| 研究課題/領域番号 |
20K03774
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| 研究機関 | 京都大学 |
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研究代表者 |
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| 研究期間 (年度) |
2020-04-01 – 2024-03-31
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| キーワード | statistical inference / quantum measurements / data-driven inference / quantum devices |
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| 研究実績の概要 |
The statistical inference of quantum measurements has been so far limited to the qubit case, due to the analytical difficulties encountered in addressing the higher dimensional quantum cases. Recently, I overcame this limitation by deriving a framework of characterization theorems for the output of the data-driven inference map, for any input data, that holds for arbitrarily dimensional quantum systems. This characterization is based on an hyper-spherical outer approximation of the quantum state space, which is strictly spherical only in the qubit case. Such an approximation is made possible by recent results in spherical designs and the role they play in differential geometry, and are in part due to the work of John Fritz (1948). As a consequence, I better clarified the role played by previously-introduced concepts, such as the observational completeness, within the framework of the statistical inference of quantum measurements. Thanks to these achievements, the statistical inference of quantum measurements has now reached the level of a complete, robust, and self-consistent inference theory. Hence, my results pave the way to the implementation of the statistical inference of quantum measurements of an arbitrary number of qubits for noisy, intermediate scale quantum computers.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
The statistical inference of quantum measurements recently developed from a proof-of-principle thought experiment into a complete inference theory ready for implementation. During this process, I have settled the initial difficulties in the operational definition of the main components of the theory -- for instance, the data-driven map, the concept of observational completeness, and the relation between the statistical inference and the quantum tomographic approach. Moreover, I have exploited relatively recent mathematical results in differential geometry and spherical designs to greatly extend the statistical inference far beyond its initial scope of qubit measurements, to include an initially unexpected analytical solution for the general and mathematically challenging quantum case.
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| 今後の研究の推進方策 |
The next natural step for the research project focusing on the statistical inference of quantum measurements is the experimental implementation, in particular in the context of noisy, intermediate scale quantum computers. As it is well known, such machines suffer from comparatively high amounts of noise, that render their calibration through a quantum tomographic approach very problematic. On the other hand, the calibration is the fundamental step in order to characterize the machine to enable fault-tolerant quantum computation. The statistical inference seems to be the perfect candidate to replace the tomographic approach in this case, because of its inherent independence from any assumption on the underlying machine, and therefore on any source of noise.
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| 次年度使用額が生じた理由 |
With the progressive containment of the pandemics and the restoration of overseas travels, for the F.Y. 2022 I plan to use a significant portion of the budget for business trips, with the aim of strengthening collaborations with international research groups. In particular, I hope the international situation will allow me to an extensive visit to the quantum information theory group in Pavia University, Italy, with whom I have previous and ongoing collaborations on the statistical inference of quantum measurements.
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