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Documents authored by Brandao, Fernando

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Brandao, Fernando

Document
Complete Volume
DOI: 10.4230/LIPIcs.TQC.2013
LIPIcs, Volume 22, TQC'13, Complete Volume

Authors: Simone Severini and Fernando Brandao

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

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

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-dev.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
DOI: 10.4230/LIPIcs.TQC.2013.i
Frontmatter, Table of Contents, Preface, Conference Organization

Authors: Simone Severini and Fernando Brandao

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

Abstract
Frontmatter, Table of Contents, Preface, Conference Organization
Cite as

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-dev.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}
}

Brandão, Fernando G. S. L.

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.27
Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning

Authors: Fernando G. S. L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank at most r, and sparsity s. The first algorithm assumes an input model where one is given access to an oracle to the entries of the matrices at unit cost. We show that it has run time O~(s^2 (sqrt{m} epsilon^{-10} + sqrt{n} epsilon^{-12})), with epsilon the error of the solution. This gives an optimal dependence in terms of m, n and quadratic improvement over previous quantum algorithms (when m ~~ n). The second algorithm assumes a fully quantum input model in which the input matrices are given as quantum states. We show that its run time is O~(sqrt{m}+poly(r))*poly(log m,log n,B,epsilon^{-1}), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only polylogarithmically in n and polynomially in r. We apply the second SDP solver to learn a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state rho with rank at most r, we show we can find in time sqrt{m}*poly(log m,log n,r,epsilon^{-1}) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as rho on the m measurements, up to error epsilon. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics. As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight update method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians, given quantum states encoding these Hamiltonians, with a poly-logarithmic dependence on its dimension, which is based on ideas developed in quantum principal component analysis. We also develop a "fast" quantum OR lemma with a quadratic improvement in gate complexity over the construction of Harrow et al. [Harrow et al., 2017]. We believe both techniques might be of independent interest.
Cite as

Fernando G. S. L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu. Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brandao_et_al:LIPIcs.ICALP.2019.27,
  author =	{Brand\~{a}o, Fernando G. S. L. and Kalev, Amir and Li, Tongyang and Lin, Cedric Yen-Yu and Svore, Krysta M. and Wu, Xiaodi},
  title =	{{Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.27},
  URN =		{urn:nbn:de:0030-drops-106036},
  doi =		{10.4230/LIPIcs.ICALP.2019.27},
  annote =	{Keywords: quantum algorithms, semidefinite program, convex optimization}
}

Brandão, Fernando G.S L.

Document
DOI: 10.4230/LIPIcs.TQC.2021.7
Fast and Robust Quantum State Tomography from Few Basis Measurements

Authors: Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
Quantum state tomography is a powerful but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
Cite as

Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng. Fast and Robust Quantum State Tomography from Few Basis Measurements. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{franca_et_al:LIPIcs.TQC.2021.7,
  author =	{Fran\c{c}a, Daniel Stilck and Brand\~{a}o, Fernando G.S L. and Kueng, Richard},
  title =	{{Fast and Robust Quantum State Tomography from Few Basis Measurements}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.7},
  URN =		{urn:nbn:de:0030-drops-140023},
  doi =		{10.4230/LIPIcs.TQC.2021.7},
  annote =	{Keywords: quantum tomography, low-rank tomography, Gibbs states, random measurements}
}
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