2 Search Results for "França, Daniel Stilck"

Document
DOI: 10.4230/LIPIcs.ITCS.2023.5
Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations

Authors: Anurag Anshu and Tony Metger

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [De Palma et al., 2022]; (ii) injective matrix product states; (iii) output states of dense Hamiltonian evolution, i.e. states of the form e^{ιH^{(p)}} ⋯ e^{ιH^{(1)}} |ψ₀⟩ for any n-qubit product state |ψ₀⟩, where each H^{(i)} can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits. Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates. An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level p = o(log log n), assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level, improving upon the recent result [Basso et al., 2022].
Cite as

Anurag Anshu and Tony Metger. Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 5:1-5:8, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{anshu_et_al:LIPIcs.ITCS.2023.5,
  author =	{Anshu, Anurag and Metger, Tony},
  title =	{{Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{5:1--5:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-175085},
  doi =		{10.4230/LIPIcs.ITCS.2023.5},
  annote =	{Keywords: quantum computing, polynomial approximation, quantum optimization algorithm, QAOA, overlap gap property}
}
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)

Copy BibTex To Clipboard

@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.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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