セミナー

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場所は主に本郷キャンパスの工学部6号館です．

研究室輪講の論文リストはこちら

July 2023

Speaker: 山口瑞樹氏 (東京大学)
Time: July 12 (Wed) 10: 30  (JST)
Place:工学部6号館 セミナー室B (ハイブリッド開催)
Title:  有限次元スピングラスの量子アニーリングにおける横磁場の量子1次相転移の回避の証明
Abstract:
量子アニーリング（QA）は、組合せ最適化問題を解くための手法の1つとして注目されている。QAは、ハミルトニアンをゆっくり動かしながら基底状態を持ち続けることで、自明な構造を持つ量子系から始め、最後に解きたい組合せ最適化問題の解を得る手法である。経験的にはいくつかの組合せ最適化問題で古典的な手法に比べて高速な計算ができる一方、計算量理論の考察から、QAは最も難しいクラスの最適化問題を効率的に解くことはできないことが知られている。量子計算の限界とその物理学的な原因の解明は重要な研究対象であるため、QAの失敗の原因は活発に研究されてきた。いくつかの先行研究[1]は、QAが失敗する多くの事例において、横磁場の量子1次相転移を伴うことを明らかにし、QAの失敗の起源をこの転移であると主張している。一方で、QAの失敗としてこの転移とは異なる要因を挙げる先行研究[2]もある。このように、QAが失敗する理由については、主に数値計算や近似的な解析計算に基づいた議論が交わされていたものの、決定的な回答は得られていなかった。
これに対して私は、QAの一種[3]を用いた有限次元スピングラスの基底状態探索問題において、横磁場の量子1次相転移が起こらないことを厳密に証明した[4]ので、それを紹介する。有限次元スピングラスの基底状態探索は難しい（NP困難な）問題であり、QAを含むいかなる量子計算を用いても効率的な求解はできないと広く信じられている。そのためこの研究結果は、横磁場の量子1次相転移は、難しい組合せ最適化問題におけるQAの失敗の主要因ではないということを強く示唆している。なおこの結果は、短距離相互作用が短距離的で、結合定数が並進対称な分布から生成されるような、任意の有限次元スピングラス系に対して成り立つ、極めて一般性の高い結果である。

[1] T. Jörg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, EPL 89, 40004 (2009).
[2] S. Knysh, Nat Commun 7, 12370 (2016).
[3] Y. Seki and H. Nishimori, Phys. Rev. 85, 051112 (2012).
[4] M. Yamaguchi, N. Shiraishi, and K. Hukushima, arXiv:2307.00791

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Speaker: Jean-Charles Delvenne, UCLouvain (Belgium)
Time: July 7 (Fri) 13: 30  (JST)
Place: Seminar Room B in Building No. 6, Faculty of Engineering
Title:  (Non-)stochastic thermodynamics for computing devices
Abstract:
In this talk I describe several theoretical bounds and illustrate them on how they can place trade-offs on the performance (in terms of dissipation, reliability and speed) of electronic devices and circuits made from them.  These results are consistent with numerical simulations and experimental measurements.  
These results will include, depending on time and interest:
-tight stochastic and deterministic Thermo-Kinetic Relations (including Speed Limits and Uncertainty Principles), quantifying for instance the amount of dissipation needed to write a bit in a memory;
-bounds on the skewness (third moment) of fluctuations, implying for instance that ‘very noisy’ devices must be exhibit non-Gaussian fluctuations;
-nonlinear response theory results, with implication on the reliability of bang-bang bit-writing.
I will also discuss open questions and possible extensions.

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February 2023

Speaker: 和田 凱渡氏 (慶應大学)
Time: February 20 (Mon) 10: 30 (JST)
Place: Zoom
Title: Quantum-enhanced mean value estimation via adaptive measurement
Abstract:
ある量子状態に対してオブザーバブルの平均値 (期待値とも呼ぶ) を推定することは量子計算において本質的に重要な役割を果たす。しかしながら、電子構造問題などの現実的な問題ではこの平均値推定に莫大な時間的コストがかかることが知られており、このため量子計算に期待される量子的な優位性が失われてしまう恐れがある。また、現在の量子計算機に存在するノイズは平均値推定の効率をさらに悪化させてしまうため、ノイズのある環境下でも効率良く平均値を推定する手法の開発が求められている。本セミナーでは量子振幅増幅と測定の適応的最適化を用いることで、ノイズのある環境下であっても理論的な推定限界を達成し、かつ、標準的な量子計算機に実装することが可能な平均値推定の手法について解説する[1]。
[1] K. Wada, K. Fukuchi, N. Yamamoto, arXiv:2210.15624.

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November 2022

Speaker: Zane Rossi (MIT)
Time: November 24 (Thu) 11: 00 (JST)
Place: Zoom
Title: Extending the theory of quantum singular value transformation (QSVT)
Abstract:
Quantum signal processing (QSP) and quantum singular value transformation (QSVT), quantum algorithms for obliviously modifying the singular values of near-arbitrary linear operators embedded in unitary processes, have had recent success in the unification, simplification, and improvement of most known quantum algorithms. QSP and QSVT leverage foundational results in representation theory and algebraic geometry to convert questions in quantum algorithms to questions in functional analysis. In this setting many basic algorithmic properties, including runtime and query complexity, become easier to calculate and optimize over. We present recent substantial elaborations on QSP, including settings with multiple signal oracles, the case of coherently self-embedding QSP protocols, and QSP-like circuit ansätze whose defining Lie group is non-compact. Additionally, we discuss how these results for QSP can be lifted to the multiple-qubit QSVT setting. Surprisingly, many formal properties of QSP/QSVT can be analogized to and proven in these expanded contexts. These results are enabled by the application of powerful, seemingly disparate methods in functional analysis, and provide novel functional interpretations for a wide class of quantum circuits. To ground this work, we also discuss concrete applications to distributed scheduling and proofs of security for quantum cryptographic protocols.

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Speaker: 岩木惇司 氏（東京大学）
Time: November 22 (Tue) 10:00
Place: Zoom
Title: MPSを用いた有限温度のためのランダムサンプリングとその計算複雑性
Abstract:
TPQ法[1]、有限温度ランチョス法[2]に代表されるランダムサンプリングは有限温度の量子多体系にアクセスするための主要な手段の一つである。近年ではMPSを用いたランダムサンプリングが盛んに研究されている[3, 4, 5]。その中で後藤らはランダムサンプリングの性能を定量的に評価する指標としてサンプル効率を定義し、トロッターゲートの有用性を実証した[5]。我々はサンプル効率を解析的に考察することで、サンプル効率と一対一対応する計算量として規格化された分配関数の揺らぎ(Normalized Fluctuation of Partition Function, NFPF)を発見し、それがランダムサンプリングにおける物理量の揺らぎと関係していることを示した[6]。NFPFはある精度で自由エネルギーを計算するために必要なサンプル数と比例しており、計算複雑性の一つの側面を担っていると言える。今回のセミナーでは、NFPFを解析的・数値的に詳しく調べた結果について報告する。相互作用がないハミルトニアンに対しNFPFを解析的に計算したところ、高温と低温でシステムサイズ依存性が変化するという非自明な現象が起こることが分かった。相互作用がある場合でも同様な傾向が見られることを数値計算によって確かめた。今回の結果はエンタングルメントと典型性に新しい進展をもたらすものでもあると考えている。
[1] M. Imada and M. Takahashi, JPSJ 55, 3354 (1986), etc.
[2] J. Jaklic and P. Prelovsek, PRB 49, 5065 (1994).
[3] S. Garnerone and T. R. de Oliveira PRB 87, 214426 (2013), S. Garnerone, PRB 88, 165140 (2013).
[4] A. Iwaki, A. Shimizu, and C. Hotta PRResearch 3, L022015 (2021).
[5] S. Goto, R. Kaneko, and I. Danshita, PRB 104, 045133 (2021).
[6] A. Iwaki and C. Hotta, PRB 106, 094409 (2022).

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October 2022

Speaker:Akira Sone (University of Massachusetts Boston)
Time: October 26 (Wed) 9:00-
Place: Zoom
Title: Computational Phase Transition of Quantum Approximate Optimization Algorithm (QAOA)
Abstract:
Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm on near-term quantum computers, which aims at searching for approximate solutions to discrete optimization problems. The trainability of the QAOA circuit is a crucial task to understand the capability of QAOA for solving hard problems such as SAT. In this work, we connect the transition of trainability of QAOA circuits with the concept of controllability developed quantum optimal control theory. We further discuss the quantum advantage of QAOA in the optimization problems.

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Speaker: Van Vu Tan (Keio University)
Time: October 5 (Wed) 13:00-14:30
Place: Seminar Room C in Building No. 6, Faculty of Engineering
Title: Thermodynamics of optimal transport and speed limits
Abstract:
Optimal transport is a mature field in mathematics and statistics, and its theory concerns the optimal planning and optimal cost of transporting a distribution. In recent years, a deep connection between optimal transport and stochastic thermodynamics has been elucidated in the context of overdamped Langevin dynamics, revealing that the problem of minimizing entropy production can be mapped to the optimal transport problem. This connection has also led to essential applications such as stringent speed limits and the finite-time Landauer principle. In this talk, I will describe an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. Specifically, I will introduce variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases but also generalize it to the quantum case. Notably, they lead to remarkable applications in stochastic and quantum thermodynamics, such as stringent thermodynamic speed limits and the finite-time Landauer principle. In addition, I will also describe a topological speed limit obtained with the optimal transport approach and demonstrate its applications to various dynamics.

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July 2022

Speaker: David Sivak (Simon Fraser University)
Time: July 28 (Thu) 13:00-14:00
Place: Faculty of Science Bldg.4 (Hongo campus), Room 1220 (Not Building No. 6.)
Title: Information thermodynamics of the transition-path ensemble
Abstract:
The reaction coordinate describing a transition between reactant and product is a fundamental concept in the theory of chemical reactions. Within transition-path theory, a quantitative definition of the reaction coordinate is found in the committor, which is the probability that a trajectory initiated from a given microstate first reaches the product before the reactant. Here we develop an information-theoretic origin for the committor and show how selecting transition paths from a long ergodic equilibrium trajectory induces entropy production which exactly equals the information that system dynamics provide about the reactivity of trajectories. This equality of entropy production and dynamical information generation also holds at the level of arbitrary individual coordinates, providing parallel measures of the coordinate’s relevance to the reaction, each of which is maximized by the committor.

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Speaker: Ryuji Takagi (Nanyang Technological University Singapore)
Time: July 20 (Wed.) 13:30-14:30
Place: Seminar Room B in Building No. 6, Faculty of Engineering
Title: Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence 
Abstract:
Quantum resource manipulation may include an ancillary state called a catalyst, which aids the transformation while restoring its original form at the end. Here, we show that allowing correlation among multiple catalysts can offer arbitrary power in the manipulation of quantum coherence. We prove that any state transformation can be accomplished with an arbitrarily small error by covariant operations with catalysts that may create a correlation within them while keeping their marginal states intact. This presents a new type of embezzlement-like phenomenon, in which the resource embezzlement is attributed to the correlation generated among multiple catalysts. We extend our analysis to general resource theories and characterize achievable transformations in relation to their asymptotic state transformations. Our results provide a step toward the complete characterization of the resource transformability in quantum thermodynamics with correlated catalysts.

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Speaker: Léonce Dupays (University of Luxembourg)
Time: July 13 (Wed.) 15:00-16:00
Place: Seminar Room C in Building No. 6, Faculty of Engineering
Title: Fast Quantum control: from open to Many-Body systems. 
Abstract:
The control of quantum systems is of crucial interest, for the fundamental purpose, to explore new states of matter that couldn’t be seen otherwise, or in the context of emergent technologies such as quantum computing. In this talk we will start by discussing control technics known as “Shortcuts to Adiabaticity” [1] that allow engineering trajectories for the quantum state by bypassing the adiabatic approximation. We will discuss the recent extension of those technics to open systems [2, 3], which notably proves useful in the context of quantum thermodynamics. In a second part, we will look at the control of many-body systems and in particular to a technic known as Delta-Kick Cooling, which we generalize to take into account particle interactions and give an exact expression for the kick strength. We show that this cooling protocol is time-optimal. To conclude, we will look at a phenomenon called “Dynamical Fermionization” [4], a hallmark of the interplay between quantum statistics and particle interactions in one-dimensional physics. We will revisit this phenomenon at the light of our previous findings, giving a new glance on the role of interactions during the process.

[1] E. Torrontegui, S. Ibà ñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga,, in Advances In Atomic, Molecular, and Optical Physics (Elsevier, 2013) pp. 117-169.
[2] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu, Phys. Rev. Research 2, 033178 (2020).
[3] S. Alipour, A. Chenu, A. T. Rezakhani, and A. del Campo, Quantum 4, 336 (2020).
[4] L. Dupays, D. C. Spierings, A. M. Steinberg, and A. del Campo, Physical Review Research 3, 10.1103/physrevresearch.3.033261 (2021).

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Speaker: 布能 謙（理研）
Time: September 24 (Thu.) 14:00-15:00
Place: Zoom
Title: コヒーレンスによる流速・散逸のトレードオフの実効的無効化
Abstract:
近年では熱力学不確定性関係をはじめとした、流速と散逸の間の様々なトレードオフ関係が導かれた[1,2]。これらの関係式は、平衡から離れて有限時間で動作する、単一分子デバイスやナノデバイスに対する普遍的な熱力学的制限を与え、大きな注目を集めている。一方で、ゆらぎの熱力学の枠組みを量子系へと拡張する試みが活発に行われているが、熱力学におけるコヒーレンスの効果[3,4]については統一的な理解に至っていない。
　この研究では、熱流と散逸の間のトレードオフ関係に着目し、量子コヒーレンスがどのような影響を与えるかを調べた[5]。その結果、次のような簡単なルールを発見した。
1. 非縮退間のコヒーレンスは、トレードオフを強める。
2. 縮退間のコヒーレンスは、トレードオフを弱める。
さらに、非常に興味深いことに、縮退間のコヒーレンスが十分に強いとき、熱流・散逸トレードオフ関係は実効的に無効化され、摩擦が実効的に0になることを発見した。つまり、マクロなオーダーの熱流を流しつつ、エントロピー生成がミクロなオーダーにとどまる。講演ではこれらの結果と熱機関への応用について述べる。
References:
[1] J. M. Horowitz and T. R. Gingrich, Nat. Phys. 16, 15 (2020).
[2] N. Shiraishi, K. Saito and H. Tasaki, PRL. 117, 190601 (2016).
[3] R. Uzdin, A. Levy, and R. Kosloff, PRX 5, 031044 (2015).
[4] K. Brandner, M. Bauer, and U. Seifert, PRL 119, 170602 (2017).
[5] H. Tajima and K. Funo arXiv: 2004.13412

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July 2020

Speaker: Hiroyasu Tajima (The University of Electro-Communications)
Time: July 27 (Mon.) 14:00-15:00
Place: Zoom
Title: Coherence costs for quantum measurements and operations under conservation laws
Abstract:
The limitation on the quantum information processing imposed by conservation laws has long been an important issue in physics. This issue was first proposed for measurements by Wigner, Araki and Yanase in 1952-1960 [1,2], and for unitary operations by Ozawa in 2002 [2]. In today’s talk, we briefly review the history of the research about operations and measurements under conservation laws, and report our recent results in this field [4,5,6]. In our results, the limitations for quantum measurements and unitary operations imposed by conservation laws are represented as two asymptotic equalities which have the same form. The message of this equality is as follows: “Quantum measurements and unitary operations under a conservation law need quantum fluctuation (i.e. coherence) with respect to the conserved quantity. The minimal sufficient amount of required coherence is inversely proportional to the implementation error and proportional to the degree of violation of the conservation law by the operations and measurements.”
References:
[1]E. P. Wigner, Die Messung quntenmechanischer Operatoren, Z. Phys. 133, 101 (1952).
[2] H. Araki and M. M. Yanase, Measurement of quantum mechanical operators, Phys. Rev.120, 622 (1960).
[3] M. Ozawa, Conservative quantum computing, Phys. Rev. Lett. 89, 057902 (2002).
[4] H. Tajima, N. Shiraishi, and K. Saito, Phys. Rev. Lett. 121, 110403 (2018)
[5] H. Tajima, N. Shiraishi, and K. Saito, arxiv:1906.04076 (2019).
[6] H. Tajima and H. Nagaoka, arXiv:1909.02904 (2019).

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June 2020

Speaker: Nobuyuki Yoshioka (RIKEN)
Time: June 22 (Mon.) 14:00-15:00
Place: Zoom
Title: Neural Networks for Open Quantum Many-body Systems
Abstract:
Recent research have demonstrated that neural networks, powerful tools to perform many machine learning tasks such as image recognition and automated translation, are highly expressive enough to represent quantum many-body states [1]. The dimension-free structure of neural networks are in sharp contrast to the well-known tensor networks which efficiently capture the small entangled states, and hence the machine-learning inspired ansatz is expected to open a new frontier in investigating quantum many-body phenomena. In this virtual seminar, we introduce in particular the restricted Boltzmann machine (RBM) and overview its property as variational ansatz. After showing some previous works in isolated systems, we discuss its application to 1. search stationary states [2] and 2. solving dynamics in open quantum many-body systems.
References:
[1] G. Carleo and M. Troyer, Science 355, 602 (2017).
[2] N. Yoshioka and R. Hamazaki, Phys. Rev. B 99, 214306 (2019).

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May 2020

Speaker: Tomotaka Kuwahara (RIKEN)
Time: May 21 (Thu.) 14:00-15:00
Place: Zoom
Title: Area law of non-critical ground states in 1D long-range interacting systems
Abstract:
The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations in the ground state (i.e., the lowest energy state). Various numerical observations have led to a strong belief that the area law is true for every non-critical phase in short-range interacting systems [1]. The so-called area-law conjecture states that the entanglement entropy is proportional to the surface region of subsystem if the ground state is non-critical (or gapped). However, the area law for long-range interacting systems is still elusive as the long-range interaction results in correlation patterns similar to the ones in critical phases. Here, we show that for generic non-critical one-dimensional ground states, the area law robustly holds without any corrections even under long-range interactions [2]. Our result guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long-range systems, which justifies the density-matrix renormalization algorithm. In the present talk, I will give an overview of the results, and show ideas of the proof if the time allows.
References:
[1] J. Eisert, M. Cramer, and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy,” Rev. Mod. Phys. 82, 277?306 (2010).
[2] T. Kuwahara and K. Saito, “Area law of non-critical ground states in 1d long-range interacting systems,” arXiv preprint arXiv:1908.11547 (2019).

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December 2019

Speaker: Prof. David H. Wolpert (Santa Fe Institute)
Time: Dec. 9 (Mon.) 15:00-16:00
Place: Faculty of Science Bldg.4 (Hongo campus), Room 1320 (Not Building No. 6.)
Title: The stochastic thermodynamics of computation
Abstract:
One of the central concerns of computer science is how the resources needed to perform a given computation depend on that computation. Moreover, one of the major resource requirements of computers-ranging from biological cells to human brains to high-performance (engineered) computers-is the energy used to run them, i.e. the thermodynamic costs of running them.Those thermodynamic costs of performing a computation have been a long-standing focus of research in physics, going back (at least) to the early work of Landauer and colleagues. However, one of the most prominent aspects of computers is that they are inherently non-equilibrium systems. Unfortunately, the research by Landauer and co-workers on the thermodynamics of computation was done when non-equilibrium statistical physics was still in its infancy, severely limiting the scope and formal detail of their analyses.The recent breakthroughs in non-equilibrium statistical physics hold the promise of allowing us to go beyond those limitations. Here I present some initial results along these lines, concerning the entropic costs of running (loop-free) digital circuits and Turing machines. These results reveal new, challenging engineering problems for how to design computers to have minimal thermodynamic costs. They also allow us to start to combine computer science theory and stochastic thermodynamics at a foundational level, thereby expanding both.
※このセミナーは、東京大学 生物普遍性研究機構 と 新学術領域「情報物理学でひもとく生命の秩序と設計原理」との共催です

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November 2019

Speaker: Prof. Erik Aurell (KTH)
Time: Nov. 5 (Tue.) 14:00-15:00
Place: Seminar Room C in Building No. 6, Faculty of Engineering
Title: Open quantum systems interacting with harmonic and anharmonic baths
Abstract:
The Feynman-Vernon approach to open quantum systems is to express the evolution of the reduced density matrix of the system as a double path integral, where one path (“forward path”) comes from the unitary U acting from the left, and one path (“backward path”) comes from the inverse unitary U† acting from the right. In the open systems context the Feynman-Vernon approach is closely related to the Keldysh theory, where the forward-backward paths correspond to the positive/negative parts of the Keldysh contour.I will first present an alternative derivation of Feynman-Vernon theory by analyzing the von-Neumann-Liouville equation as a linear evolution law in the space of Hermitian operators. Results on full counting statistics (generating functions of energy changes in one or several baths), that are somewhat complicated to obtain in the path integral language, then emerge in a much simpler way.I will then look at systems interacting linearly with baths that are not harmonic, but instead characterized by an expansion in cumulants. Every non-zero cumulant of certain environment correlation functions then gives a kernel in a higher-order term in the Feynman-Vernon action, and I will discuss a few of these higher-order terms.This talks is partly work in progress; results so far are presented in joint paper with Ryoichi Kawai and Ketan Goyal, available as arXiv:1907.02671.

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October 2019

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May 2019

Speaker: Zongping Gong (University of Tokyo)
Time: May 20 (Mon.) 14:00-15:00
Place: 工学部6号館 3F セミナー室A,D
Title: Topological Phases of Non-Hermitian Systems
Abstract:
Topological insulators and superconductors described by gapped, Hermitian free-fermion Hamiltonians with certain symmetries are well understood and their systematic classifications have been achieved [1]. On the other hand, recent experimental developments on controlling dissipation have enabled us to flexibly engineer non-Hermitian Hamiltonians in open classical and quantum systems [2], which may exhibit unique topological properties with no Hermitian counterparts [3]. In this seminar, we address the issue on classifying free-fermion-like non-Hermitian topological phases [4]. We generalize the notion of gap and introduce a coherent framework within which we figure out the periodic table for all the non-Hermitian systems with Altland-Zirnbauer symmetries in all dimensions. In particular, we find that a one-dimensional non-Hermitian lattice can be topologically nontrivial even without symmetry protection (class A), reminiscent of the quantum Hall insulator in Hermitian systems. The primary example is the Hatano-Nelson model [5], in which the Anderson transition can be understood from a topological perspective. We also provide some examples in other symmetry classes in zero and one dimensions.
References:
[1] C.-K. Chiu, J. C. Y. Teo, A. Schnyder, and S. Ryu, Rev. Mod. Phys. 88, 035005 (2016).
[2] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Nat. Phys. 14, 11 (2018).
[3] M. A. Bandres and M. Segev, Physics 11, 96 (2018).
[4] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018).
[5] N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996).

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Speaker: Kohei Kawabata (University of Tokyo)
Time: May 20 (Mon.) 15:30-16:30
Place: 工学部6号館 3F セミナー室A,D
Title: Symmetry and Topology in Non-Hermitian Physics
Abstract:
Non-Hermiticity enriches topological phases beyond the existing framework for Hermitian topological phases. Here we develop a general theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies and unifies the celebrated Altland-Zirnbauer symmetry for insulators and superconductors, leading to 38-fold symmetry instead of the 10-fold one. Moreover, we reveal that two types of energy gaps are relevant for non-Hermitian systems due to the complex nature of energy spectra, both of which constitute non-Hermitian topology. Based on these fundamental insights in non-Hermitian physics, we completely classify topological phases of non-Hermitian insulators and superconductors, as well as semimetals that support exceptional points. Our work paves the way toward unique phenomena and functionalities that emerge from the interplay of non-Hermiticity and topology, such as symmetry-protected topological lasers and non-Hermitian topological quantum computation.
References:
[1] K. Kawabata, S. Higashikawa, Z. Gong, Y. Ashida, and M. Ueda, Nat. Commun. 10, 297 (2019).
[2] K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, arXiv: 1812.09133.
[3] K. Kawabata*, T. Bessho*, and M. Sato, arXiv: 1902.08479 [*equal contributions].

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April 2019

Speaker: Sreekanth K Manikandan (Stockholm University)
Time: April 26 (Fri) 13:30-14:30
Place: 工学部6号館 3F セミナー室A,D
Title: Efficiency fluctuations in microscopic machines
Abstract:
Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a “universal theory of efficiency fluctuations” at long times, for machines with a finite state space, was developed by Verley et al. [Nat. Commun. 5, 4721 (2014); Phys. Rev. E 90, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the “universal features” and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two nontrivial models of colloidal engines.
Reference: S. K. Manikandan et al., Phys. Rev. Lett. 122, 140601 (2019).

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December 2018

Speaker: Prof. Simone Pigolotti (Okinawa Institute of Science and Technology)
Time: December 18 (Tue) 14:00-15:00
Place: 工学部6号館 3F セミナー室B
Title: Generic Properties of Stochastic Entropy Production
Abstract:
Entropy production is a central quantity to characterize non-equilibrium mesoscopic systems. Recently, new (and surprising) generic properties of entropy production have been discovered. It is unclear if there are even more generic properties of entropy production, and how these properties are related. In this talk, I will present a general theory for non-equilibrium physical systems described by overdamped Langevin equations. For these system, entropy production evolves according to a simple stochastic differential equation. At steady state, a random time transformation maps this evolution into a model-independent form. This implies several generic properties for the entropy production, such as a finite-time uncertainty equality, universal distributions of the infimum and the supremum before the infimum, and universal distribution of the number of zero-crossings. In the second part of my talk I will discuss how the arcsine law, a general result in the theory of Brownian motion, applies to currents in stochastic thermodynamics.

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April 2018

Speaker: 松本啓史氏（国立情報学研究所）
Time: December 18 (Tue) 14:00-15:00
Place: 工学部6号館 3F セミナー室B
Title: Generic Properties of Stochastic Entropy Production
Abstract:
確率分布のペアの変換可能性の条件を、近年、Horodecki -OppenheimらがThemo Majorizationと名付けた。これらは実は数理物理学や数理統計学で古くから知られている。加えて、より一般的な変換に誤差を許したものが知られている。本講演では、この条件を用いて漸近的な変換可能性がdivergence rateという量で特徴づけられることを示す。この量は情報スペクトルの理論で用いられ、エルゴード的な場合はKL divergence (相対エントロピー)と一致する。 さらに一歩進んで、量子論の場合にも全く同様の条件が成立することも示す。この漸近論においては、独立性やエルゴード性などは課さないし、システムのサイズが大きくなる事も仮定しない。 講演の中で、divergence rateや divergenceの特徴づけにも言及する。

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February 2018

Speaker: 塩崎謙氏（理研）
Time: 2月20日(火) 13:00-17:00 & 21日(水) 13:00-17:00
Place: 工学部6号館 3F セミナー室A/D
Title: バンド理論におけるK理論入門
Abstract:
固体結晶中の電子状態は，Bloch状態と呼ばれる波数空間上の波動関数によって記述される．与えられた対称性のもと，ある電子状態 A と別の電子状態 B が連続変形により繋がるかどうかを考えよう．明らかに，ある対称点 k における小群（波数 k を固定する対称性群の部分群）の表現が異なれば A と B は繋がらない．対称点における既約表現の数は連続変形をしても変わらない性質であり，トポロジカル不変量の一種である．では，全ての対称点における小群の表現が同一であれば２つの電子状態が連続的に繋がるかというと，一般には可能ではない．なぜなら，線，面，体積など波数空間内のより高次元の領域において定義されるトポロジカル不変量が存在するからである．例えばChern数はよく知られた例である．
　トポロジカル結晶絶縁体・超伝導体，あるいは半金属，ギャップレス超伝導の分類は，トポロジカル不変量の分類と言ってもよい．与えられた対称性のもと，波数空間において定義されるトポロジカル不変量を全て挙げよ，という問いである．磁気空間群は1651種類存在するが，数十通りの対称性を除き，トポロジカル不変量の分類は未解決である．未知のトポロジカル不変量が多く残されているだろう．
　K理論は，トポロジカル不変量の存在/非存在の系統的な計算手法を提供する．本セミナーでは，K理論の系統的な計算手法について，バンド理論の言葉を用いて解説する．

※桂研（東大理物）・渡辺研（物工）と合同で開催します．

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November 2017

Speaker: Dr. Hao Ge (Peking University, China)
Time: November 24 (Fri) 15:00-16:00
Place: 工学部6号館 3F セミナー室C
Title: Nonequilibrium landscape theory of chemical reaction systems: from stochastic thermodynamics to single-cell biology
Abstract:
Due to the advance of single-molecule techniques, stochastic modeling and computation become more and more useful and popular recently. I will discuss two related theories. One is a unifying mathematical theory of nonequilibrium thermodynamics of chemical reaction systems. A generalized macroscopic free energy called landscape emerges and satisfies a balance equation. The balance equation is valid generally in isothermal driven systems, which is actually an unknown form of the second law. This framework is totally based on the internal kinetics of the system, without knowing every details of the interaction between internal kinetics that we can measure in most experiments with all the surroundings. The other is the landscape theory and a new rate formula for the phenotype transition in an intermediate scenario of a single cell, which is more general and more close to the reality of living cells. The new rate formula can explain a “noise enhancer” therapy for HIV reported recently, which motivated a future project of us.

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Speaker: Dr. Raphael Chetrite (CNRS, France)
Time: November 13 (Mon) 15:00-16:00
Place: 工学部6号館 3F セミナー室B
Title: On Gibbs-Shannon Entropy
Abstract: This talk will be focus on the question of the physical contents of the Gibbs-Shannon entropy outside equilibrium. Article : Gavrilov-Chetrite-Bechhoeffer : Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs-Shannon. PNAS (2017)

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July ＆ August 2017

Speaker: 中田芳史氏（東京大学）
Time: July 31 (Mon) 13:00-17:00 August 1 (Tue)　13:00-17:00
Place: 工学部6号館 3F セミナー室B
Title: 量子ランダムネス ーランダムダイナミクスがもたらす複雑性の極限における物理ー
Abstract:
極めて強い複雑性を持つ量子多体系ではしばしば非直感的な現象が起こることが知られている。例えば、孤立系での熱緩和現象やブラックホールの情報パラドクス、scramblingやそれに付随する量子双対性などはその一例であり、近年、活発に研究が行われている。このような現象を理解する鍵になると考えられているのが、量子ランダムネス(Haarランダムユニタリ）と、その近似である量子疑似ランダムネス（ユニタリ・デザイン）である。量子ランダムネスは古くはランダム行列理論に端を発する概念であるが、近年の量子情報科学の発展と共にその重要性が再認識されるようになり、量子疑似ランダムネスの理論へと拡張され、現在は量子情報科学のみならず、高エネルギー物理、強相関系物理などの新発展に繋がるアイデアではないかと期待されている。
　本セミナーでは、量子ランダムネス（Haarランダムユニタリ）および量子疑似ランダムネス（ユニタリ・デザイン）について、その基礎から物理への応用までを分かりやすく解説したいと考えている。現在の予定では、ランダムユニタリの数理として「測度の集中化現象」や「large deviation bound」、「ユニタリデザインの生成方法」など、また、物理への応用としては「canonical typicality」や「one-shot decoupling」、「ブラックホールの情報パラドクスとscrambling」などについて解説するつもりである。セミナーは板書で行い、「広く浅く」ではなく「（使いたくなったら）使えるようになること」を目指して、時間が許す限りで上記のトピックに関して比較的詳細に解説する予定である。

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May 2017

Speaker: 白石直人氏（慶應）
Time: May 31 (Wed) 14:00-16:00
Place: 工学部6号館 3F セミナー室C
Title: Power and Efficiency: a fundamental problem
Abstract:
Efficiency and power (extracted work per unit time) are two important quantities to characterize heat engines. It has been believed that these two quantities are complementary, i.e., an engine with high efficiency inevitably works slowly. However, this belief has not yet been proven, and even worse, maybe surprisingly, whether finite power and the maximum efficiency (Carnot efficiency) are compatible has still been an open problem. We note that conventional thermodynamics does not prohibit the compatibility because speed of the opera tion is out of the scope of thermodynamics, and linear irreversible thermodynamics neither prohibit even in the linear response regime if time-reversal symmetry is broken [1]. Triggered by the latter work, many works have investigated the relation between finite power and the Carnot efficiency on the basis of specific models mostly within the linear response regime [2-9]. Although some papers have proposed abstract ideas for the coexistence [2-4], all analyses on concrete models in the linear response regime have shown that finite power and the Carnot efficiency are incompatible within these models [5-9]. In spite of these intensive efforts, a general and decisive result on power and efficiency has completely been missing.

In this talk, we will derive universal trade-off relations between power and efficiency, and as their corollary we will give a no-go theorem which prohibits the coexistence of finite power and the Carnot efficiency. For the case of Markovian engines, inspired by the partial entropy production [10], or the idea of decomposition of entropy production, we first derive a trade-off inequality between heat exchange and entropy production rate. Using this, we easily show the inequality between power and efficiency [11]. For the case of non-Markovian engines, with the aid of the Lieb-Robinson bound [12], we derive the inequality between the speed of operation and efficiency [13].

[1] G. Benenti, K. Saito, and G. Casati, Phys. Rev. Lett. 106, 230602 (2011).
[2] M. Campisi and R. Fazio, Nature Commun. 7, 11895 (2016).
[3] M. Ponmurugan, arXiv:1604.01912 (2016).
[4] M. Polettini, M. Esposito, arXiv:1611.08192 (2016).
[5] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. Lett. 110, 070603 (2013).
[6] V. Balachandran, G. Benenti, and G. Casati, Phys. Rev. B 87, 165419 (2013).
[7] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. X 5, 031019 (2015).
[8] K. Proesmans and C. Van den Broeck, Phys. Rev. Lett. 115, 090601 (2015).
[9] K. Yamamoto, O. Entin-Wohlman, A. Aharony, and N. Hatano, Phys. Rev. B 94, 121402 (2016).
[10] N. Shiraishi and T. Sagawa, Phys. Rev. E 91, 012130 (2015).
[11] N. Shiraishi, K. Saito, and H. Tasaki, Phys. Rev. Lett. 17, 190601 (2016).
[12] E. Lieb and D. Robinson, Commun. Math. Phys. 28, 251 (1972).
[13] N. Shiraishi and H. Tajima, arXiv:1701.01914 (2017).

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Speaker: 田島裕康氏（理研）
Time: May 31 (Wed) 16:00-18:00
Place: 工学部6号館 3F セミナー室C
Title: Large Deviation implies First and Second Laws of Thermodynamics
Abstract:
To reconstruct thermodynamics based on the microscopic laws is one of the most important unfulfilled goals of statistical physics. Recently, with using quantum informational techniques, many researches have tried to reconstruct and/or expand the second law of thermodynamics [1-3]. However, the following open problems remain: 1. The results are based on strong assumptions about thermodynamic systems and heat baths, e.g., the i.i.d. feature and/or the number of degeneracy. These assumptions are not necessarily satisfied by actual thermodynamic systems. 2. The analysis is mainly limited to cases isothermal case, in which the temperatures of the baths do not change. Adiabatic processes which changes temperatures of all systems radically are not clarified.

Here, we show that the first law and the second law for adiabatic processes are derived from an assumption that “probability distributions of energy in Gibbs states satisfy large deviation, which is widely accepted as a property of thermodynamic equilibrium states [4]. We define an adiabatic transformation as a randomized energy-preserving unitary transformations on the many-body systems and the work storage. As the second law, we show that an adiabatic transformation from a set of Gibbs states to another set of Gibbs states is possible if and only if the regularized von Neumann entropy becomes large. As the first law, we show that the energy loss of the thermodynamic systems during the adiabatic transformation is stored in the work storage as “work,” in the following meaning:
(i) the energy of the work storage takes certain values macroscopically, in the initial state and the final state.
(ii) the entropy of the work storage in the final state is macroscopically equal to the entropy of the initial state.
As corollaries, our results give other forms of the first and second laws, e.g., the principle of maximum work and the first law for the isothermal processes.

[1] M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).
[2] F. G. S. L. Brandao, M. Horodeck, N. H. Y. Ng, J. Oppenheim, and S. Wehner, PNAS, 112,3215(2015).
[3] P. Skrzypczyk, A. J. Short and S. Popescu, Nature Communications 5, 4185, (2014).
[4] H. Tajima, E. Wakakuwa and T. Ogawa, arXiv:1611.06614 (2016).

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October 2016

Speaker: Dr. David Lacoste (ESPCI)
Time: October 26 (Wed) 15:00-16:00
Place: 工学部6号館 3F セミナー室A/B
Title: Kinetics and thermodynamics of reversible polymerization
Abstract:
Biological systems make extensive use of reversible polymerization: peptides are assembled from amino-acids, actin filaments are assembled from G-actin and glucans (carbohydrates) are assembled from monosaccharides. In this talk, inspired by a recent experimental study on the metabolism of glucans, we study the self-assembly of such polymers from the point of view of non-equilibrium thermodynamics. We first consider a closed system in which polymers dynamically evolve towards equilibrium where detailed balance is satisfied and the entropy is maximum. We then consider open systems, in which the polymers are in contact with chemostats, characterized by fixed concentrations of polymers of a given length. In accordance to a general theoretical result, we find new dynamic regimes when the number of chemostats is larger than the number of conservation laws of the chemical network. We will then discuss extensions of this framework for the self-assembly of polymers which carry information in their sequence.

REFERENCES:
[1] Kinetics and thermodynamics of reversible polymerization in closed systems, S. Lahiri, Y. Wang, M. Esposito, and D. Lacoste, New J. Phys., 17, 085008 (2015).
[2] Glucans monomer exchange dynamics as an open chemical network, R. Rao, D. Lacoste and M. Esposito, J. Chem. Phys., 143, 244903 (2015).

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March 2016

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Speaker: Antony Milne (Imperial College London)
Time: March 1 (Tue) 15:30-16:30
Place: 工学部6号館 3F セミナー室C
Title: Visualising two-qubit correlations using quantum steering ellipsoids
Abstract:
The quantum steering ellipsoid formalism naturally extends the Bloch vector picture to provide a visualisation of two-qubit systems. If Alice and Bob share an entangled state then a local measurement by Bob steers Alice’s Bloch vector; given all possible measurements by Bob, the set of states to which Alice can be steered forms her steering ellipsoid inside the Bloch sphere. This gives us a novel geometric perspective on a number of quantum correlation measures such as entanglement, CHSH nonlocality and singlet fraction. In particular, by analysing a tripartite scenario we find that steering ellipsoid volumes obey a simple monogamy relation from which one can derive the well-known CKW (Coffman-Kundu-Wootters) inequality for the monogamy of entanglement. Remarkably, we can also use steering ellipsoids to derive some highly non-trivial results in classical Euclidean geometry, extending Euler’s inequality for the circumradius and inradius of a triangle.

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February 2016

Speaker: Prof. Jean-Charles Delvenne (Université catholique de Louvain)
Time: February 12 (Fri) 10:00-11:00
Place: 工学部6号館 3F セミナー室C
Title: Entropy reduction and energy extraction in controlled systems
Abstract:
We will discuss the possibility to extract energy and reduce entropy from a dynamical system thanks to feedback control, ie from the exploitation of observations on the system. In particular we will re-derive the Kalman filter from an information-theoretic perspective and discuss the impact of discrete-time dynamics, as opposed to continuous-time dynamics, on the efficiency of extraction with respect to information contained in the observation. We will also exhibit the simplest class of systems where Carnot’s theorem, an open-loop statement, can be formulated and proved, leaving the possibility for feedback and finite-time extensions.

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October 2015

Speaker: 布能謙氏（東京大学）
Time: October 19 (Mon) 13:00-15:00
Place: 工学部6号館 3F セミナー室B
Title: Work fluctuation-dissipation trade-off in heat engines
Abstract:
Recent developments of nonequilibrium statistical mechanics allow us to formulate thermodynamic relations for arbitrary nonequilibrium initial and final states [1]. They can be used to quantify thermodynamic costs of information encoding and erasure processes as well as to quantify the extractable work from information heat engines. In those general situations, reducing energy dissipation allows us to increase the efficiency of a given thermodynamic task, and reducing work fluctuation allows us to prepare an exact amount of work needed to complete the task, or to extract a deterministic amount of work from the system. Thus, suppressing both work fluctuation and energy dissipation is vital to control nanosystems that work at the level of thermal fluctuations. Previous studies have explored the regime around vanishing work fluctuations by using techniques of quantum information theory, known as the single-shot statistical mechanics [2, 3] and the regime around vanishing energy dissipation by using the fluctuation-dissipation relation and the second law of thermodynamics [1]. However, the single-shot statistical mechanics and the fluctuation-dissipation relation cannot be applied to the intermediate regime in which work fluctuation and energy dissipation take finite values. We report the trade-off relation between work fluctuation and energy dissipation for the entire regime, where the lower bound is quantified by the measure of distance between the nonequilibrium distribution and the equilibrium distribution [4]. We propose a method to construct explicit protocols that achieve the lower bound of the trade-off relation. An application of the trade-off relation to information heat engines is carried out, including a numerical simulation to test the trade-off relation. The seminar is presented using chalk on a blackboard. Details of the proof of the trade-off relation are presented in the seminar.

[1] M. Esposito and C. Van den Broeck, Euro. Phys. Lett. 95, 40004 (2011).
[2] J. Aberg, Nat. Commun. 4, 1925 (2013).
[3] M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).
[4] K. Funo and M. Ueda, arXiv:1508.04042.

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August 2015

Speaker: Prof. Cheng-Hung Chang (National Chiao Tung University)
Time: August 27 (Thu) 13:30-14:30
Place: 工学部6号館 207号室
Title: Lumping fluctuations and noises on hierarchical kinetic networks
Abstract:
In this work, we introduce stochasticity into the traditional lumping analysis, extend the lumping process from the rate equation to the chemical master equation and the stochastic differential equation, and derive the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The result provides a theoretical basis for the legitimate use of low-dimensional network models in the studies of macromolecular fluctuations and related biological functions. More widely, it reveals which stochastic features different levels of contracted transition networks will or should exhibit, shedding light on the fluctuations of hierarchical networks in systems biology, chemical reactions, and general complex systems.

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Speaker: Prof. Christian Van den Broeck (Universiteit Hasselt)
Time: August 24 (Mon) 10:30-11:30
Place: Faculty of Science Bldg.1, Room 913 （※理物の上田研と合同で，場所は理学部1号館です．）
Title: Onsager symmetry in periodically driven systems
Abstract:
We show that — while asymmetric Onsager matrices may appear in a system under time-asymmetric periodic driving — the matrix necessarily converges to a symmetric matrix in the limit of zero dissipation. In particular, reversible efficiency can not be reached at finite power [1].
[1] Karel Proesmans & Christian Van den Broeck, arXiv:1507.00841.

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June 2015

Speaker: 田中宗氏 (早稲田大学)
Time: June 29 (Mon) 14:00-15:00
Place: 工学部6号館 3F セミナー室C
Title: 次世代計算技術「量子アニーリング」が拓く機械学習の新展開
Abstract:
　2011年５月「世界初の商用量子コンピュータ」D-Wave が、D-Wave Systems Inc. より発表された[1]。D-Wave は量子アニーリングと呼ばれる方式を採用した量子計算デバイスである。量子アニーリングは、1998年に門脇、西森によって理論提案がなされた日本発の計算技術である[2]。量子アニーリングは、量子揺らぎに駆動された自己組織化現象を用いた計算技術と考えることもできる方法である。物理現象を積極的に活かした計算手法であり、物理学と情報科学の境界領域に位置づけられる研究の一例である。 　量子アニーリングは、組合せ最適化問題に対する最適解を効率良く得ることが期待されている汎用的な計算技術である。組合せ最適化問題は、最適解を得ることが難しい問題とされている。適用範囲は極めて広範に渡っている。一例として、化学物質の安定構造探索や、集積回路網や通信回路網の最適設計などがある。また機械学習の抱える課題の一つとして、最適化問題を解くということが挙げられる。これらのことから、組合せ最適化問題を効率よく得る計算技術の開発が強く求められている。
　我々は2009年から量子アニーリングの本格的活用を視野に入れた研究として、機械学習の一手法であるクラスタ分析に対する量子アニーリングの有用性を検討してきた[3-7]。クラスタ分析とは、膨大なデータを潜在的意味によって分類する方法である。我々は、論文データベースなどの実データを用いた本格的な数値実験を行った。量子モンテカルロ法を用いた擬似シミュレーションの結果、従来の手法であるシミュレーテッドアニーリングに比べ、量子アニーリングが有用であることを示唆する結果を得た。
　本講演ではまず、量子アニーリングの基礎の紹介を行う[8,9]。ここでは量子アニーリングの原理に加え、D-Wave の内部構造に関する解説を行う。D-Wave の内部構造の説明を通じ、量子アニーリングの実験的実装法の概観を行う。D-Wave の内部構造は、超伝導エレクトロニクスのこれまでの蓄積[10,11]が活用されている。次に、我々の研究である、量子アニーリングを用いたクラスタ分析について紹介する。最後に時間の許す限り、量子アニーリングをはじめとしたイジングモデル型量子情報処理に関する研究の今後の展開に関して述べる。 　本講演で発表する内容の一部は、佐藤一誠博士(東京大学情報基盤センター、さきがけ研究員)、栗原賢一博士(グーグル株式会社)、中川裕志教授(東京大学情報基盤センター)、宮下精二教授(東京大学大学院理学系研究科物理学専攻)との共同研究である。

[1] D-Wave Systems Inc. website, http://www.dwavesys.com/
[2] T. Kadowaki and H. Nishimori, Phys. Rev. E, Vol. 58, p. 5355 (1998).
[3] K. Kurihara, S. Tanaka, and S. Miyashita, Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI2009).
[4] I. Sato, K. Kurihara, S. Tanaka, H. Nakagawa, and S. Miyashita, Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI2009).
[5] I. Sato, S. Tanaka, K. Kurihara, S. Miyashita, and H. Nakagawa, Neurocomputing, Vol. 121, p. 523 (2013).
[6] http://www.shutanaka.com/papers_files/ShuTanaka_DEXSMI_10.pdf [7] 次のサイトの slideshare に幾つかのプレゼンテーション形式ファイルを掲載しています　http://www.shutanaka.com/study.html
[8] 西森秀稔教授(東京工業大学)の次のwebサイト　http://www.stat.phys.titech.ac.jp/~nishimori/QA/q-annealing.html
[9] S. Tanaka and R. Tamura, “Quantum Annealing from the Viewpoint of Statistical Physics, Condensed Matter Physics, and Computational Physics” in “Lectures on Quantum Computing, Thermodynamics and Statistical Physics”, (World Scientific, 2012) [プレプリントは、arXiv:1204.2907 にあります].
[10] Y. Nakamura, Y. A. Pashkin, J. S. Tsai, Nature, Vol. 398, p. 786 (1999).
[11] M. Hosoya, W. Hioe, J. Casas, R. Kamikawai, Y. Harada, Y. Wada, H. Nakane, R. Suda, and E. Goto, Applied Superconductivity, IEEE Transactions, Vol. 1, p. 77 (1991).

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February 2015

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October 2014

Speaker: 森前智行氏（群馬大学）
Time: October 3 (Fri) 10:30-11:30
Place: Bldg.16, #827
Title: Highly-mixed quantum computingモデルの古典シミレート不可能性について
Abstract:
量子計算においては通常は、入力状態は完全に純粋な状態である。しかし、入力状態として、非常にデコヒアーした（混合された）状態を用いたらどうなるであろうか？直感的には、もはや量子計算機にはなっておらず、古典計算機で簡単にシミレートできそうである。（実際、もし入力が完全混合状態であれば、トリビアルにシミレートできる。）しかし驚くことに、入力が１キュービットだけ純粋状態でそれ以外が完全混合状態であるような量子計算モデルは、現在古典計算機では効率的に解く方法が知られていないいくつかの問題を効率的に解く事ができるのである[1]。（たとえば、結び目不変量であるJones多項式の計算など[2])この、１キュービットのみ純粋状態でそれ以外が完全混合状態であるような入力を持つ量子計算のモデルはone-clean qubit modelあるいは（歴史上の理由により） DQC1 modelと呼ばれており[1]、もともとはNMR量子計算のモデルとして提案された。

DQC1モデルは本当に古典計算機よりも速いのだろうか？単に「これまで古典計算機で効率的に解く方法が知られていない問題を効率的に解くことができる」というだけでは、将来誰かが古典計算機で効率的に解く方法を見つけるかもしれない。つまり、DQC1モデルが真に古典計算機より速いのかはopen problemであった。我々は、DQC1モデルにおいて出力の３キュービットを測定する場合、その出力確率分布を古典計算機で効率的にサンプルすることは多項式階層が第三レベルで崩壊しない限り不可能であることを示した[3]。多項式階層とは、P,NPを一般化したものであり、崩壊しないだろうと計算機科学では強く信じられている。(量子計算機は古典計算機と同じである、BPP=BQP、というものよりも起こりえないだろうと強く信じられている。)つまり、DQC1モデルが古典計算機より速いだろうという長年のconjectureに対し、初めて、計算量理論に基づいた証拠を得ることができたのである。

DQC1モデルは古典計算機よりも高速であるが、ユニバーサル量子計算機（つまり任意の量子計算ができる量子計算機）ではない。このように、ユニバーサル量子計算機ではないが、古典計算機より速い（速そう）なモデルは近年注目を集めている。ユニバーサル量子計算機を作るのは大変であるが、わざわざユニバーサル量子計算機をつくらなくても、古典計算機を上回るなんらかの性能が得られるのであれば、実験的にもうれしいからである。DQC1モデル以外にもこのような例として、相互作用無しボソン量子計算機（Boson sampling）[4]、交換するゲートのみの量子計算機（IQP model）[5,6]などがある。本講演ではこれらについても軽く触れる予定である。

[1] E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998).
[2] P. W. Shor and S. P. Jordan, Quant. Inf. Comput. 8, 681 (2008).
[3] T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014)
[4] S. Aaronson and A. Arkhipov, Theory of Computing 9, 143 (2013).
[5] M. J. Bremner, R. Jozsa, and D. J. Shepherd, Proc. R. Soc. A 467, 2126 (2011).
[6] K. Fujii and T. Morimae, arXiv:1311.2128

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July 2014

Speaker: Max F. Frenzel (Imperial College London)
Time: July 18 (Fri) 10:30-11:30
Place: Bldg.3, #119
Title: Pure Qubit Work Extraction Revisited
Abstract:
Many work extraction or information erasure processes in the literature involve the raising and lowering of energy levels via external fields. But even if the actual system is treated quantum mechanically, the field is assumed to be classical and of infinite strength, hence not developing any correlations with the system or experiencing back-actions. We extend these considerations to a fully quantum mechanical treatment, by studying a spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-l system, which models an external field. With this concrete model together with a bosonic thermal bath, we analyse the back-action a finite-size field suffers during a quantum-mechanical work extraction process, the effect this has on the extractable work, and highlight a range of assumptions commonly made when considering such processes. The well-known semi-classical treatment of work extraction from a pure qubit predicts a maximum extractable work W = kT log 2 for a quasi-static process. We show that this holds as a strict upper bound in the fully quantum mechanical case, and is only attained in the classical limit. (arXiv:1406.3937)

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June 2014

Speaker: 大関真之氏（京都大学）
Time: June 10 (Tue) 15:30-16:30
Place: Bldg.16, #827
Title: スピングラス理論と量子誤り訂正符号
Abstract:
不純物を含む磁性体の中で強い興味が持たれている対象がスピングラスである．その物性の理解のために発展したスピングラス理論は、情報科学の諸問題の性質を明らかにする情報統計力学や最適化問題との接点から計算アルゴリズムの開発やその計算量評価等、様々な展開を見せている．本講演では、2000年代始めから発展し始めた量子誤り訂正符号の一つ表面符号とスピングラス理論の接点に焦点をあてる．スピングラスの中でも有限次元のスピングラス模型の解析は難解を極めるものであり、系統的解析手法は西森のゲージ理論以降目覚ましい発展を遂げたものは数少ない．そのような現況のなかで、分配関数の対称性に注目した双対変換、及びそれに関連したグラフ多項式の性質を利用した解析手法が発展しつつある．この手法は表面符号の性能評価を非常に精度よく行うことが出来る．講演では、それらの結果について紹介する．それを更に発展させて、表面符号の誤り訂正にどう生かすかを含め、今後の展開についても議論したい．

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Speaker: 藤井啓祐氏（京都大学）
Time: June 10 (Tue) 14:30-15:30
Place: Bldg.16, #827
Title: 量子ダイナミクスの量子・古典境界
Abstract:
量子系はそれを取り巻く環境系との相互作用によるデコヒーレンスによって古典的な系になるとよく言われる．本研究では，デコヒーレンス下にある量子系が古典計算機によって効率よく模倣が出来るか否かという観点から，量子・古典の境界の線引きを行う．また，これを導出するために用いる２つの量子情報的手法，模倣が可能であることを構成論的に示す方法，そして計算量的な仮定に基づいて模倣が不可能であることを示す方法について解説を行い，その応用例も紹介する．このような手法はより効率よく量子系を記述するため，そして実験的に実現されたダイナミクス（量子シミュレーション等）に対する量子性を保障することに用いる事が出来る．

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November & December 2013

Speaker: 渡辺優氏（京都大学）
Time: November 19 (Tue) 14:00-18:00　November 26 (Tue) 14:00-18:00　December 10 (Tue) 14:00-16:00　December 17 (Tue) 14:00-18:00
Place: Bldg.3, #119
Title: 量子エントロピーと量子Fisher情報量の数理（全４回）
Abstract:
本セミナーシリーズでは、量子相対エントロピーおよび量子Fisher情報量の背後にある数学的な定理を紹介する。また、時間があれば、そこから導かれるハイゼンベルグの不確定性関係についても紹介する。

第１回: 11月19日(火) 14:00-18:00
「古典相対エントロピーとFisher情報量の復習、作用素単調関数(operator monotone)」
本セミナーシリーズの主題である量子相対エントロピーや量子Fisher情報量を紹介する前に、まず、古典的な相対エントロピーおよびFisher情報量について紹介する。また、量子系のエントロピーや情報量を語る上でキーとなる作用素単調関数(operator monotone)について紹介する。

第２回：11月26日(火) 14:00-18:00
「量子相対エントロピーとその単調性」
2つの異なる量子状態の’距離’を特徴付ける量子相対エントロピーについて、特に、その単調性を中心に紹介する。

第３回: 12月10日(火) 14:00-16:00
「量子Fisher情報量とその単調性」
量子Fisher情報量は量子状態空間における単調計量として定義される。すなわち、2つの量子状態の差が小さい場合の距離を与える。量子Fisher情報量について、その単調性を紹介し、さらに、そこから示される量子Cramer-Rao不等式などを紹介し、量子推定理論との関係を示していく。

第４回: 12月17日(火) 14:00-18:00
「量子Fisher情報量を用いた不確定性関係の定式化」
ハイゼンベルグによって示唆された不確定性関係を量子Fisher情報量を用いることで示す。一般の量子測定過程についての誤差や擾乱を定式化するためには、量子推定理論を用いる必要があることを紹介し、誤差や擾乱を量子Fisher情報量を用いて定式化する。さらに、それらに成り立つトレードオフ関係を示す。

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September 2013

Speaker: 森貴司氏（東京大学）
Time: September 9 (Mon) 13:30-17:30
Place: Bldg.3, #119
Title: 長距離相互作用系の熱力学的極限
Abstract:
　長距離相互作用系は、マクロ系の各部分が独立とみなせないことによって、短距離相互作用系とは異なった熱力学的振る舞いを見せる。長距離相互作用系では、エネルギーの寄与がエントロピー的な寄与を圧倒するために、通常の熱力学的極限は存在しないか、もしくは自明な極限になってしまう。
　そこで、長距離相互作用系の非自明な熱力学的性質が現れるパラメター領域を調べるため、相互作用ポテンシャルを系の体積に依存させて、単位スピンあたりのエネルギーを固定した上で通常の熱力学的極限を取る、いわゆるKacの処方がよく用いられる。
　今回の講義では、Kacの処方のもとでの熱力学的極限の存在をスピン系に対して証明し、極限でのエントロピー密度の性質を調べる。
　具体的には、まずミクロカノニカルとカノニカルの間のアンサンブルの等価性とミクロカノニカルエントロピーの凸性が等価であることを一般的に示し、続いて短距離相互作用系と長距離相互作用系のそれぞれについて、熱力学的極限の存在の証明と極限でのエントロピーの凸性について話をする。

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July 2013

Speaker: Jordan M. Horowitz (University of Massachusetts)
Time: July 4 (Thu) 16:30-17:30
Place: Bldg.16, #827
Title: Thermodynamics for quantum trajectories
Abstract:
Stochastic thermodynamics is a theoretical framework that assigns thermodynamic quantities — such as work and entropy — to individual fluctuating trajectories of small systems. As a theoretical tool, it has been useful in refining our understanding of irreversibility at the micron scale. In this talk, I develop an analogous framework for open quantum systems using the quantum trajectories formalism. By considering thermal reservoirs engineered from sequences of small quantum systems, I will be able to introduce consistent trajectory-dependent definitions of thermodynamic quantities. Furthermore, I will briefly discuss the connection between entropy production within this framework and irreversibility by way of a detailed fluctuation theorem.

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Speaker: Gavin E. Crooks (Lawrence Berkeley National Laboratory)
Time: July 4 (Thu) 15:30-16:30
Place: Bldg.16, #827
Title: Molecular machines and the thermodynamic cost of nostalgia
Abstract:
Molecular scale machines not only manipulate energy and matter at the nanoscale, they must also manipulate information. As a consequence, there’s a tradeoff between thermodynamic efficiency, memory and prediction. A prodigious memory allows more accurate prediction of the future, which can be exploited to reduce dissipation. But the persistence of memory is a liability, since information erasure leads to increased dissipation. A thermodynamically optimal machine must balance memory versus prediction by minimizing its nostalgia, the useless information about the past [1].

[1] Thermodynamics of prediction, Susanne Still, David A. Sivak, Anthony J. Bell and Gavin E. Crooks, Phys. Rev. Lett. 109, 120604 (2012).

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June 2013

Speaker: 越野和樹氏（東京医科歯科大学）
Time: June 19 (Wed) 14:00-15:30
Place: Bldg.3, #119
Title: 一般的量子測定による量子ゼノン・逆ゼノン効果
Abstract:
量子不安定系に対してそれが崩壊したか否かを頻繁に測定すると不安定系の崩壊 レートが変化する．崩壊が遅くなる場合を量子ゼノン効果(QZE)，早くなる場合 を量子逆ゼノン効果(AZE)と呼ぶ．従来のQZE/AZEの理論では，理想測定を仮定し て射影仮設により測定の効果を議論していたが，本講演では不安定系の自由度に 測定器の自由度も加えた「拡張量子系」の厳密な解析により，一般的な測定によ るQZE/AZEを議論する．具体例として，励起原子の輻射崩壊の光子検出による測 定を議論する．拡張量子系を用いる定式化の下では，測定の反作用として不安定 系の form factor が繰り込みを受け，その結果崩壊レートが変化する．射影仮 設による従来型理論は，測定器があらゆる光子に対して同じ反応速度で応答する という特殊な状況下で再現される．厳密に指数関数的に崩壊する系において は，QZE/AZEが決して発現しないというのが従来型理論の予言であった．しか し，このような系においても，現実的な測定器のもつ有限の検出バンド幅を考慮 すると，QZE/AZEが起こりうることを示す．この事実は，従来型理論の予言より も遥かに緩い条件下でQZE/AZEが発現しうることを示唆する．

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Speaker: Martin L. Rosinberg (LPTMC, France)
Time: June 5 (Wed) 15:00-16:30
Place: Bldg.16, #827
Title: Entropy production and 2nd law in stochastic systems under continuous feedback control
Abstract:
Entropy production (EP) in small stochastic systems under feedback control is an issue that has attracted much theoretical attention over the last few years, at the crossroad between statistical physics and information theory [1]. In this talk, I will present some recent work in collaboration with T. Munakata (Kyoto Univ.) that focuses on systems in which measurements and actuation are performed continuously, i.e., repeated with a period shorter than the characteristic time scales of the dynamics – typically an under-damped Langevin dynamics. Two problems are investigated that correspond to actual situations:

i) the influence of measurement errors (i.e. detector noise) in a cold damping setup in which a harmonic oscillator (e.g. the cantilever of an AFM or the mirror of an interferometric detector) in contact with a heat bath is submitted to a velocity-dependent feedback force that reduces the random motion. We distinguish whether the sensor continuously measures the position of the resonator or directly its velocity (in practice, an electric current). We also assign a relaxation dynamics to the feedback mechanism and compare the apparent entropy production in the system plus the heat bath to the total entropy production in the super-system that includes the controller [2].

ii) the influence of a time delay between the input signal and the output control action, a situation that occurs in many biological or artificial systems (e.g. in the control of vision and posture, or in laser networks). We show that the system spontaneously settles into a nonequilibrium steady state where entropy is permanently produced (cooling or heating is achieved depending on the delay). However, since the feedback makes the dynamics non-Markovian, this supposes to properly revisit the definition of EP as a measure of time-irreversibility within the framework of stochastic thermodynamics [3].

In both cases, we adopt the standpoint of the controlled system and, in the spirit of [4,5], we identify the entropy pumping contribution that describes the influence of the external agent and that modifies the second law of thermodynamics and the fluctuation theorems.

[1] T. Sagawa and M. Ueda, Phys. Rev. E 85, 021104 (2012).
[2] T. Munakata and M.L. Rosinberg, preprint arXiv:1303.2969, to appear in J. Stat. Mech.
[3] T. Munakata and M.L. Rosinberg (in preparation).
[4] K. H. Kim and H. Qian, Phys. Rev. Lett. 93, 120602 (2004); Phys. Rev. E 75, 022102 (2007).
[5] T. Munakata and M. L. Rosinberg, J. Stat. Mech. P05010 (2012).