|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.
|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.