classical Simulation of Yang-Baxter Gates

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