Quantum Information, Algebra and Geometry Workgroup

Who we are

We were born in 2016 as a cycle of interdisciplinary meetings in which we try to lay the foundations for a common language between Geometry, Algebra, Analysis and Physics starting from Quantum Information.

This is the mailinglist of the workgroup.

Form June 2018 we are part of the Q@TN initiative.

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Organizers

Alessandra Bernardi (Department of Mathematics)
Iacopo Carusotto (CNR)

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EDITION 2017/2018

NEXT MEETINGS

  • -- Iacopo Carusotto: A few steps from cluster states towards one way quantum computing (Part 2).

PAST MEETINGS

  • 17/11/2017: Francesco Pederiva:  Computer quantistici basati su circuit-QED.
    https://quantumexperience.ng.bluemix.net/qx/experience
  • 1/12/2017: Elia Macaluso e Alessandra Bernardi: Un po' di matematica per i tensor network.
  • 11/12/2107: Roberto Sebastiani: Solving SAT and MaxSAT with a Quantum Annealer: Foundations and Preliminary Report. (Organized by Massimiliano Sala).
  • 26/1/2018: Ivan Amelio: Quantum computation: some key ingredients in a standard example.
  • 16/2/2018: Davide Pastorello: An overview on Adiabatic Quantum Computing.
  • 2/3/2018: Iacopo Carusotto: A few steps from cluster states towards one way quantum computing (Part 1).
  • 14/3/2018: Edoardo Ballico: Grover's algorithm, secant varieties and a measure of entanglement (Geometric Measure of Entanglement) (Holweck, Rossi-Bruss-Machiavello and co.).
  • 28/3/2018: Luca Dellantonio:
    1. Quantum nondemolition measurement of mechanical motion quanta
    2. High dimensional mdi-QKD on 2D subspaces (organized with Davide Pastorello)
  • 13/04/2018: Francesco Pederiva: Hamiltonian Engineering: qualche aspetto (sparso) sulla teoria del controllo”.
  • 9/5/18: Alessio Recati: Basics on entanglement of quantum states.
  • 23/05/2018:
    1. Giorgio Cartechini: Characterization of a quantum random number generator based on superposition principle
    2. Rocco Mora: Quantum Shor Algorithm
  • 6/6/2018: Iacopo Carusotto: "The superconducting qubit platform at Google Labs and the Google quantum innovation award: let's brainstorm all together!"
  • 20/6/2018: Giovanni Garberoglio: Applicazioni del machine learning alla meccanica quantistica (https://arxiv.org/abs/1606.02318).
  • 4/7/2018: Fulvio Gesmundo (QMATH University of Copenhagen): SLOCC transformations, tensor degeneration and Strassen's asymptotic rank conjecture.

EDITION 2016/2017

6/10/2016: Davide Pastorello, Fondamenti di meccanica quantistica in dimensione finita con introduzione all'entanglement.

20/10/2016: Davide Pastorello, Un'introduzione all'entanglement.

10/11/2016: Iacopo Carusotto, Paradossi e misteri legati all'entanglement.
Notes: http://www.science.unitn.it/~carusott/lecture_entanglement.pdf

17/11/2016: Alessandro Tomasi. Qubits: computing with probability.
Slides: https://me.unitn.it/system/files/Bernardi%20Alessandra/qubits_20161117_0.pdf

1/12/2016: Edoardo Ballico. Schmidt Rank.

15/12/2016: Luis Sola Conde. Tensor Network States.

19/01/2017: Giovanni Garberoglio: Second sortie in the qubit arena.

16/02/2017: Alessandra Bernardi: SLOCC e orbite di gruppi.

01/03/2017: Edoardo Ballico: Da Shannon fro Dummies a Schumacher for Dummies.

17/03/2017: Iacopo Carusotto: Quel poco che ho capito della classificazione dell'entanglement via SLOCC.

31/3/2017: Alessandro Tomasi Quantum error correction.
Slides: qecc_20170331_0.pdf

21/4/2017: Francesco Pederiva. First steps into quantum probability theory.

Bibliography

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  2. Albash et al. Rev. Mod. Phys. 20 (2014)
  3. C.H. Bennet, S. Popescu, D. Rohrlich, J.A. Smolin, A.V. Thapliyal, Exact and Asymptotic Measures of Multipartite Pure State EntanglementPhysical Review A 63(1), 1999.
  4. Briegel and Raussendorf, Phys Rev Lett 86, 910 (2001)
  5. Draisma, Ottaviani, Tocino,  Best rank-k approximations for tensors: generalizing Eckart-Young, arXiv:1711.06443
  6. W. Dür, G. Vidal, J.I. Cirac, Three qubits can be entangled in two inequivalent waysPhysical Review A 62(6), 2000.
  7. Farhi et al, Science 292 (2001)
  8. R. Feynman, QED. D.F. Walls, Gerard J. Milburn, Quantum Optics.V. Scarani, Quantum information: primitive notions and quantum correlations, IN Ultracold Gases and Quantum Information: Lecture Notes of the Les Houches Summer School in Singapore: Volume 91, July 2009.
  9. F. Holweck, J,-G. Luque, J.-Y. Thibon, Geometric description of entangled states by auxiliary varietiesJournal of Mathematical Physics 53, 102203 (2012).
  10. Kitaev, A. Yu.; Shen, A. H.; Vyalyi, M. N., Classical and quantum computation, Translated from the 1999 Russian original by Lester J. Senechal. Graduate Studies in Mathematics, 47. American Mathematical Society, Providence, RI, 2002. xiv+257.
  11. Jansen et al. J. Math Phys. 48 (2007)
  12. J. M. Landsberg, Tensors: geometry and applications. Graduate Studies in Mathematics, 128. American Mathematical Society, Providence, RI, 2012. xx+439 pp.
  13. Landsberg, Qi, Ye, On the geometry of tensor network states, Journal Quantum Information & Computation archive Volume 12 Issue 3-4, March 2012, Pages 346-354 .
  14. Landsberg,  New Lower Bounds for the Rank of Matrix Multiplication, SIAM J. Comput., 43(1), 144–149. (6 pages).
  15. Christian Miniatura, Leong-Chuan Kwek, Martial Ducloy, Benoît Grémaud, Berthold-Georg Englert, Leticia Cugliandolo, Artur Ekert, and Kok Khoo Phua.
  16. S. Olivares Notes, Quantum lower bounds by quantum arguments, A. Ambainis (2000).
  17. R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangles pair states, Annals of Physics, 349 (2014), 117--158.
  18. D. Pastorello, A Mathematical introduction to quantum information theory, (Available here).
  19. J. Preskill,  Lecture notes on Quantum Information Theory (http://www.theory.caltech.edu/~preskill/ph229/#lecture).
  20. Raussendorf and Briegel, PRL 86, 5188 (2001)