Stability of quantum states of finite macroscopic systems

We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which describes the strength of spatial correlations of fluctuations of local observables, and to fluctuations of additive operators. The present theory has many applications, among which we discuss the mechanism of phase transitions in finite systems and quantum computers with a huge number of qubits.Comment: Proceedings of the Japan-Italy Joint Waseda Workshop on "Fundamental Problems in Quantum Mechanics", 27-29 September, 2001, Tokyo, Japan. (Edited by S. Tasaki, to be published from World Scientific, 2002) 7 pages, no figure

HIVの変異と特異的T細胞受容体の分子間相互作用の研究

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 岩本 愛吉, 東京大学教授 渡邉 俊樹, 東京大学教授 東條 有伸, 東京大学教授 川口 寧, 東京大学教授 井上 純一郎, 東京大学准教授 深井 周也University of Tokyo(東京大学

Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm

We analyze quantum computers which perform Shor's factoring algorithm, paying attention to asymptotic properties as the number L of qubits is increased. Using numerical simulations and a general theory of the stabilities of many-body quantum states, we show the following: Anomalously fluctuating states (AFSs), which have anomalously large fluctuations of additive operators, appear in various stages of the computation. For large L, they decohere at anomalously great rates by weak noises that simulate noises in real systems. Decoherence of some of the AFSs is fatal to the results of the computation, whereas decoherence of some of the other AFSs does not have strong influence on the results of the computation. When such a crucial AFS decoheres, the probability of getting the correct computational result is reduced approximately proportional to L^2. The reduction thus becomes anomalously large with increasing L, even when the coupling constant to the noise is rather small. Therefore, quantum computations should be improved in such a way that all AFSs appearing in the algorithms do not decohere at such great rates in the existing noises.Comment: 11 figures. A few discussions were added in verion 2. Version 3 is the SAME as version 2; only errors during the Web-upload were fixed. Version 4 is the publised version, in which several typos are fixed and the reference list is update

Assessment of hydrogen embrittlement behavior in Al-Zn-Mg alloys by multi- modal 3D image-based simulation

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