Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla.

In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system-environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure.

Specifying the Unitary Evolution of a Qudit for a General Nonstationary Hamiltonian via the Generalized Gell-Mann Representation.

Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a -level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit ( d ≥ 2 ) in terms of the Bloch-like vector space and specify how, in a general case, this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case ( d = 2 ) , we specify the unitary evolution of a qubit via the evolution of a unit vector in R 4 , and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians.

p-Adic mathematics and theoretical biology.

The principal objective of this article is a brief overview of the main parts of p-adic mathematics, which have already had valuable applications and may have a significant impact in the near future on the further development of some fields of theoretical and mathematical biology. In particular, we present the basics of ultrametrics, p-adic numbers and p-adic analysis, as well as insight into their applications for modeling some cognitive processes, genetic code and protein dynamics. We also argue that ultrametric concepts and p-adic mathematics are natural tools for the viable description of biological systems and phenomena with a hierarchical structure.

Bosonic Quantum Communication across Arbitrarily High Loss Channels.

A general attenuator Φ_{λ,σ} is a bosonic quantum channel that acts by combining the input with a fixed environment state σ in a beam splitter of transmissivity λ. If σ is a thermal state, the resulting channel is a thermal attenuator, whose quantum capacity vanishes for λ≤1/2. We study the quantum capacity of these objects for generic σ, proving a number of unexpected results.

Tilings by hexagonal prisms and embeddings into primitive cubic networks.

All possible combinatorial embeddings into primitive cubic networks of arbitrary tilings of 3D space by pairwise congruent and parallel regular hexagonal prisms are discussed and classified.

Exactly Solvable Magnet of Conformal Spins in Four Dimensions.

We provide the eigenfunctions for a quantum chain of N conformal spins with nearest-neighbor interaction and open boundary conditions in the irreducible representation of SO(1,5) of scaling dimension Δ=2-iλ and spin numbers ℓ=ℓ[over ˙]=0. The spectrum of the model is separated into N equal contributions, each dependent on a quantum number Y_{a}=[ν_{a},n_{a}] which labels a representation of the principal series. The eigenfunctions are orthogonal and we computed the spectral measure by means of a new star-triangle identity.

Machine Learning Non-Markovian Quantum Dynamics.

Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects.

Effect of a small loss or gain in the periodic nonlinear Schrödinger anomalous wave dynamics.

The focusing nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability of quasimonochromatic waves in weakly nonlinear media, the main physical mechanism for the appearance of anomalous (rogue) waves (AWs) in nature. In this paper, concentrating on the simplest case of a single unstable mode, we study the special Cauchy problem for the NLS equation perturbed by a linear loss or gain term, corresponding to periodic initial perturbations of the unstable background solution of the NLS. Using the finite gap method and the theory of perturbations of soliton partial differential equations, we construct the proper analytic model describing quantitatively how the solution evolves after a suitable transient into slowly varying lower dimensional patterns (attractors) on the (x,t) plane, characterized by ΔX=L/2 in the case of loss and by ΔX=0 in the case of gain, where ΔX is the x shift of the position of the AW during the recurrence, and L is the period.

Multiple features for clinical relation extraction: A machine learning approach.

Relation extraction aims to discover relational facts about entity mentions from plain texts. In this work, we focus on clinical relation extraction; namely, given a medical record with mentions of drugs and their attributes, we identify relations between these entities. We propose a machine learning model with a novel set of knowledge-based and BioSentVec embedding features.

Uncomputability and complexity of quantum control.

In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e.

Structural Transition States Explored With Minimalist Coarse Grained Models: Applications to Calmodulin.

Transitions between different conformational states are ubiquitous in proteins, being involved in signaling, catalysis, and other fundamental activities in cells. However, modeling those processes is extremely difficult, due to the need of efficiently exploring a vast conformational space in order to seek for the actual transition path for systems whose complexity is already high in the stable states. Here we report a strategy that simplifies this task attacking the complexity on several sides.

Calculation of coherences in Förster and modified Redfield theories of excitation energy transfer.

Förster and modified Redfield theories play one of the central roles in the description of excitation energy transfer in molecular systems. However, in the present state, these theories describe only the dynamics of populations of local electronic excitations or delocalized exciton eigenstates, respectively, i.e.

Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems.

Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particles and harmonic systems evolving in a bounded phase-space in such a way that entropy is nonconserved.

Simulation Complexity of Open Quantum Dynamics: Connection with Tensor Networks.

The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective small reservoirs can be defined and used for modeling open quantum dynamics. The key element of our technique is the timeline reservoir network (TRN), which contains all the information on the reservoir's characteristics, in particular, the memory effects timescale.

On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular.

Medical concept normalization in social media posts with recurrent neural networks.

Text mining of scientific libraries and social media has already proven itself as a reliable tool for drug repurposing and hypothesis generation. The task of mapping a disease mention to a concept in a controlled vocabulary, typically to the standard thesaurus in the Unified Medical Language System (UMLS), is known as medical concept normalization. This task is challenging due to the differences in the use of medical terminology between health care professionals and social media texts coming from the lay public.

Impact of the Injection Protocol on an Impurity's Stationary State.

We examine stationary-state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of the Landau approach to superfluidity.

Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe.

The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space.

Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics.

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point.

druGAN: An Advanced Generative Adversarial Autoencoder Model for de Novo Generation of New Molecules with Desired Molecular Properties in Silico.

Deep generative adversarial networks (GANs) are the emerging technology in drug discovery and biomarker development. In our recent work, we demonstrated a proof-of-concept of implementing deep generative adversarial autoencoder (AAE) to identify new molecular fingerprints with predefined anticancer properties. Another popular generative model is the variational autoencoder (VAE), which is based on deep neural architectures.

Destabilization of rotating flows with positive shear by azimuthal magnetic fields.

According to Rayleigh's criterion, rotating flows are linearly stable when their specific angular momentum increases radially outward. The celebrated magnetorotational instability opens a way to destabilize those flows, as long as the angular velocity is decreasing outward. Using a local approximation we demonstrate that even flows with very steep positive shear can be destabilized by azimuthal magnetic fields which are current free within the fluid.

Modeling conformational redox-switch modulation of human succinic semialdehyde dehydrogenase.

Succinic semialdehyde dehydrogenase (SSADH) converts succinic semialdehyde (SSA) to succinic acid in the mitochondrial matrix and is involved in the metabolism of the inhibitory neurotransmitter γ-aminobutyric acid (GABA). The molecular structure of human SSADH revealed the intrinsic regulatory mechanism--redox-switch modulation--by which large conformational changes are brought about in the catalytic loop through disulfide bonding. The crystal structures revealed two SSADH conformations, and computational modeling of transformation between them can provide substantial insights into detailed dynamic redox modulation.

Quantum state majorization at the output of bosonic Gaussian channels.

Quantum communication theory explores the implications of quantum mechanics to the tasks of information transmission. Many physical channels can be formally described as quantum Gaussian operations acting on bosonic quantum states. Depending on the input state and on the quality of the channel, the output suffers certain amount of noise.

Quantum channels and their entropic characteristics.

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of a quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems.