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Generalized Wigner quasi-probability distribution function and its application to various quantum systems

Research Project

Project/Area Number 17K05569
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionTokyo Institute of Technology

Principal Investigator

Tilma Todd  東京工業大学, 理学院, 特任准教授 (80530279)

Co-Investigator(Kenkyū-buntansha) 根本 香絵  国立情報学研究所, 情報学プリンシプル研究系, 教授 (80370104)
Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords擬確率関数 / 量子相関 / 高次元量子系 / 数理物理 / 量子細線
Outline of Final Research Achievements

Project members were able to meet and fulfill all major goals of the grant. To begin, project members were able to derive an extension and reformulation of the Wigner function. Project members were then able to verify that the updated formalism elucidates various quantum properties, such as entanglement, through the visualization of specific "slices" of the various representations of the aforementioned functions. Lastly, project members were successful in developing two visualization packages for said Wigner functions based upon the updated formalism; the first being done in Python and integrated into IBM's QISKit software package; the second being done in Swift for analysis of chemical systems.

Academic Significance and Societal Importance of the Research Achievements

Our work generated two software packages; a half-dozen papers; advanced the visualization of quantum correlations in atomic, molecular, and chemical systems; and was instrumental in verifying the quantumness of a 20-qubit Schrodinger cat state (see Song et al., Science 365, 574-577 (2019)).

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (31 results)

All 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (6 results) Journal Article (10 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 2 results,  Open Access: 9 results) Presentation (11 results) (of which Int'l Joint Research: 11 results,  Invited: 3 results) Remarks (4 results)

  • [Int'l Joint Research] Loughborough University(英国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Loughborough University(英国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Loughborough University(英国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Universita degli Studi Roma Tre/Sapienza Universita di Roma(イタリア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Loughborough University(United Kingdom)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Universita degli Studi Roma Tre/Sapienza Universita di Roma(Italy)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies2021

    • Author(s)
      Mark J. Everitt and Russell P. Rundle
    • Journal Title

      Advanced Quantum Technologies

      Volume: N/A Issue: 6 Pages: 1-29

    • DOI

      10.1002/qute.202100016

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Visualization of correlations in hybrid discrete-continuous variable quantum systems2020

    • Author(s)
      Rundle R P、Davies B I、Dwyer V M、Tilma Todd、Everitt M J
    • Journal Title

      Journal of Physics Communications

      Volume: 4 Issue: 2 Pages: 025002-025002

    • DOI

      10.1088/2399-6528/ab6fb6

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Quantum invariants and the graph isomorphism problem2019

    • Author(s)
      Mills P. W.、Rundle R. P.、Samson J. H.、Devitt Simon J.、Tilma Todd、Dwyer V. M.、Everitt Mark J.
    • Journal Title

      Physical Review A

      Volume: 100 Issue: 5

    • DOI

      10.1103/physreva.100.052317

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Visualizing spin degrees of freedom in atoms and molecules2019

    • Author(s)
      Davies B. I.、Rundle R. P.、Dwyer V. M.、Samson J. H.、Tilma Todd、Everitt M. J.
    • Journal Title

      Physical Review A

      Volume: 100 Issue: 4

    • DOI

      10.1103/physreva.100.042102

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] General approach to quantum mechanics as a statistical theory2019

    • Author(s)
      Rundle R. P.、Tilma Todd、Samson J. H.、Dwyer V. M.、Bishop R. F.、Everitt M. J.
    • Journal Title

      Physical Review A

      Volume: 99 Issue: 1 Pages: 1-13

    • DOI

      10.1103/physreva.99.012115

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Quantum State Spectroscopy of Atom-Cavity Systems2018

    • Author(s)
      R. P. Rundle, B. I. Davies, V. M. Dwyer, Todd Tilma, M. J. Everitt
    • Journal Title

      arXiv:1809.10564

      Volume: 1 Pages: 1-10

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Visualising entanglement in atoms and molecules2018

    • Author(s)
      B. I. Davies, R. P. Rundle, V. M. Dwyer, J. H. Samson, Todd Tilma, M. J. Everitt
    • Journal Title

      arXiv:1809.05431

      Volume: 1 Pages: 1-10

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Complete correlation characteristic (Weyl) functions for any quantum system or ensemble2017

    • Author(s)
      R. P. Rundle, Todd Tilma, V. M. Dwyer, R. F. Bishop, Mark J. Everitt
    • Journal Title

      arXiv:1708.03814

      Volume: 1 Pages: 1-16

    • Related Report
      2017 Research-status Report
    • Open Access / Int'l Joint Research
  • [Journal Article] Wigner function reconstruction of experimental three-qubit GHZ and W states2017

    • Author(s)
      Mario A. Ciampini, Todd Tilma, Mark J. Everitt, W. J. Munro, Paolo Mataloni, Kae Nemoto, Marco Barbieri
    • Journal Title

      arXiv:1710.02460

      Volume: 1 Pages: 1-8

    • Related Report
      2017 Research-status Report
    • Open Access / Int'l Joint Research
  • [Journal Article] A proposal for an efficient quantum algorithm solving the graph isomorphism problem2017

    • Author(s)
      P. W. Mills, R. P. Rundle, V. M. Dwyer, Todd Tilma, Simon J. Devitt, J. H. Samson, Mark J. Everitt
    • Journal Title

      arXiv:1711.09842

      Volume: 1 Pages: 1-6

    • Related Report
      2017 Research-status Report
    • Open Access / Int'l Joint Research
  • [Presentation] Quantum State Spectroscopy of Atom-Cavity Systems2019

    • Author(s)
      Todd Tilma
    • Organizer
      The Japan Society of Applied Physics (JSAP) Autumn Meeting
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum State Verification, Validation, and Visualisation via Phase Space Methods2019

    • Author(s)
      Russell Rundle
    • Organizer
      Lindau Nobel Laureate Meeting
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum Mechanics of Anything (From Qubits to Atoms and Molecules) as a Statistical Theory (i.e. in Phase Space)2019

    • Author(s)
      Mark Everitt
    • Organizer
      International Wigner Workshop
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum mechanics of any system in phase space2018

    • Author(s)
      Mark Everitt
    • Organizer
      The 32nd International Colloquium on Group Theoretical Methods in Physics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] A general approach to quantum mechanics as a statistical theory2018

    • Author(s)
      Mark Everitt
    • Organizer
      Dynamics Days
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum Advantage: The Graph Isomorphism Problem2018

    • Author(s)
      Patrick Mills
    • Organizer
      Quantum Simulation and Computation
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Introduction to Phase Space Methods2017

    • Author(s)
      Todd Tilma
    • Organizer
      Landau Lecture - Loughborough University
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A simple way to preform quantum phase space measurement and state verification on arbitrary systems2017

    • Author(s)
      Mark Everitt
    • Organizer
      Quantum Optics to Quantum Technology
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum State Verification, Validation, and Visualisation via Phase Space Methods2017

    • Author(s)
      Russell Rundle
    • Organizer
      Young Quantum Information Scientists
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum State Imaging In Phase Space2017

    • Author(s)
      Russell Rundle
    • Organizer
      Doctoral College Research Conference
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum State Imaging In Phase Space2017

    • Author(s)
      Russell Rundle
    • Organizer
      Science Matters
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Remarks] Tilma Labs

    • URL

      https://tilma-labs.org

    • Related Report
      2020 Annual Research Report
  • [Remarks] Quantum Systems Engineering Research Group

    • URL

      http://www.lboro.ac.uk/research/quantum-systems/

    • Related Report
      2020 Annual Research Report 2019 Research-status Report 2018 Research-status Report 2017 Research-status Report
  • [Remarks] Global Research Center for QIS

    • URL

      https://qis1.ex.nii.ac.jp/qi/

    • Related Report
      2020 Annual Research Report 2019 Research-status Report 2018 Research-status Report 2017 Research-status Report
  • [Remarks] Tilma Labs

    • URL

      https://tilma-labs.org/

    • Related Report
      2019 Research-status Report 2018 Research-status Report 2017 Research-status Report

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Published: 2017-04-28   Modified: 2022-01-27  

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