|title||Quantum Edge Detection|
Last year, the speaker has discussed the theoretical bounds on estimating continuous data as a function, in which both the standard quantum limit (SQL) and the Heisenberg limit (HL) have altered its scaling law according to the smoothness of the function.
On the other hand, detection of rapid changes in a continuous data — edge detection — is a particularly important problem, which can be applied to the anomaly detection in a time-series signal and the feature extraction in a two-dimensional image.
Noting that different edges will be marked in different lengthscales, we expect that selectively detecting edges from a signal be more efficient than estimating entire function before computing edges.
In this seminar, we present theoretical analysis of detecting edges in a quantum signal. We propose a setup in a optical system, in which we directly measure the wavelet transform of the signal by measuring the momenta of spatially spread beams. It is shown that probe beam with classical/quantum correlation will lead to the SQL/Heisenberg limit, respectively, which is consistent with the parameter estimation. Furthermore, we derive more rigorous results on multiscale edge detection by taking the smoothness of functions in consideration. In fact, the result is shown to be consistent with the speaker's previous study on function estimation, indicating the asymptotic optimality of the edge-detection protocol proposed above.
|title||Non-Hermitian many-body localization|
The reality of eigenenergies of a Hamiltonian is closely related to the dynamical stability. While Hermiticity guarantees the reality of the eigenspectrum, it is known that certain classes of non-Hermitian Hamiltonians have real eigenenergies. In particular, a real-complex transition of eigenenergies of non-Hermitian systems has recently attracted growing interest motivated by their experimental realizations . In this seminar, we analyze non-Hermitian quantum many-body systems in the presence of interaction and disorder. We show that many-body localization (MBL) induced by strong disorder suppresses imaginary parts of complex eigenenergies for general non-Hermitian Hamiltonians having time-reversal symmetry . We demonstrate that a novel real-complex transition occurs upon MBL and profoundly affects the dynamical stability of non-Hermitian interacting systems with asymmetric hopping that respect time-reversal symmetry. Furthermore, the real-complex transition is shown to be absent in non-Hermitian many-body systems with gain and/or loss that breaks time-reversal symmetry, even though the MBL transition still occurs.
 R. El-Ganainy et al., Nat. Phys. 14, 11 (2018).
 RH, K. Kawabata, and M. Ueda, Phys. Rev. Lett. 123, 090603 (2019).
|speaker||Dr. Hidenori Tanaka (Stanford University)|
|title||From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction|
|abstract||Recently, deep feedforward neural networks have achieved considerable success in modeling biological sensory processing, in terms of reproducing the input-output map of sensory neurons. However, such models raise profound questions about the very nature of explanation in neuroscience. Are we simply replacing one complex system (a biological circuit) with another (a deep network), without understanding either? Moreover, beyond neural representations, are the deep network's computational mechanisms for generating neural responses the same as those in the brain? Without an algorithmic approach to extracting and understanding computational mechanisms from deep neural network models, it can be difficult both to assess the degree of utility of deep learning approaches in neuroscience, and to extract experimentally testable hypotheses from deep networks. We develop such an algorithmic approach by combining dimensionality reduction and modern attribution methods for determining the relative importance of interneurons for specific visual computations. We apply this approach to deep network models of the retina, revealing a conceptual understanding of how the retina acts as a predictive feature extractor that signals deviations from expectations for diverse spatiotemporal stimuli. For each stimulus, our extracted computational mechanisms are consistent with prior scientific literature, and in one case yields a new mechanistic hypothesis. Thus overall, this work not only yields insights into the computational mechanisms underlying the striking predictive capabilities of the retina, but also places the framework of deep networks as neuroscientific models on firmer theoretical foundations, by providing an algorithmic path to go beyond comparing neural representations to extracting and understand computational mechanisms.|
|speaker||Prof. Yuval Gefen (The Weizmann Institute of Science)|
|title||Multidimensional Dark Spaces in Open Driven Systems|
|abstract||Quantum systems are always subject to effects from the environment. This interaction usually induces decoherence, destroying the quantum properties of isolated systems. Recently, it has been suggested that a controlled interaction with the environment can help to maintain quantum correlations, by creating a state immune to decoherence, characterized by a density operator. In order to encode quantum information in this state, the dimension of the steady state density operator has to be larger than one, so different orthogonal states can be accessed within the subspace to act as a computational basis. We have devised a symmetry-based conceptual framework to create qbits, and generally qdits, by encoding them in the multidimensional subspace protected from decoherence with the environment.This framework allows us to drive the system into a pure state residing completely in the protected subspace, which is stabilized due to the effect of the dissipative environment. We illustrate this construction with an example protocol inspired by the fractional quantum hall effect in the narrow-torus-limit. The long-time steady state subspace displays characteristics of a degenerate ground-state of a topological system described by a Hamiltonian. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.|
|title||Rigorous bounds in nonequilibrium quantum dynamics|
Rigorous results play a vital role in physics. In the context of nonequilibrium quantum dynamics, two well-known rigorous results are the Lieb-Robinson bound for correlation propagation in quantum many-body systems with locality  and the Maldacena-Shenker-Stanford bound on quantum chaos characterized by the out-of-time-order correlator . In this seminar, we introduce another two rigorous bounds in nonequilibrium quantum dynamics. The first bound is a Lieb-Robinson-like bound on the entanglement gap of quenched symmetry-protected topological systems in one dimension . In addition to the results presented last year on interacting systems, we have also obtained the bound for free-fermion systems and a remarkable byproduct that greatly improves the conventional Lieb-Robinson bound. The second bound is a universal error bound for gap-induced constrained dynamics in quantum systems with isolated energy bands . By universal, we mean that the bound only involves two parameters – the energy gap and the driving strength, and is valid even in the “worst” case. This is similar to that the Maldacena-Shenker-Stanford bound only involves the temperature and is valid even for the most chaotic systems. We analyze several minimal models to corroborate the validity and tightness of our bound and discuss some applications and generalizations.|
 E. H. Lieb and D. W. Robinson, Commun. Math. Phys. 28, 251 (1972).
 J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106.
 Z. Gong, N. Kura, M. Sato, and M. Ueda, arXiv:1904.12464.
 Z. Gong, R. Hamazaki, N. Shibata, and N. Yoshioka, in preparation.
|title||Non-Hermitian Hubbard physics in ultracold atoms|
The Hubbard model is a paradigmatic model in condensed matter physics and plays an essential role in our understanding of strongly correlated systems. Recently, controlled dissipation has been experimentally introduced in cold-atom Hubbard simulators, enabling us to study open quantum many-body dynamics in the Hubbard model . In this seminar, motivated by the experimental development in ultracold atoms, we discuss how dissipation alters the basic properties of the Hubbard model by solving a non-Hermitian generalization of the one-dimensional Hubbard model. First, we show that a finite lifetime of intermediate states in spin-exchange processes qualitatively changes the magnetism of the Hubbard model from antiferromagnetism to ferromagnetism, realizing magnetic correlations characterized by a negative absolute temperature . Second, we show that an interplay between kinetic energy, interaction, and dissipation yields a many-body exceptional point, which is accompanied by critical behavior in a Mott insulator.|
 K. Sponselee et al., Quantum Sci. Technol. 4, 014002 (2018).
 M. Nakagawa, N. Tsuji, N. Kawakami, and M. Ueda, arXiv:1904.00154.
|title||Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems|
Quantum phase transitions have long been a subject of active research in quantum many-body physics. For conventional quantum many-body systems described by local and Hermitian Hamiltonians, continuous phase transitions are accompanied by closing of an excitation gap. Thus two gapped ground states which are connected without gap closing are generally considered to belong to the same quantum phase . Meanwhile, non-Hermitian physics has recently attracted widespread attention. Some fundamental principles in conventional Hermitian systems break down in non-Hermitian systems, and alternative ones have yet to be established. In particular, the role of an energy gap in quantum phase transitions has remained unclear in non-Hermitian many-body systems.
In this study, we find that a continuous quantum phase transition can occur without gap closing in non-Hermitian quantum many-body systems. In such a transition, the susceptibility exhibits a singularity due to the nonorthogonality of eigenstates. By way of illustration, we construct an exactly solvable non-Hermitian model by introducing non-Hermiticity to Kitaev’s toric-code model . |
 M. B. Hastings and X.-G. Wen, Phys. Rev. B 72, 045141 (2005).
 A. Y. Kitaev, Ann. Phys. 303, 2 (2003).
|title||Morphological superfluid in a nonmagnetic spin-2 Bose-Einstein condensate|
Superflow is usually generated by a gradient of the U(1) phase.
In spinor Bose-Einstein condensates (BECs), the spin-gauge symmetry provides the second mechanism of superfluidity.
In the case of a spin-1 BEC, a superflow can be induced by a spin texture via the spin-gauge symmetry in the ferromagnetic phase,
while it can only be carried by the gradient of the U(1) phase in the polar phase.
However, it has not been clarified if a superflow is essentially zero in a nonmagnetic phase for any spin degrees of freedom.
In this presentation, we report that for the case of a spin-2 BEC, a spatial variation of the order parameter shape can generate
a supercurrent even in the nonmagnetic phases, such as the nematic and cyclic phases, offering the hitherto unexplored the third
mechanism of superfluidity .
We analytically derive the superfluid current in a nonmagnetic spin-2 BEC, that involves components that originate from the
magnetic degrees of freedom and determine the symmetry of the order parameter.
These components can be induced between two weakly coupled BECs with different order-parameter symmetries.
We also demonstrate that the morphological supercurrent can be generated by the spatially dependent quadratic Zeeman effect,
which is numerically shown.
E. Yukawa, and M. Ueda, arXiv:1905.07217.
|title||Quantum fluctuations of vortex lattices and intercomponent entanglement spectra in binary Bose-Einstein condensates|
Synthetic gauge fields have been realized in ultracold atomic gases composed of two components. While mechanical rotation induces mutually parallel magnetic fields, optical dressing of atoms induces mutually antiparallel magnetic fields. It is useful to introduce the filling factor, which is the ratio of the number of atoms to the number of flux quanta piercing the system. Within the mean-field theory valid for high filling factors, binary Bose-Einstein condensates (BECs) under parallel and antiparallel fields are known to show the same ground-state phase diagrams that consist of a variety of vortex lattices depending on the ratio of the intercomponent interaction to the intracomponent one. In contrast, in the quantum Hall regime where the filling factor is of the order of unity, the ground-state phase diagrams are markedly different between the parallel- and antiparallel-field cases, especially in view of the entanglement formation between the two components. It is thus interesting to investigate the ground-state phase diagrams and the intercomponent entanglement entropy (EE) in the intermediate regime of the filling factor, say, of order of 10.
In this seminar, we demonstrate that the boundaries between different vortex-lattice phases shift appreciably as the filling factor is lowered. This is done by calculating the correction to the ground-state energy due to zero-point fluctuations in the Bogoliubov theory. Furthermore, we find that the intercomponent EE tends to be larger for repulsive (attractive) intercomponent interaction in the case of parallel (antiparallel) fields, which qualitatively agrees with the results for the quantum Hall regime.
We also present an extensive study on the intercomponent entanglement spectra (ES) in binary BECs. By means of effective field theory, we show that the intercomponent entanglement spectra for homogeneous binary BECs exhibits an anomalous square-root dispersion relation in the presence of an intercomponent tunneling and a gapped dispersion relation in its absence. For binary BECs under synthetic magnetic fields, where a variety of vortex lattices appear, the ES exhibits an anisotropic square-root dispersion relation, which is also confirmed by numerical calculations based on the Bogoliubov theory. We related these anomalous dispersion relations in the ES with the emergence of long-range interactions in the entanglement Hamiltonian.
|title||Deep reinforcement learning control of quantum cartpoles|
|abstract||We generalize a standard benchmark of reinforcement learning, the classical cartpole balancing problem, to the quantum regime by stabilizing a particle in an unstable potential through measurement and feedback. We use the state-of-the-art deep reinforcement learning to stabilize the quantum cartpole and find that our deep learning approach performs comparably to or better than other strategies in standard control theory. Our approach also applies to measurement-feedback cooling of quantum oscillators, showing the applicability of deep learning to general continuous-space quantum control. Especially, deep learning outperforms other known control strategies when the state is sufficiently non-Gaussian and difficult to analyze.|
|title||Generalization performance of deep and shallow neural networks for simple examples|
|abstract||Deep neural networks are successful at various tasks such as image classification and speech recognition. Despite their success, the theoretical understanding of deep neural networks is quite poor. There are indeed some mysteries in deep learning. There are huge number of parameters in deep neural networks. Then, why can we find a global minimum of the loss function with many degrees of freedom without trapping by bad local minima? More importantly, why do deep neural networks achieve such good generalization without overfitting? In my talk, I first review theoretical aspect of machine learning. I want to convey to you a message that modern machine learning is a fascinating subject not only from a practical point of view, but also from a theoretical point of view. Then, I explain my attempt to understand generalization performance of deep neural networks.|
|title||Thermodynamic Uncertainty Relation for Arbitrary Initial States|
In recent years, the thermodynamic uncertainty relation (TUR) , which sets a universal lower bound for the
product of current fluctuation and entropy production, was discovered as a fundamental principle of nonequilibrium
thermodynamics. However, previous TURs require either specific initial states or infinitely long time,
which severely limit their applications. Here we derive a finite-time TUR valid for arbitrary initial states via the Cramer-Rao inequality in information theory . We find that fluctuation of an accumulated current is bounded by
the final time instantaneous current. Our bound thus suggests that "the boundary is constrained by the bulk". We
illustrate our bound with two minimal models with equilibrium and nonequilibrium steady states, respectively.
We apply our results to feedback-control processes and explain a recent experiment which found a violation in
modified TUR for feedback control.|
 J. M. Horowitz and T. R. Gingrich, Nat. Phys. (2019), 10.1038/s41567-019-0702-6.
 K. Liu, Z. Gong, and M. Ueda, in preparation
|title||Laminar-turbulent transition in open quantum systems|
|abstract||Laminar-turbulent transition in classical fluids has been a central issue in fluid mechanics since a famous experiment by Reynolds in 19th century. This is a transition from a stationary and stable flow (Laminar flow) at low Reynolds number to a time-dependent flow characterized by irregular spatiotemporal dynamics (Turbulence) at high Reynolds number. How the notion of turbulence is defined in quantum many-body systems is an intriguing question considering the recent progress of the experimental technique in ultracold atomic gases. The purpose of this study is to seek for microscopic signatures of laminar-turbulent transition in a driven open quantum system. We consider a one-dimensional dissipative Bose-Hubbard model with a uniform driving that induces a stationary current. In the mean-field level, this model exhibits a laminar-turbulent transition at some critical flow momentum. By diagonalizing the Liouvillian superoperator of the quantum master equation, we find that for the turbulent phase there exist a nonzero gap in the spectrum, while for the laminar flow phase the gap vanishes in the thermodynamics limit.|
|title||Effective Volume and Entropic Force in Neural Networks|
|abstract||The study of neural networks using statistical physics began almost as early as the invention of artificial neural networks. In this work, we take a phenomenological approach in the hope to establish a statistical-physical model to study neural networks. In particular, we impose a boundary condition for parameters of a two layer neural network. Physically, this is equivalent to defining a physical volume in which the parameters travel, only affected by dissipation and the external potential. We demonstrate that, having a physical volume thus defined, we are able to observe many interesting phenomenon such as an entropic force between the parameters. This also makes definitions of physical quantities such as (effective) exclusion volume and pressure possible. If time allows, we will also discuss its implication for deep learning research.|
|title||Topological Origin of Non-Hermitian Skin Effects|
A unique feature of non-Hermitian systems is the skin effect [1,2], which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology . Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects --- symmetry-protected skin effects. In particular, we discover the Z2 skin effect protected by time-reversal symmetry. On the basis of topological classification , we also discuss possible other skin effects in arbitrary dimensions. Our work provides a unified understanding about the bulk-boundary correspondence and the skin effects in non-Hermitian systems.|
 S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).
 F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Phys. Rev. Lett. 121, 026808 (2019).
 N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, arXiv:1910.02878.
 K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Phys. Rev. X 9, 041015 (2019).
|title||SYK strange metal and spin freezing crossover|
|abstract||The Sachdev-Ye-Kitaev (SYK) model describes a strange metal state that shows anomalous non-Fermi liquid properties without quasiparticles and maximally scrambled behavior characterized by out-of-time-ordered correlators (OTOCs). While a faithful realization of the SYK model in condensed matter systems may be involved, there is a striking similarity between the SYK model and the spin-freezing crossover ("Hund metal" state) in multiorbital Hubbard models with Hund coupling. In this talk, we study OTOCs in Hubbard models using the dynamical mean-field theory and quantum Monte Carlo method, and discuss the relation between the SYK model and spin freezing crossover.|
|title||Typical properties of Local Hamiltonians|
Thermodynamics postulates that any macroscopic system thermalize after a sufficiently long time and statistical mechanics gives a way to calculate the values of observables at equilibrium as an ensemble average. This ensemble is a mixed state. On the other hand, the state of an isolated quantum system remains pure if it is initially in a pure state. Therefore, the state of an isolated quantum system cannot be a mixed state which is utilized in statistical mechanics. The eigenstate thermalization hypothesis (ETH) is a possible scenario for the thermalization of an isolated quantum system. As a possible justification of the ETH from quantum mechanics, P.Reimann gave a mathematically rigorous bound on the probability of the ETH breaking Hamiltonians. However, his argument is found to be inapplicable to realistic situations . In this seminar, we take locality into consideration so that the argument can be applied to realistic situations and estimate how many local Hamiltonians and observables satisfy the ETH by numerical calculation.|
 P.Reimann, Phys. Rev. Lett.115.010403 (2015)
 R.Hamazaki and M.Ueda, Phys. Rev. Lett.120.080603 (2018)
|speaker||Prof. Tanmoy Das (the Indian Institute of Science)|
|title||The non-Hermitian world|
Exploration of non-Hermitian systems dates back to the early days of quantum theory. However, the progress of this field has exploded in the recent years with the development of a parallel quantum theory, and experimental verifications. The key advantage is that the relaxation of the Hermiticity constraint opens up a huge phase space for many unique features that may or may not have any direct analog with the Hermitian counterparts. Furthermore, parity and time-reversal symmetries render a parallel quantum world with a new way of defining conservation laws and associated properties. With a short overview on these new developments, I shall focus the discussions on the new topological phases and non-Hermitian superconductors when Hermiticity constraint is removed and/or replaced with other symmetry constraints. I shall also touch upon some of the experimental demonstrations in Photonic crystals and future realization in quantum matters.|
 A. Ghatak and T. Das, arXiv:1902.07972.
 A. Ghatak and T. Das, Phys. Rev. B 97, 014512 (2018).
|speaker||Mr. Kazuki Yokomizo （Tokyo Institute of Technology）|
|title||Bloch Band Theory for Non-Hermitian Systems|
|abstract||Non-Hermitian systems, which are described by non-Hermitian Hamiltonians have been attracting much attention. In particular, the bulk-edge correspondence has been intensively studied in topological systems. In contrast to Hermitian systems, it seems to be violated in some cases. The reasons for this violation is that the Bloch wave vector is treated as real in non-Hermitian systems similarly to Hermitian ones. In this presentation, we establish a generalized band theory in a one-dimensional tight-binding model. In particular, we explain how to determine the generalized Brillouin zone C_β for the complex Bloch wave number β=e^ik, k∈C. In contrast to Hermitian cases, where C_β is always a unit circle, in non-Hermitian systems, C_β is a closed curve, not necessarily a unit circle. Furthermore, we find that C_β can have cusps, and its shape depends on system parameters. A byproduct of our theory is that one can prove the bulk-edge correspondence between the winding number defined from C_β and existence of topological edge states in the one-dimensional non-Hermitian systems.|
|speaker||Prof. Keiji Saito (Keio University)|
|title||Ensemble equivalence and eigenstate thermalization from clustering of correlation|
Clustering of an equilibrium bipartite correlation is widely observed in non-critical many-body quantum systems. In this talk, we consider the thermalization phenomenon in generic finite systems exhibiting clustering. We demonstrate that such classes of systems exhibit the ensemble equivalence between microcanonical and canonical ensembles even for subexponetially small energy shell with respect to the system size. Most remarkably, in low-energy regime, the thermalization for single eigenstate is proven. In this seminar, I will provide several examples satisfying the eigenstate thermalization. I will also explain several key-ingredients in mathematical aspect also. |
Ref.: T. Kuwahara and KS, arXiv:1905.01886.