arXiv subjects

Masahito Ueda

Publications and source records attributed to Masahito Ueda.

At least 73 records · Page 4Linked to original sources

arXiv2020

Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

Contrary to the conventional wisdom in Hermitian systems, a continuous quantum phase transition between gapped phases is shown to occur without closing the energy gap $Δ$ in non-Hermitian quantum many-body systems. Here, the relevant length scale $ξ\simeq v_{\rm LR}/Δ$ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i.e., unboundedness of $v_{\rm LR}$) rather than vanishing of the energy gap $Δ$. The susceptibility to a change in the system parameter exhibits a singularity due to nonorthogonality of eigenstates. As an illustrative example, we present an exactly solvable model by generalizing Kitaev's toric-code model to a non-Hermitian regime.

cond-mat.stat-mech↗

arXiv2020

Effective temperature of a superfluid flowing in a random potential

The spatial fluctuations of a superfluid flowing in a weak random potential are investigated. We employ classical field theory to demonstrate that the disorder-averaged nonequilibrium second-order correlation of the order parameter at zero temperature is identical to the thermally averaged equilibrium counterpart of a uniform superfluid at an effective temperature. The physics behind this equivalence is that scattering of a moving condensate by disorder has the same effect on the correlation function as equilibrium thermal excitations. The correlation function exhibits an exponential decay in one dimension and a power-law decay in two dimensions. We show that the effective temperature can be measured in an interference experiment of ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2020

Neural Networks Fail to Learn Periodic Functions and How to Fix It

Previous literature offers limited clues on how to learn a periodic function using modern neural networks. We start with a study of the extrapolation properties of neural networks; we prove and demonstrate experimentally that the standard activations functions, such as ReLU, tanh, sigmoid, along with their variants, all fail to learn to extrapolate simple periodic functions. We hypothesize that this is due to their lack of a "periodic" inductive bias. As a fix of this problem, we propose a new activation, namely, $x + \sin^2(x)$, which achieves the desired periodic inductive bias to learn a periodic function while maintaining a favorable optimization property of the ReLU-based activations. Experimentally, we apply the proposed method to temperature and financial data prediction.

cs.LG↗

arXiv2020

Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory

We verify that the eigenstate thermalization hypothesis (ETH) holds universally for locally interacting quantum many-body systems. Introducing random-matrix ensembles with interactions, we numerically obtain a distribution of maximum fluctuations of eigenstate expectation values for different realizations of the interactions. This distribution, which cannot be obtained from the conventional random matrix theory involving nonlocal correlations, demonstrates that an overwhelming majority of pairs of local Hamiltonians and observables satisfy the ETH with exponentially small fluctuations. The ergodicity of our random matrix ensembles breaks down due to locality.

cond-mat.stat-mech↗

arXiv2020

Improved generalization by noise enhancement

Recent studies have demonstrated that noise in stochastic gradient descent (SGD) is closely related to generalization: A larger SGD noise, if not too large, results in better generalization. Since the covariance of the SGD noise is proportional to $η^2/B$, where $η$ is the learning rate and $B$ is the minibatch size of SGD, the SGD noise has so far been controlled by changing $η$ and/or $B$. However, too large $η$ results in instability in the training dynamics and a small $B$ prevents scalable parallel computation. It is thus desirable to develop a method of controlling the SGD noise without changing $η$ and $B$. In this paper, we propose a method that achieves this goal using ``noise enhancement'', which is easily implemented in practice. We expound the underlying theoretical idea and demonstrate that the noise enhancement actually improves generalization for real datasets. It turns out that large-batch training with the noise enhancement even shows better generalization compared with small-batch training.

cs.LG↗

arXiv2020

Deep Reinforcement Learning Control of Quantum Cartpoles

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 state-of-the-art deep reinforcement learning to stabilize a 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.

quant-ph↗

arXiv2020

Thermodynamic Uncertainty Relation for Arbitrary Initial States

The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs presuppose either specific initial states or an infinite-time average, which severely limits the range of applicability. Here we derive a finite-time TUR valid for arbitrary initial states from the Cramér-Rao inequality. We find that the variance of an accumulated current is bounded by the instantaneous current at the final time, which suggests that ``the boundary is constrained by the bulk". We apply our results to feedback-controlled processes and successfully explain a recent experiment which reports a violation of a modified TUR with feedback control. We also derive a TUR that is linear in the total entropy production and valid for discrete-time Markov chains with non-steady initial states. The obtained bound exponentially improves the existing bounds in a discrete-time regime.

cond-mat.stat-mech↗

arXiv2020

Universality classes of non-Hermitian random matrices

Non-Hermitian random matrices have been utilized in such diverse fields as dissipative and stochastic processes, mesoscopic physics, nuclear physics, and neural networks. However, the only known universal level-spacing statistics is that of the Ginibre ensemble characterized by complex-conjugation symmetry. Here we report our discovery of two other distinct universality classes characterized by transposition symmetry. We find that transposition symmetry alters repulsive interactions between two neighboring eigenvalues and deforms their spacing distribution. Such alteration is not possible with other symmetries including Ginibre's complex-conjugation symmetry which can affect only nonlocal correlations. Our results complete the non-Hermitian counterpart of Wigner-Dyson's threefold universal statistics of Hermitian random matrices and serve as a basis for characterizing nonintegrability and chaos in open quantum systems with symmetry.

cond-mat.stat-mech↗

arXiv2020

Non-Hermitian Physics

A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, firstly given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.

cond-mat.mes-hall↗

arXiv2020

Dynamical sign reversal of magnetic correlations in dissipative Hubbard models

In quantum magnetism, the virtual exchange of particles mediates an interaction between spins. Here, we show that an inelastic Hubbard interaction fundamentally alters the magnetism of the Hubbard model due to dissipation in spin-exchange processes, leading to sign reversal of magnetic correlations in dissipative quantum dynamics. This mechanism is applicable to both fermionic and bosonic Mott insulators, and can naturally be realized with ultracold atoms undergoing two-body inelastic collisions. The dynamical reversal of magnetic correlations can be detected by using a double-well optical lattice or quantum-gas microscopy, the latter of which facilitates the detection of the magnetic correlations in one-dimensional systems because of spin-charge separation. Our results open a new avenue toward controlling quantum magnetism by dissipation.

cond-mat.quant-gas↗

arXiv2020

Volumization as a Natural Generalization of Weight Decay

We propose a novel regularization method, called \textit{volumization}, for neural networks. Inspired by physics, we define a physical volume for the weight parameters in neural networks, and we show that this method is an effective way of regularizing neural networks. Intuitively, this method interpolates between an $L_2$ and $L_\infty$ regularization. Therefore, weight decay and weight clipping become special cases of the proposed algorithm. We prove, on a toy example, that the essence of this method is a regularization technique to control bias-variance tradeoff. The method is shown to do well in the categories where the standard weight decay method is shown to work well, including improving the generalization of networks and preventing memorization. Moreover, we show that the volumization might lead to a simple method for training a neural network whose weight is binary or ternary.

cs.LG↗

arXiv2020

Learning Not to Learn in the Presence of Noisy Labels

Learning in the presence of label noise is a challenging yet important task: it is crucial to design models that are robust in the presence of mislabeled datasets. In this paper, we discover that a new class of loss functions called the gambler's loss provides strong robustness to label noise across various levels of corruption. We show that training with this loss function encourages the model to "abstain" from learning on the data points with noisy labels, resulting in a simple and effective method to improve robustness and generalization. In addition, we propose two practical extensions of the method: 1) an analytical early stopping criterion to approximately stop training before the memorization of noisy labels, as well as 2) a heuristic for setting hyperparameters which do not require knowledge of the noise corruption rate. We demonstrate the effectiveness of our method by achieving strong results across three image and text classification tasks as compared to existing baselines.

cs.LG↗

arXiv2020

Standard Quantum Limit and Heisenberg Limit in Function Estimation

Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees of smooth functions are considered. The error bounds are identified in both cases of absence and presence of interparticle entanglement, which correspond to the standard quantum limit and the Heisenberg limit, respectively. Notably, these error bounds can be reached by either position-localized states or wavenumber-localized ones. In fact, we show that these error bounds are theoretically optimal for any type of probe states, indicating that quantum metrology on functions is also subject to the Nyquist-Shannon sampling theorem, even if classical detection is replaced by quantum measurement.

quant-ph↗

arXiv2019

Magnetic solitons in a spin-1 Bose-Einstein condensate

Vector solitons are a type of solitary, or non-spreading wavepacket occurring in a nonlinear medium comprised of multiple components. As such, a variety of synthetic systems can be constructed to explore their properties, from nonlinear optics to ultracold atoms, and even in human-scale metamaterials. In quantum systems such as photons or Bose-Einstein condensates (BECs), such vector nonlinearities offer a window into complex many-body dynamics, and offer possibilities for quantum communication and information processing. BECs have a rich panoply of internal hyperfine levels, or spin components, which make them a unique platform for exploring these solitary waves. However, existing experimental work has focused largely on binary systems confined to the Manakov limit of the nonlinear equations governing the soliton behavior, where quantum magnetism plays no role. Here we observe, using a ``magnetic shadowing'' technique, a new type of soliton in a spinor BEC, one that exists only when the underlying interactions are antiferromagnetic, and which is deeply embedded within a full spin-1 quantum system. Our approach opens up a vista for future studies of ``solitonic matter'' whereby multiple solitons interact with one another at deterministic locations, and eventually to the realization of quantum correlated states of solitons, a longstanding and unrealized goal.

cond-mat.quant-gas↗

arXiv2019

Symmetry and Topology in Non-Hermitian Physics

We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, point-like and line-like vacant regions. On the basis of these concepts and K-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons.

cond-mat.mes-hall↗

arXiv2019

Robustness of cluster states and surface code states against random local fields

In ideal quantum circuits, qubits are tacitly assumed to be uniformly fabricated and operated by prescribed signals. In reality, however, we must cope with different control signals to adjust individual qubits, which requires a large overhead of control circuits. Here, we theoretically investigate how random local fields affect cluster states and surface code states which constitute the key highly entangled states in quantum computation. We find similar behavior of temporal degradation of the fidelity for both cluster states and surface code states for the number of qubits up to ten. We find that the effect of local field fluctuations is greatly mitigated if the magnitude of fluctuations can be suppressed below 10 % of the energy gap $Δ$ for both cluster states and surface code states. If the magnitude of fluctuations exceeds $Δ/2$, the fidelity for both states deteriorates dramatically. A simple estimation based on the average fidelity up to $t\sim 2\hbar/Δ$ shows that the maximum number of qubits that can be corrected with the 1 % error threshold is less than 31 for surface code states and 27 for cluster states. This means that the error correction should be carried out during a time shorter than $2\hbar/Δ$.

quant-ph↗

arXiv2019

Deep Gamblers: Learning to Abstain with Portfolio Theory

We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class classification problem to $(m+1)$-class where the $(m+1)$-th class represents the model abstaining from making a prediction due to disconfidence. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. Minimizing this loss function corresponds naturally to maximizing the return of a \textit{horse race}, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the disconfidence of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or model architecture. Experiments show that our method can identify uncertainty in data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.

cs.LG↗

arXiv2019

Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of non-diagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.

cond-mat.quant-gas↗