RIKEN Quantumレクチャー
7 イベント
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講演会・レクチャーAn optimal transport and information geometric framework for infinite-dimensional Gaussian measures and Gaussian processes (II)
2026年7月28日(火) 15:00 - 16:15
Minh Ha Quang (理化学研究所 革新知能統合研究センター (AIP) 不完全情報学習チーム 上級研究員)
Divergences between probability distributions play a crucial role in many areas of probability theory, statistics, machine learning, and their applications. While a large part of the literature is focused on divergences between finite-dimensional distributions, there is a growing body of work on infinite-dimensional distances/divergences, which are motivated by applications in functional data analysis, Bayesian inverse problems, and functional Bayesian neural networks, among others. In this lecture, we present an overview of recent results on some of the most important divergences being studied, including the Kullback-Leibler, Renyi, and Geometric Jensen-Shannon divergences. We discuss the many challenges that arise in the infinite-dimensional setting, e.g. the lack of a natural reference measure such as the Lebesgue measure and the fact that many functions such as determinants and logarithm are only well-defined in specific settings. In particular, in the setting of Gaussian measures on infinite-dimensional Hilbert spaces, the closed form expressions for the above divergences are only generalizable to equivalent Gaussian measures. We present the resolution to the above challenges via the geometrical framework of positive definite unitized (or regularized) trace class and Hilbert-Schmidt operators, including the Alpha and Alpha-Beta Log-Determinant divergences. Using this framework and the methodology of reproducing kernel Hilbert spaces (RKHS), we furthermore obtain consistent finite-dimensional approximations of the above divergences in the Gaussian process setting, with dimensional-independent sample complexities. The resulting numerical algorithms can be readily employed in practical applications. We shall also discuss the generalization of the above classical divergences above to the quantum setting, namely the Quantum Jensen-Shannon divergence between quantum states, defined in terms of the von Neumann and Tsallis entropies, from finite to infinite-dimensional settings.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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講演会・レクチャー
An optimal transport and information geometric framework for infinite-dimensional Gaussian measures and Gaussian processes (I)
2026年7月28日(火) 13:30 - 14:45
Minh Ha Quang (理化学研究所 革新知能統合研究センター (AIP) 不完全情報学習チーム 上級研究員)
Optimal transport (OT) and information geometry (IG) have been attracting much research attention in various fields, in particular machine learning and statistics. In this lecture, we present results on the generalization of IG and OT distances for finite-dimensional Gaussian measures to the setting of infinite-dimensional Gaussian measures and Gaussian processes. Our focus is on the Entropic Regularization of the 2-Wasserstein distance and the generalization of the Fisher-Rao Riemannian metric and related quantities. In both settings, regularization leads to many desirable theoretical properties, including in particular dimension-independent convergence and sample complexity. The mathematical formulation involves the interplay of IG and OT with Gaussian processes and the methodology of reproducing kernel Hilbert spaces (RKHS). All of the presented formulations admit closed form expressions that can be efficiently computed and applied practically. The mathematical formulations will be illustrated with numerical experiments on Gaussian processes.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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講演会・レクチャー
Lectures on Quantum Measurement Theory: IV
2026年6月30日(火) 15:30 - 17:00
小澤 正直 (名古屋大学 名誉教授)
Lecture IV: Instruments in classical mechanics, quantum field theory, and cognitive science In algebraic quantum field theory, measurements describable by interactions between the field and the measuring apparatus are characterized by the class of completely positive instruments that satisfy the condition called the normal extension property (NEP) (Okamura-Ozawa 2016). In classical mechanics, traditionally only non-invasive measurements—those with trivial interaction—were considered admissible, for the observability of the trajectory of motion. Here, however, the full class of measurements realizable by classical-mechanical interactions is characterized in terms of instruments with NEP for the basis of the study of invasive measurements of classical systems. Cognitive processes are also represented by completely positive instruments, along with the long-standing paradigm provided by von Helmholtz, who described a sensation-perception process as a sort of measuring interaction and referred to it as an unconscious inference. This framework is used to show the compatibility of the question order effect and the response replicability effect (Ozawa-Khrennikov 2019), which failed to be explained in an earlier approach using only projective measurement models. It is shown that there exists an instrument model, realizing both the question order effect and the response replicability effect, that is also capable of almost faithfully reproducing public-opinion survey data such as the well-known Clinton-Gore survey by Gallup in 1997 (Ozawa-Khrennikov 2021).
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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講演会・レクチャー
Lectures on Quantum Measurement Theory: III
2026年6月23日(火) 15:30 - 17:00
小澤 正直 (名古屋大学 名誉教授)
Lecture III: Measurement error, disturbance, the universally valid reformulation of Heisenberg’s uncertainty principle, and a quantitative generalization of the Wigner–Araki–Yanase theorem Definitions of measurement error and disturbance are introduced (Ozawa 2002, 2019) and it is shown that there exists a solvable model for a physically realizable measurement that serves as a counterexample both to Heisenberg’s uncertainty principle in the conventional formulation and to the SQL (Ozawa 1988, 1989, 2002). Thus, those limits are no more considered as universal limits. In fact, the above counter example to SQL was found in 1988 using the idea of contractive state measurements by Yuen (1983) and the LIGO was started in 1994 to succeed in the gravitational wave detection in 2015 as announced in 2016. New formulations are then proved for the uncertainty principle concerning the errors in the approximate simultaneous measurement of two physical quantities, called the "joint error relation" (Ozawa 2003b, 2004), and for the uncertainty principle concerning the error and disturbance associated with the measurement of a single physical quantity, called the "error-disturbance relation" (Ozawa 2003a). From the error-disturbance relation, a quantitative relation for measurement error under an additive conservation law is proved (Ozawa 2002a, 2003b), generalizing the "Wigner–Araki–Yanase theorem" (Wigner 1952, Araki-Yanase 1960), which states that a physical quantity not commuting with a conserved quantity cannot be measured accurately by a measurement interaction satisfying an additive conservation law. The above relation also derives limits for realizing quantum computing and operations under conservation laws (Ozawa 2002b), the results later developed as the resource theory of asymmetry.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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講演会・レクチャー
Lectures on Quantum Measurement Theory: II
2026年6月16日(火) 15:30 - 17:00
小澤 正直 (名古屋大学 名誉教授)
Lecture II: Modern approach: Quantum instruments, POVMs, measuring processes, intersubjectivity, and value reproducibility The modern approach to quantum measurement theory is based on the "realizability theorem" stating that a measurement is physically realizable if and only if its statistical properties are represented by a completely positive instrument, and this is also equivalent to saying that the measurement can be described by an interaction with a measuring apparatus (Ozawa 1984, 2004). The conventional analysis of a measuring process determines the post-measurement object state by applying the "projection postulate" to the meter measurement in the post-measurement state that "entangles" the object and the apparatus, but the above result has been established without assuming the projection postulate altogether; rather we use only the classical Bayesian probability update rule (Ozawa 1984). We introduce the "intersubjectivity theorem" that states that, when multiple observers simultaneously and statistically correctly measure the same physical quantity, they obtain the same measurement value and the "value reproducibility theorem" that states that a statistically correct measurement correctly reproduces the value of the physical quantity immediately before the measurement (Ozawa 2025). The above three theorems essentially solves the so-called measurement problem, since we eliminate the collapse of the wave function and we establish the reality of the the pre-measurement value of the measured observable to be copied to the meter value and to be recorded by the observer.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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講演会・レクチャー
Lectures on Quantum Measurement Theory: I
2026年6月2日(火) 15:30 - 17:00
小澤 正直 (名古屋大学 名誉教授)
Lecture I: Conventional approach: Repeatability, Heisenberg’s original uncertainty principle, and the SQL for gravitational-wave detection The conventional approach to quantum measurement theory taken by von Neumann (1932), Dirac (1958), and Schrödinger (1935) assumes the "repeatability hypothesis" stating that if a physical quantity is measured twice in succession, then the same value is obtained each time, which is often quantitatively generalized to the "approximately repeatable hypothesis" stating that after a measurement of a physical quantity with error ε, the post-measurement deviation around the measured value is no larger than ε; this is equivalent to saying that the state after obtaining a measurement result with error ε becomes an ε-approximate eigenstate corresponding to that measurement result. From the approximate repeatability hypothesis, one can derive "Heisenberg’s original formulation of the uncertainty principle," namely, that when position and momentum are approximately measured simultaneously, the product of their respective errors is at least ℏ/2 (Heisenberg 1927, Kennard 1927, Ozawa 2015), as well as the "standard quantum limit (SQL) for monitoring the free-mass position", which states that when the position of a free mass m is measured at a time interval τ, the result of the second measurement cannot be predicted with uncertainty smaller than (ℏτ/ m)^{1/2} (Caves 1985). The last result leads to a sensitivity limit for interferometric gravitational-wave detectors, and in the early 1980s it was therefore argued that gravitational waves of the expected strength could not be observed using interferometric detectors (Braginsky et al. 1980, Caves et al. 1980).
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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講演会・レクチャー
Rapid development of cold-atom quantum computers and their prospect
2023年12月26日(火) 13:30 - 17:00
富田 隆文 (分子科学研究所 光分子科学研究領域 助教)
Note for participants: For on-site participants, please register via the registration form. For online participants finding the Zoom link, you can get it after filling the registration form. Program: 13:30-15:00 Lecture 1 15:00-15:30 Coffee break 15:30-17:00 Lecture 2 Abstract: In this talk, I will give an overview of the recent rapid progress of cold-atom quantum computers. In a cold-atom quantum computer, a laser-cooled atomic gas in a vacuum chamber is captured with a two-dimensional trap array called an optical tweezers array, which is an array of tightly focused laser beams. An array of cold single atoms thus created is initialized, gate operated, and readout with other laser beams. Because of its controllability and scalability, the cold-atom quantum computer has been attracting much attention, as one of the most promising candidates in the race to develop quantum-computer hardware. I will describe the characteristics and development trends of the cold-atom hardware, as well as the development of a cold-atom quantum computer at Institute for Molecular Science including the realization of an ultrafast quantum gate using ultrashort laser pulses.
会場: 研究本館 4階 435-437号室 (メイン会場) / via Zoom
イベント公式言語: 英語
7 イベント