統計力学セミナー予定表 2017年度


連絡先: 島田尚(shimadaあっと ap.t.u-tokyo.ac.jp)、 森貴司(moriあっと spin.phys.s.u-tokyo.ac.jp)
宮下研究室伊藤研究室 (セミナー)| 藤堂研究室羽田野研究室 (セミナー)| 桂研究室

これからのセミナー

日時 場所 講演者(敬称略) 講演題目
12月18日13時 理学部4号館1320教室 龍田 真美子 (東大総文, 清水研) Measurement-induced superpositions of macroscopically distinct states from thermal equilibrium states
12月25日13時 理学部4号館1320教室 中村 勝弘 (National University of Uzbekistan, Uzbekistan) Force and equation of states of quantum gas confined in a rapidly dilating cavity

これまでのセミナー

日時 講演者(敬称略) 講演題目
4月17日13時 Ramis Movassagh (MIT, US) Eigenvalue Attraction
4月24日13時 大久保 毅 Ground state properties of Na2IrO3 determined from ab initio Hamiltonian
5月8日13時 桂 法称 Quantum Hangul
5月15日13時 Kay Brandner (Aalto University, Finland) Experimental Determination of Dynamical Lee-Yang Zeros
5月22日13時 伊藤 伸泰 Data-transfer optimization of quantum simulation on massive parallel computers
5月29日13時 藤堂 眞治 Crystal Structure Prediction Supported by Incomplete Experimental Data
6月5日13時 羽田野 直道 Does non-Hermiticity weaken localization?
6月12日13時 鈴木 貴文 (東大物工, 今田研) Nonequilibrium Kondo Resonance from Viewpoints of Electron Quantum Optics
6月26日13時 宮下 精二 Elastic effect on the phase transitions of the spin-crossover systems
7月3日13時 森 貴司 Counterexamples to eigenstate thermalization hypothesis
7月10日13時 赤城 裕 Noncommutative Z2 index of 3D topological insulators with disorder
10月16日13時 檜原 太一 Theoretical Study of Dipole-dipole Interaction in Atomistic Spin Model of Neodymium Magnets
10月23日13時 白井 達彦 Microscopic description of Optical Bistability
10月30日13時 李 宰河 Quantisations and quasi-probabilities as adjoint pairs and the uncertainty relation for approximation-estimation
11月13日13時 高橋 惇 (東大総文, 福島研) Numerical studies on stoquastic quantum annealing as a computational model
11月20日13時 藤本 和也 (東大理物, 上田研) Turbulent cascade in a 3D ultracold Bose gas
11月27日13時 田島 裕康 (理研, CEMS) Uncertainty relations in implementation of unitary control
12月4日13時 若村 浩明 (慶応大, 古池研) Suppressibility of noise by quantum control before and after the noise process
12月11日13時 Guang-Ming Zhang (清華大学, China) Quantum antiferromagnetic Heisenberg half-odd integer spin model as the entanglement Hamiltonian of the integer spin Affleck-Kennedy-Lieb-Tasaki states
所属が書かれていない講演者は、宮下研、伊藤研、藤堂研、羽田野研、桂研の所属です。
過去のセミナー: 2016年度| 2015年度2015年度2014年度2013年度2012年度2011年度2010年度2009年度2008年度2007年度2006年度2005年度2004年度2003年度2002年度2001年度2000年度1999年度

第1回

日時: 4月17日13時より

場所: 1320教室

講演者: Ramis Movassagh (MIT, US)

講演タイトル:Eigenvalue Attraction

講演要旨:
Much work has been developed to the understanding of the motion of eigenvalues in response to randomness. The folklore of randam matrix analysis, especially in the case of Hermitian matrices, suggests that the eigenvalues of a perturbed matrix repel. We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract. We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. We apply the results to the Hatano-Nelson model, random perturbations of a fixed matrix, real stochastic processes with zero-mean and independent intervals and discuss open problems. Time permitting we will discuss a joint work with Leo Kadanoff, on Toeplitz matrices with singular Fisher-Hartwig symbols.

Reference: J. Stat. Phys. 162, 615 (2016).

第2回

日時: 4月24日13時より

場所: 1320教室

講演者: 大久保 毅

講演タイトル:Ground state properties of Na2IrO3 determined from ab initio Hamiltonian

講演要旨:
Novel quantum phenomena induced by strong spin-orbit interaction have recently attracted much interest in condensed matter physics. Iridium oxides offer a typical example that shows rich phenomena. Among them, A2IrO3 (A=Na or Li) have intensively been investigated since the theoretical proposal that the Kitaev spin liquid would be realized [1, 2].

In this seminar, we discuss the ground state properties of Na2IrO3 based on the ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions [3]. By means of the infinite-size PEPS tensor network method, the two-dimensional density matrix renormalization group, and the exact diagonalization we show that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations [4]. We also discuss the phase diagram in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion. It turns out that the phase diagram contains several magnetically ordered phases near the zigzag phase [4]. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na.

[1]. G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).
[2]. J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).
[3]. Y. Yamaji, Y. Nomura, M. Kurita, R. Arita, and M. Imada, Phys. Rev. Lett. 113, 107201 (2014).
[4]. T. Okubo, K. Shinjo, Y. Yamaji, N. Kawashima, S. Sota, T. Tohyama, M. Imada, arXiv:1611.03614.

第3回

日時: 5月8日13時より

場所: 1320教室

講演者: 桂 法称

講演タイトル:Quantum Hangul

講演要旨:
Resonating valence bond (RVB) states proposed by Anderson have been the focus of much attention because of their relevance to the physics of spin liquids. However, previous work was overwhelmingly dominated by RVB states built out of dimers, each of which is made up of two S=1/2 spins. As an alternative route to spin liquids, we propose RVB states consisting of trimer motifs. Here by trimer we mean the spin singlet made up of three S=1 spins. The trimer RVB (tRVB) state is an equal-weight superposition of all possible trimer arrangements. The problem of counting trimer coverings is, in itself, a fascinating combinatorial problem. In the talk, we introduce a quantum trimer model on a square lattice for which the tRVB state becomes the exact ground state. The state is shown to be 9-fold degenerate on a torus. We also show that the correlation functions in the ground state are extremely short-ranged, suggesting that the model is gapped and exhibits Z_3 topological order.

Reference:
[1] H. Lee, Y-T. Oh, J.H. Han, and H. Katsura, Phys. Rev. B, 95, 060413(R) (2017).

第4回

日時: 5月15日13時より

場所: 1320教室

講演者: Kar Brandner (Aalt University, Finland)

講演タイトル:Experimental Determination of Dynamical Lee-Yang Zeros

講演要旨:
Conventional phase transitions involve abrupt changes of a macroscopic system in response to small variations of an external control parameter. This exceptional behaviour can be understood from the complex zeros of the partition function of the finite-sized system: in the thermodynamic limit, these Lee-Yang zeros, which correspond to logarithmic singularities of the free energy, approach the critical value of the control parameter on the real axis.

This general scheme also applies to dynamical phase transitions in non-equilibrium systems. The partition function is thereby replaced with the moment-generating function of a stochastic process with the counting field playing the role of the external control parameter. Here, we demonstrate that the corresponding dynamical Lee-Yang zeors are not only a theoretical conecept but physical observables, which encode remarkable information on the long-time statistics and the dynamical fluctuations of the system. To this end, we analyze a stochastic process involving Andreev-tunneling events in a mesososcopic device consisting of a normal-state island and two superconducting leads. From measurements of the dynamical activity, we extract the Lee-Yang zeros, which reveal a smeared dynamical phase transition outside the range of direct observations. Being obtaind only from short-time data, this information allows us to predict the large-deviation statistics of the dynamical activity at long times, which is otherwise difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

Reference: K. Brandner, V. F. Maisi, J. P. Pekola, J. P. Garrahan, C. Flindt, "Experimental Determination of Dynamical Lee-Yang Zeros", Phys. Rev. Lett. 118, 180601 (2017).

第5回

日時: 5月22日13時より

場所: 1320教室

講演者: 伊藤 伸泰

講演タイトル: Data-transfer optimization of quantum simulation on massive parallel computers

講演要旨:
Brute force simulations using full vectors in Hilbert spaces requre exponentially large memory spaces versus degree-of-freedom. Memory space and its band-width of modern massive-parallel supercomputers are useful for the purpose, but internode datat-ransfer is order-of-magnitude more expensive than intranode operations, so optimization of data-transfer is important for such simulation. A heuristic algorithm for the world-record simulation of qbit simulation will be discussed as an example.

第6回

日時: 5月29日13時より

場所: 1320教室

講演者: 藤堂 眞治

講演タイトル: Crystal Structure Prediction Supported by Incomplete Experimental Data

講演要旨:
The prediction of crystal structure from chemical composition has been a long-standing challenge in natural science. Although various numerical methods have been developed over last decades, it i remains still difficult to numerically predict crystal structures comprising more than several tens of atoms in the supercell due to the many degrees of freedom, which increase exponentially with the number of atoms. Here, we propose a new method for crystal structure prediction from numerical simulations with support of X-ray diffraction experimental data [1]. We show that even if the experimental data is totally insufficient for conventional structure analysis, it can still support and substantially accelerate structure simulation. In particular, we formulate a cost function based on a weighted sum of interatomic potential energy and a penalty function referred to as "crystallinity", which is defined by using limited X-ray diffraction data. We present the simulation results for well-known polymorphs of SiO2 with up to 96 atoms in the supercell, in which the correct structures can be reproduced with high probability with a very limited number of diffraction peaks. We also present an optimization method for simultaneous minimization of two or more cost functions which share the same global minimum point, but have different distributions of local minima. We discuss the possibility that our new optimization method can further accelerate the convergence to the global minimum in the crystal structure simulation [2].

[1] N. Tsujimoto, D. Adachi, R. Akashi, S. Todo, S. Tsuneyuki, arXiv:1705.08613.
[2] D. Adachi, N. Tsujimoto, R. Akashi, S. Todo, S. Tsuneyuki, in preparation.

第7回

日時: 6月5日13時より

場所: 1320教室

講演者: 羽田野 直道

講演タイトル: Does non-Hermiticity weaken localization?

講演要旨:
The Anderson localization refers to a phenomenon of spatial localization of waves in random media. It is often explained to be originated in coherence; the destructive interference among the incident wave and all randomly scattered waves makes the wave stay in a region where the randomness happens to be strong. Many people therefore have suggested that one can weaken the wave localization by undermining the wave coherence.

One important way of possibly eroding the coherence is to introduce the non-Hermiticity. Indeed, we have shown that the off-diagonal non-Hermiticity destroys the localization even in one spatial dimension [1-4], where the Anderson localization takes place most strongly. Several other studies also suggested that complex potentials on the diagonal randomness weakens the Anderson localization.

Does the non-Hermiticity universally weaken the Anderson localization by impairing the coherence? Is there a counter-example? I will discuss this issue utilizing our recent algorithm of computing the localization length of non-Hermitian random systems [5].

Collaborators: Amnon Aharony (Tel Aviv University & Ben-Gurion University of the Negev); Joshua Feinberg (University of Haifa)

References
[1] N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570―573 (1996)
[2] N. Hatano and D.R. Nelson, Phys. Rev. B 56, 8651―8673 (1997)
[3] N. Hatano, Physica A 254, 317―331 (1998)
[4] A. Amir, N. Hatano and D.R. Nelson, Phys. Rev. E 93, 042310 (2016)
[5] N. Hatano and J. Feinberg, Phys. Rev. E 94, 063305 (2016)

第8回

日時: 6月12日13時より

場所: 1320教室

講演者: 鈴木 貴文 (東大物工, 今田研)

講演タイトル: Nonequilibrium Kondo Resonance from Viewpoints of Electron Quantum Optics

講演要旨:
The Kondo effect has attracted renewed attention in the condensed matter physics because of rapid development in nanotechnologies. In particular, a quantum dot (QD) system enables us to study the nonequilibrium Kondo effect with experimentally tuned parameters. The interplay between the coherent many-body resonance and the nonequilibrium field has posed fundamental problems of determining the elementary excitation in the Kondo systems driven out of equilibrium [1,2].

Recently, it was experimentally demonstrated that Lorentzian-shaped periodic pulses can create an ideal fermionic excitation above the Fermi sea [3]. The quasiparticle was named "leviton" after Leonid S. Levitov, who theoretically predicted the nontrivial property of the Lorentzian pulse over twenty years ago [4]. The experimental realization of the on-demand single-electron generator has made significant contributions to advancing the emerging field of electron quantum optics.

In this talk, we discuss the coherent transport of levitons through the QD system in the Kondo regime [5]. The Kondo resonance repeatedly emerges in the nonequilibrium regimes where the Fermi sea is driven by optimal Lorentzian pulses without particle-hole excitations.

[1] A. Oguri, J. Phys. Soc. Jpn. 74, 110 (2005).
[2] M. Ferrier et al., Nat. Phys. 12, 230 (2016)
[3] J. Dubois et al., Nature (London) 502, 659 (2013)
[4] L. S. Levitov et al., J. Math. Phys. 37, 4845 (1996).
[5] T. J. Suzuki, arXiv:1703.05198 (to be published in PRB)

第9回

日時: 6月26日13時より

場所: 1320教室

講演者: 宮下 精二

講演タイトル: Elastic effects on the phase transitions of the spin-crossover systems

講演要旨:
The elastic interaction causes interesting effects on the phase transitions of the bi-stable spin-crossover systems. The elastic interaction causes an effective long-range ferromagnetic interaction among the spins. Competition and synergetic effects of long-range interaction and short-range interaction provide various interesting properties in phase transitions. In the case of ferromagnetic short-range interaction, the long-range interaction causes to change the universality class of the transition to the so-called mean-field universality class [1,2]. In the case of antiferromagnetic interaction on a bipartite lattice, it was shown that the long-range interaction does not cause the change of universality class of the short-range model [3]. However, recently the competition between the short-range antiferromagnetic interaction and long-range ferromagnetic causes an interesting structure in the temperature-field (T,H) phase diagram with horn-like branch [4,5]. We also study dynamical processes after the photo-irradiation which causes high excitation at the irradiated site. We find two types of expansions which are attributed to the elastic effect and also the thermal effect [6].

[1] S. Miyashita, Y. Konishi, M. Nishino, H. Tokoro, and P. A. Rikvold, Phys. Rev. B 77, 014105 (2008).
[2] T. Nakada, P. A. Rikvold, T. Mori, M. Nishino, and S. Miyashita, Phys. Rev. B 84, 054433 (2011). T. Nakada, T. Mori, S.M, M. Nishino, S. Todo, W. Nicolazzai and P. A. Rikvold, Phys. Rev. B 85, 054408 (2012).
[3] M. Nishino and S. Miyashita, Phys. Rev. B 88, 014108 (2013).
[4] P. A. Rikvold, G. Brown, S. Miyashita, C. Omand and M. Nishino, Phys. Rev. B. 93, 064109, (2016).
[5] M. Nishino, P. A. Rikvold, G. Brown, C. Omand and S. Miyashita, in preparation.
[6] C. Enachescu, L. Stoleriu, M. Nishino, S. Miyashita, A. Stancu. M. Lorenc, R. Bertoni, H. Cailleau,4 and E. Collet, PRB (2017) in press.

第10回

日時: 7月3日13時より

場所: 1320教室

講演者: 森 貴司

講演タイトル: Counterexamples to eigenstate thermalization hypothesis

講演要旨:
In recent years, quantum dynamics in isolated systems has attracted much attention. In particular, it has been a fundamental problem whether an isolated quantum system exhibits thermalization (approach to thermal equilibrium). It is now recognized that thermal equilibrium state is typical in the sense that an overwhelming majority of pure states with a definite macroscopic energy correspond to thermal equilibrium. Approach to thermal equilibrium is then interpreted as an evolution from an atypical nonequilibrium state to a typical equilibrium state. Although this interpretation is quite natural, typicality of thermal equilibrium does not explain the presence or absence of thermalization in a given system. For example, typicality argument holds in an integrable system, but it fails to thermalize. In order to characterize the presence or absence of thermalization, properties of quantum dynamics should be further investigated.
A plausible scenario of thermalization is the one based on the property called the eigenstate thermalization hypothesis (ETH). The ETH states that every energy eigenstate represents thermal equilibrium. If the ETH is correct, we can generally show thermalization with an additional mild condition on the initial state. Numerically it has been shown that nonintegrable systems satisfy the ETH while integrable systems and many-body localized systems do not. Therefore, the ETH has been regarded as a good characterization of a quantum system exhibiting thermalization.
In this talk, we propose a systematic construction of counterexamples to this scenario. We construct a family of models without the ETH [1]. In particular, constructed models are neither integrable nor many-body localized, so our method gives a novel class of systems violating the ETH. We will show that our model thermalizes after an arbitrary quantum quench from an equilibrium state of another local Hamiltonian at finite temperature [2]. In other words, our model thermalizes for a general class of initial states although the ETH does not hold. It means that the ETH is not a necessary condition of thermalization against conventional beliefs.

References:
[1] N. Shiraishi and T. Mori, arXiv: 1702.08227 (to appear in Phys. Rev. Lett.)
[2] T. Mori and N. Shiraishi, in preparation.

第11回

日時: 7月10日13時より

場所: 1320教室

講演者: 赤城 裕

講演タイトル: Noncommutative Z2 index of 3D topological insulators with disorder

講演要旨:
Topological insulators in three dimensions characterized by a Z2 topological invariant have attracted much attention due to their gapless surface states robust against perturbations. In translationally invariant systems, the Z2 invariant is defined in terms of Bloch wave functions [1]. However, it is not obvious how to define such an invariant in disordered systems, where the Bloch momentum is no longer a good quantum number.

Recently, it was found that the methods of noncommutative geometry [2] provide a mathematically rigorous representation of the Z2 invariant [3,4], which is particularly useful for studying systems without translational symmetry. We take the Wilson-Dirac-type Hamiltonian as an example and demonstrate how the noncommutative formula allows us to map out the phase diagram numerically. Our results [5] are consistent with those obtained by a transfer-matrix method in previous work [6]. In this presentation, I will explain how to define the noncommutative Z2 index, and numerically demonstrate its robustness against disorder.

[1] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
[2] J. E. Avron, R. Seiler, and B. Simon, J. Func. Anal. 120, 220 (1994).
[3] H. Katsura and T. Koma, J. Math. Phys. 57, 021903 (2016).
[4] H. Katsura and T. Koma, Preprint, arXiv:1611.01928.
[5] Y. Akagi, H. Katsura, and T. Koma, in preparation.
[6] K. Kobayashi, T. Ohtsuki, and K. Imura, Phys. Rev. Lett. 110, 236803 (2013).

第12回

日時: 10月16日13時より

場所: 1320教室

講演者: 檜原 太一

講演タイトル: Theoretical Study of Dipole-dipole Interaction in Atomistic Spin Model of Neodymium Magnets

講演要旨:
It has been pointed out that the magnetic properties based on the atomistic spin model of Nd2Fe14Be well reproduce the experimental results [1].
By using this model, estimation of the coercivity in a micrometer-size system is required to reveal the mechanism of the magnetization reversal process in this magnet.

For this purpose, we improved the stochastically cutoff (SCO) method [2], which is a Monte Carlo (MC) method for long-range interacting systems, by implementing the efficient algorithm proposed by Fukui and Todo in a cluster MC method [3].
In addition, we proposed a kind of the coarse-graining procedure of this system.

In this talk, we introduce these methods and discuss the sample-size dependence of the coercivity.

[1] Y. Toga, M. Matsumoto, S. Miyashita, H. Akai, S. Doi, T. Miyake, and A. Sakuma, Phys. Rev B 94 174433 (2016).
[2] M. Sasaki and F. Matsubara, J. Phys. Soc. Jpn. 77, 024004 (2008).
[3] K. Fukui and S. Todo, J. Comput. Phys. 228, 2629 (2009).

第13回

日時: 10月23日13時より

場所: 1320教室

講演者: 白井 達彦

講演タイトル: Microscopic description of Optical Bistability

講演要旨:
A cavity system has a single-quantized photon field. Embedding an ensemble of atoms inside it a variety of cooperative phenomena appear. The advance of experiments allows to control the size of the atomic medium even in a single-atom resolution. From the theoretical side it has been shown that a mean-field treatment (classical treatment) gives a good approximation as the size is increased. Thus this system is appropriate to study the crossover between the quantum regime and the classical regime.

We discuss one of the cooperative phenomena called optical bistability, which occurs under pumping of cavity photons by a laser field. As the laser amplitude is increased an intracavity field shows a discontinuous jump. As the laser amplitude is then decreased it also shows a discontinuous jump. But the transition points are different, and thus the curve of the intracavity field as a function of the laser amplitude shows a hysteresis loop. Experimental data for large-size systems are well described by the mean-field treatment. However it is still a challenging issue to understand this phenomenon from the side of quantum regime. It is mainly due to the nonequilibrium nature of this phenomenon, and thus we have to solve the quantum dynamics instead of using the well-established methods of statistical mechanics.

Here we numerically solve a quantum master equation, which describes time evolution of cavity systems. We investigate the size dependence of both the static properties and the dynamical properties up to 25 atoms, and find that this nonequilibrium phenomenon can be understood with an analogy of the first-order phase transition. Thus we show that there exists a large-deviation function which plays the role of the free energy in equilibrium statistical mechanics.

第14回

日時: 10月30日13時より

場所: 1320教室

講演者: 李 宰河

講演タイトル: Quantisations and quasi-probabilities as adjoint pairs and the uncertainty relation for approximation-estimation

講演要旨:
In this presentation, the speaker introduces some recent results [1-2] in the general study of quantisations and quasi-probabilities, the topic of which is known to have a long history dating back to the early days of quantum theory, where Weyl [3] and Wigner [4] were among the many prominent figures who have made much contribution in this area. The crux of the argument is to focus on the duality between observables and states, so that quantisations and quasi-probabilities can be understood as adjoint pairs. Specifically, generators of the adjoint pairs are introduced in explicit forms, by which all the previous works can be understood as special cases under this framework. Subsequently, the speaker introduces some recent advances in the study of uncertainty relations, which is originally advocated by Heisenberg in his celebrated Gedankenexperiment on the gamma-ray microscope [5]. The general framework of quantisation and quasi-probability is shown to result in a novel type of inequality [6] the authors call the uncertainty relation for approximation-estimation. Most notably, this inequality is found to yield both the Kennard-Robertson [7-8] inequality and the trade-off relation between time and energy [9-10], thus unifying the two uncertainty relations previously thought to be mutually incomparable. The inequality also reveals its relation to Aharonov’s weak value [11], which has recently been attracting attention in the quantum physics community.

[1] J. Lee and I. Tsutsui, Prog. Theor. Exp. Phys. 2017 (5): 052A01 (2017).
[2] J. Lee and I. Tsutsui, NWW 2015, Proceedings (2017). arXiv:1703.06068.
[3] H. Weyl, Z. Phys. 46(1): 1-46 (1927).
[4] E. Wigner, Phys. Rev. 40: 749-759 (1932).
[5] W. K. Heisenberg, Z. Phys. 43: 172-198 (1927).
[6] J. Lee and I. Tsutsui, Phys. Lett. A 380: 2045-2048 (2016).
[7] E.H. Kennard, Z. Phys. 44: 326-352 (1927).
[8] H.P. Robertson, Phys. Rev. 34: 163-164 (1929).
[9] L.I. Mandelshtam and I.E. Tamm, Izv. Akad. Nauk SSSR, Ser. Fiz. 9:122-128 (1945).
[10] C.W. Helstrom, Quantum Detection and Estimation Theory, Academic Press (1976).
[11] Y. Aharonov, P. G. Bergmann and L. Lebowitz, Phys. Rev. 134: B1410-1416 (1964).

第15回

日時: 11月13日13時より

場所: 1320教室

講演者: 高橋 惇 (東大総文, 福島研)

講演タイトル: Numerical studies on stoquastic quantum annealing as a computational model

講演要旨:
Quantum annealing (QA) is currently the only “quantum” computer with large-scale implementation up to 2000 qubits, utilizing physical concepts such as the adiabatic theorem to compute optimization problems. While there have been numbers of claims in favor of QA with major advancements from classical computers [1,2], they seem not to apply for the actual built QA devise. In this talk, we see two cases where in fact QA seems to be not so powerful.
First, we see the case where QA is applied to an NP-hard problem. Although polynomial time computations with QA for NP problems were suggested in the early days [1], we find first-order phase transitions emerging in the large scale limit. Furthermore, using the fidelity susceptibility, we find an underlying phase transition among all of the instances, suggesting a non spin glass transition responsible for the failure of QA [3].
Secondly, we focus on the “stoquasticity” (a definition will be given in the talk) of currently built QA. While an unrestricted version of QA is proven to be equivalent to the standard quantum circuit model [2], the stoquastic version seems to have limited computational power. We investigate some approaches for simulating stoquastic QA classically by Monte Carlo methods.

[1] E. Farhi et al., Science 292, 472 (2001)
[2] D. Aharonov et al., SIAM Rev. 50, 755 (2008)
[3] J. Takahashi & K. Hukushima, arXiv:1612.08554 (2016)

第16回

日時: 11月20日13時より

場所: 1320教室

講演者: 藤本 和也 (東大理物, 上田研)

講演タイトル: Turbulent cascade in a 3D ultracold Bose gas

講演要旨:
Turbulence is ubiquitous non-equilibrium fluid dynamics with many degrees of freedom, and has been studied for many years from the perspective of both basic and applied physics. Throughout the long history, the K41 theory suggested by Kolmogorov at 1941 plays a significant role in understanding universal behaviors of turbulence. In this theory, a turbulent cascade picture is known to be of great importance and characterized by an energy flux in wave number space [1].
Recently, this kind of turbulence is experimentally and theoretically studied in ultracold atomic gases, and is discussed in relation to thermalization in an isolated quantum system [2]. However, because of experimental difficulties, properties of a turbulent cascade in an ultracold atomic gas are not sufficiently addressed in experiments, so that theoretical studies for experimental observation of a turbulent cascade are needed.
In this talk, we show two results for turbulence in a 3D ultracold Bose gas. One is a theoretical study of weak-wave turbulence, where we investigate a property of a turbulent cascade and discuss how to observe the cascade behavior [3]. The other is an ongoing experimental and theoretical study of a turbulent cascade [4] related to the previous result [5]. In collaboration with the experimental group, we can experimentally observe the energy flux in wave number space, investigating details of the turbulent cascade.

[1] U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995).
[2] B. Nowak et al., Lecture Notes of the Les Houches Summer School Vol. 99, 2016
[3] K. Fujimoto and M. Tsubota, Phys. Rev. A 91, 053620 (2015).
[4] N. Nir et al., in preparation.
[5] N. Nir et al., Nature 539, 72 (2016).

第17回

日時: 11月27日13時より

場所: 1320教室

講演者: 田島 裕康 (理研, CEMS)

講演タイトル: Uncertainty relations in implementation of unitary control

講演要旨:
Controlling the dynamics of quantum systems is one of central subjects for many experimental situations [1-3]. Usually one realizes a desired unitary dynamics on a system as a physical phenomenon that results from the interaction between the system and the experimental apparatus. However, it is still unclear what is going on between the system and the apparatus. Although there are several specific examples to study the mechanism [4,5], general natures on this has not been addressed so far.

Here, we study the fundamental limitation in the implementation of unitary control on the system with the experimental apparatus [6]. As in the previous studies [4,5], we model this situation using the setup of the system and an external system that represents the apparatus. We consider the conditions required to approximate the dynamics of the reduced density matrix of the system by the desired unitary time evolution. Then, we derive a fundamental trade-off relation to implement the unitary dynamics:

δ_Uδ_E ≧|[H_S, U_S]|/40,

where,*δ_U* is the implementation error of the desired unitary *U_S*, and *δ_E* is the energy fluctuation of the external system, and H_S is the initial Hamiltonian of the system. We also derive another trade-off, which shows that the origin of the energy fluctuationδ_E should be a quantum superposition, not a classical mixture. The results show that achieving perfect unitary control in the system and eliminating the quantum fluctuation of energy in the external system are incompatible.

[1] Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Nature 398, 786 (1999).
[2] N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffves, R. Azouitd, Pi. Rouchond, and B. Huard, PNAS, 114, 7561 (2017).
[3]Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda and Y. Nakamura, arXiv:1709.00548, (2017).
[4] E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[5] J. Aberg, Phys. Rev. Lett. 113, 150402 (2014).
[6] H. Tajima, N. Shiraishi and K. Saito, arXiv:1709.06920 (2017).

第18回

日時: 12月4日13時より

場所: 1320教室

講演者: 若村 浩明 (慶応大, 古池研)

講演タイトル: Suppressibility of noise by quantum control before and after the noise process

講演要旨:
Suppression of noise in quantum systems is an important task in quantum information science. We consider protecting a quantum state by measurements and operations performed before and after, respectively, the noise process. The aim is to seek the optimal protocol that makes the input and output states as close as possible. This problem is related to the studies on continuous time feedback control of noisy quantum systems [1], which aim to stabilize a state of the noisy system to a known initial state. However it is more important to investigate state protection in the case of unknown initial state in order to clarify the ability to control quantum systems in general.
Discrete time formulation (measurements and operations before and after the noise process) describes one-time feedback control and hence is a minimal framework for noise suppression, which simplifies the problem and enables us to investigate protection of unknown state for more general class of noise. Protection of two states of a qubit has been well studied [2,3]. The optimal protocol does not include projective measurements but include weak (less-disturbing) measurements of the system. However, the importance of weak measurement is unclear in general settings.
In this talk, we discuss the possibility of protecting a completely unknown state of a quantum system [4,5]. We first consider the suppression of unital noise (including common class of noise in quantum information science, such as dephasing noise) for a qubit system. We find that the optimal protocol is either the “no measurement” protocol or the “discriminate and reprepare” protocol. Since they involve no measurement or only strong measurements, they can be understood by the concept of classical control and therefore are not “truly quantum.” Furthermore, we find the essentially same statement is true for the case of depolarizing noise in a finite dimensional system. These results describe the fundamental limitations in quantum mechanics from the viewpoint of control theory.

[1] J. Wang and H. M. Wiseman, Phys. Rev. A 64, 063810 (2001).
[2] A. M. Branczyk, et al., Phys. Rev. A 75, 012329 (2007).
[3] P. E. M. F. Mendonca, et al., Phys. Rev. A 78, 012319 (2008).
[4] H. Wakamura, et al., Phys. Rev. A 95, 022321 (2017).
[5] H. Wakamura, et al., Phys. Rev. A 96, 022325 (2017).

第19回

日時: 12月11日13時より

場所: 1320教室

講演者: Guang-Ming Zhang (清華大学, China)

講演タイトル: Quantum antiferromagnetic Heisenberg half-odd integer spin model as the entanglement Hamiltonian of the integer spin Affleck-Kennedy-Lieb-Tasaki states

講演要旨:
Applying a symmetric bulk bipartition to the one-dimensional Affleck-Kennedy- Lieb-Tasaki valence bond solid (VBS) states for the integer spin-S Haldane gapped phase, we can create an array of fractionalized spin-S/2 edge states with the super unit cell l in the reduced bulk system, and the topological properties encoded in the VBS wave functions can be revealed. The entanglement Hamiltonian (EH) with l=even corresponds to the quantum antiferromagnetic Heisenberg spin-S/2 model. For the even integer spins, the EH still describes the Haldane gapped phase. For the odd integer spins, however, the EH just corresponds to the quantum antiferromagnetic Heisenberg half-odd integer spin model with spinon excitations, characterizing the critical point separating the topological Haldane phase from the trivial gapped phase. Our results thus demonstrate that the topological bulk property not only determines its fractionalized edge states, but also the quantum criticality associated with the topological phase, where the elementary excitations are precisely those fractionalized edge degrees of freedom confined in the bulk of the topological phase.

Reference:
1. W. J. Rao, X. Wan, and G. M. Zhang, Phys. Rev. B 90, 075151 (2014).
2. W. J. Rao, G. M. Zhang, and K. Yang, Phys. Rev. B 93, 115125 (2016).
3. W. J. Rao, G. Y. Zhu, and G. M. Zhang, Phys. Rev. B 93, 165135 (2016).

第20回

日時: 12月18日13時より

場所: 1320教室

講演者: 龍田 真美子 (東大総文, 清水研)

講演タイトル: Measurement-induced superpositions of macroscopically distinct states from thermal equilibrium states

講演要旨:
Superpositions of macroscopically distincts states, so-called "cat states," have always been a curious topic since the birth of quantum physics. In this seminar, we show that such states are actually obtainable from thermal equilibrium states through a single global measurement [1]. For spin systems, for example, one can obtain a "cat state" through a projection measurement of the magnetization of a certain equilibrium state.
We start the seminar from explaining how to characterize "cat states" for mixed states [2], since the post-measurement state is a mixed state. Then we exemplify with free spins and the XYZ model. For general systems and other initial states, we give two conditions for generating "cat states." We also discuss the trade-off between resolution of the measurement and the success probability. Briefly discussing the feasibility of this proposal, we finish with possible applications of the obtained "cat state."

[1]MT and A. Shimizu, arXiv: 1703.05034 (2017).
[2]A. Shimizu and T. Morimae, Phys. Rev. Lett. 95, 090401 (2005).

第21回

日時: 12月25日13時より

場所: 1320教室

講演者: 中村 勝弘 (National University of Uzbekistan, Uzbekistan)

講演タイトル: Force and equation of states of quantum gas confined in a rapidly dilating cavity

講演要旨:
A shorter time in manufacturing products is becoming an important factor in nanotechnology. In designing quantum computers, the coherence of systems is degraded by their interaction with the environment, and therefore the acceleration of adiabatic quantum dynamics is highly desirable. A theory of fast forward (FF) of adiabatic control of quantum dynamics proposed by Masuda and Nakamura (Proc. R. Soc. A 466, 1135 (2010)) is useful in FF of quantum adiabatic dynamics of tunneling states[1] and entangled states[2]. In this talk [3], with use of the scheme of FF which realizes quasi-static or adiabatic dynamics in shortened time scale, we investigate a thermally-isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size $L=L(t)$, and find its nonequilibrium equation of states. In the FF variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity ($¥dot{L}$) and acceleration ($¥ddot{L}$) besides rapidly-changing state variables like effective temperature ($T$) and $L$ itself. We reveal the condition when the nonadiabatic contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.

[1 ] K. N., A. Khujakulov, S. Avazbaev and S. Masuda, Phys. Rev. A 95, 062108 (2017).
[2] I. Setiawan, Bobby Eka Gunara, S. Masuda and K. N., Phys.Rev. A, 96, 052106 (2017).
[3] G. Babajanova, J. Matrasulov and K. N., Quantum gas in the fast forward of adiabatically expanding cavities: force and equation of states, preprint.