2019 Fiscal Year Research-status Report
Generalized Wigner quasi-probability distribution function and its application to various quantum systems
| Project/Area Number |
17K05569
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Tilma Todd 東京工業大学, 理学院, 特任准教授 (80530279)
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| 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)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | 数理物理 / 擬確率関数 / 量子相関 / 高次元量子系 |
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| Outline of Annual Research Achievements |
Wigner 関数の拡張と定式化: Project members have achieved an extension and reformulation of the Wigner function. This was done through the derivation of a SU(N)-symmetric Weyl function based on the Stratonovich-Weyl relation, and finding the appropriate transformations between the two. These results were published during H30.
エンタングルメントなど量子的な性質と Wigner 関数の関係の解明: Project members have developed a viable formalism that elucidates various quantum properties, such as entanglement, through the visualization of specific properties contained within various representations of the aforementioned functions. These results, which advance the state of the art in visualizing quantum correlations in atomic, molecular, and chemical systems, were published during H31 and were instrumental in verifying the quantumness of a 20-qubit Schrodinger cat state (see Song et al., Science 365, 574-577 (2019) ).
実験的なデータの有効な表示方法の開発: Project members have successfully developed two visualization packages for Wigner functions; the first being done in Python and integrated into IBM's "Quantum Experience" QISKit software package; the second being done in Swift for analysis of chemical systems. The later work is currently available upon request, but our plan is to make it widely available thru an open software repository during the second half of R2.
Lastly, project members have also completed their studies on encoding graph states in phase space using a variation of the Wigner formalism. This work was published during H31.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Project members have achieved a majority of the goals put forward in the initial research plan. Members are now exploring two new avenues of research based on discoveries made during this research project.
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| Strategy for Future Research Activity |
Going forward, project members will be exploring two areas of research. The first is applying the Wigner and Weyl formalisms developed during this current project to “designer” Hamiltonians; in particular lattice systems and small-scale molecular systems. The second is developing the underlying mathematical concepts that will unify the two phase-space formalisms currently in use: the finite-system/continuous space formalism preferred by quantum optics theorists and the finite-system/discrete space formalism preferred by quantum information theorists.
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| Causes of Carryover |
Due to personal reasons, and the corresponding COVID-19 pandemic, Dr. Mark Everitt has not been able to travel to Japan during the last 6 months of the project. This travel will occur later this year. Usage plan is as follows:
Travel: ~300,000\
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| Remarks |
From 2019, PI Todd Tilma has been a member of the 東京工業大学科学技術創成研究院量子コンピューティング研究ユニット
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