ShantanuT01/DACTYL-Pretraining huggingface dataset:
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic classical computer, or is provably hard to simulate, depends quite critically on the precise notion of "classical simulation" and in particular on the required accuracy. We argue that a notion of classical simulation, which we call epsilon-simulation, captures the essence of possessing "equivalent computational power" as the quantum system it simulates: It is statistically impossible to distinguish an agent with access to an epsilon-simulator from one possessing the simulated quantum system. We relate epsilon-simulation to various alternative notions of simulation predominantly focusing on a simulator we call a poly-box. A poly-box outputs 1/poly precision additive estimates of Born probabilities and marginals. This notion of simulation has gained prominence through a number of recent simulability results. Accepting some plausible computational theoretic assumptions, we show that epsilon-simulation is strictly stronger than a poly-box by showing that IQP circuits and unconditioned magic-state injected Clifford circuits are both hard to epsilon-simulate and yet admit a poly-box. In contrast, we also show that these two notions are equivalent under an additional assumption on the sparsity of the output distribution (poly-sparsity).
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined globally in time for general initial data (with finite energy).
Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability etc.) for the processes are presented.
In this paper, we first analyze the horizon structure of the acoustic charged black hole in curved spacetime, and then study its acoustic shadow as well as the near-horizon characteristics including the quasinormal modes (QNM) frequencies and analogue Hawking radiation. We find that the radius of the acoustic shadow for acoustic charged black hole is larger than that for Reissner-Nordstr\"{o}m (RN) black hole, and both of them are suppressed by increasing the black hole charge because their related outer horizons become smaller. Then the QNM frequencies under scalar field perturbation and its eikonal limit are computed via numeric method and acoustic shadow, respectively. We find that the acoustic charged black hole is stable under the perturbation and the QNM frequencies are much weaker than that for the astrophysical black hole. Moreover, as the tuning parameter increases, the perturbation oscillates more mildly and its damping time becomes longer, while as the charge increases, the oscillation is enhanced slightly and the perturbation decays a little faster which is different from that in RN black hole. Finally, we numerically study the analogue Hawking radiation. We find that the grey-body factor and energy emission rate are suppressed by the angular number and the charge, but they do not monotonically depend on the tuning parameter in the acoustic charged black hole. The behavior of the energy emission rate affected by the parameters could be explained by the dependent behavior of the Hawking temperature. We expect that our results could shed light to the study of black holes in both theoretical and experimental perspectives.
We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.
A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our methodology. Provided a shape database, a graph encapsulating the structural relationships among all the available shapes, is first constructed and then employed in defining low-dimensional sparse projections. The recently introduced method of CRPs (collaborative representation based projections), which is based on L2-Graph, is the first variant that is included towards this end. A second algorithm, that particularizes the CRPs to shape descriptors that are inherently nonnegative, is also introduced as potential alternative. In both cases, the weights in the graph reflecting the database structure are calculated so as to approximate each shape as a sparse linear combination of the remaining dataset objects. By way of solving a generalized eigenanalysis problem, a linear matrix operator is designed that will act as the feature extractor. Two popular, inherently high dimensional descriptors, namely ShapeDNA and Global Point Signature (GPS), are employed in our experimentations with SHREC10, SHREC11 and SCHREC 15 datasets, where shape recognition is cast as a multi-class classification problem that is tackled by means of an SVM (support vector machine) acting within the reduced dimensional space of the crafted projections. The results are very promising and outperform state of the art methods, providing evidence about the highly discriminative nature of the introduced 3D shape representations.
In multiview geometry when correspondences among multiple views are unknown the image points can be understood as being unlabeled. This is a common problem in computer vision. We give a novel approach to handle such a situation by regarding unlabeled point configurations as points on the Chow variety $\text{Sym}_m(\mathbb{P}^2)$. For two unlabeled points we design an algorithm that solves the triangulation problem with unknown correspondences. Further the unlabeled multiview variety $\text{Sym}_m(V_A)$ is studied.
We present predictions based on the heavy quark expansion in QCD. We find SU(3) breaking in B mesons suppressed in the framework of the HQE. B_s is expected to have the semileptonic width about 1% lower and Lambda_b about 3% higher when compared to Gamma_{sl}(B_d). The largest partial-rate preasymptotic effect is Pauli interference in the b-->u ell nu channel in Lambda_b, about +10%. We point out that the Omega_b semileptonic width is expected not to exceed that of B_d and may turn out to be the smallest among stable b hadrons despite the large mass. The underlying differences with phase-space models are briefly addressed through the heavy mass expansion.
About a hundred tidal disruption events (TDEs) have been observed and they exhibit a wide range of emission properties both at peak and over their lifetimes. Some TDEs peak predominantly at X-ray energies while others radiate chiefly at UV and optical wavelengths. While the peak luminosities across TDEs show distinct properties, the evolutionary behavior can also vary between TDEs with similar peak emission properties. At late time, some optical TDEs rebrighten in X-rays, while others maintain strong UV/optical emission components. In this Letter, we conduct three-dimensional general relativistic radiation magnetohydrodynamics simulations of TDE accretion disks at varying accretion rates ranging from a few to a few tens of the Eddington accretion rate. We make use of Monte Carlo radiative transfer simulations to calculate the reprocessed spectra at various inclinations and at different evolutionary stages. We confirm the unified model proposed by Dai et al. (2018), which predicts that the observed emission largely depends on the viewing angle of the observer with respect to the disk orientation (X-ray strong when viewed face-on and UV/optically strong when viewed disk-on). What is more, we find that disks with higher accretion rates have elevated wind and disk densities, which increases the reprocessing of the high-energy radiation and thus generally augments the optical-to-X-ray flux ratio along a particular viewing angle. This implies that at later times, as the accretion level declines, we expect the funnel to effectively open up and allow more X-rays to leak out along intermediate viewing angles. Such dynamical model for TDEs can provide a natural explanation for the diversity in the emission properties observed in TDEs at peak and along their temporal evolution.
It is shown using a space-time curvature classification and decomposition that for certain holonomy types of a space-time, proper projective vector fields cannot exist. Existence is confirmed, by example, for the remaining holonomy types. In all except the most general holonomy type, a local uniqueness theorem for proper projective symmetry is established.
We show that the fractional Laplacian on $\mathbb{R}^d$ fails to satisfy the Bakry-\'Emery curvature-dimension inequality $CD(\kappa,N)$ for all curvature bounds $\kappa\in \mathbb{R}$ and all finite dimensions $N>0$.
We calculate the partition function of the $SU(N)$ ( and $U(N)$) generalized $YM_2$ theory defined on an arbitrary Riemann surface. The result which is expressed as a sum over irreducible representations generalizes the Rusakov formula for ordinary YM_2 theory. A diagrammatic expansion of the formula enables us to derive a Gross-Taylor like stringy description of the model. A sum of 2D string maps is shown to reproduce the gauge theory results. Maps with branch points of degree higher than one, as well as ``microscopic surfaces'' play an important role in the sum. We discuss the underlying string theory.
Recent semi-supervised learning methods use pseudo supervision as core idea, especially self-training methods that generate pseudo labels. However, pseudo labels are unreliable. Self-training methods usually rely on single model prediction confidence to filter low-confidence pseudo labels, thus remaining high-confidence errors and wasting many low-confidence correct labels. In this paper, we point out it is difficult for a model to counter its own errors. Instead, leveraging inter-model disagreement between different models is a key to locate pseudo label errors. With this new viewpoint, we propose mutual training between two different models by a dynamically re-weighted loss function, called Dynamic Mutual Training (DMT). We quantify inter-model disagreement by comparing predictions from two different models to dynamically re-weight loss in training, where a larger disagreement indicates a possible error and corresponds to a lower loss value. Extensive experiments show that DMT achieves state-of-the-art performance in both image classification and semantic segmentation. Our codes are released at https://github.com/voldemortX/DST-CBC .
The X-ray and radio flares observed in X-ray binaries and active galactic nuclei (AGN) are attributed to energetic electrons in the plasma ejecta from the accretion flows near the black hole in these systems. It is argued that magnetic reconnection could occur in the coronae above the accretion disk around the black hole, and that this drives plasmoid outflows resembling the solar coronal mass ejection (CME) phenomenon. The X-ray and radio flares are emission from energetic electrons produced in the process. As the emission region is located near the black hole event horizon, the flare emission would be subject to special- and general-relativistic effects. We present calculations of the flaring emission from plasmoids orbiting around a black hole and plasmoid ejecta launched from the inner accretion disk when general-relativistic effects are crucial in determining the observed time-dependent properties of the emission. We consider fully general-relativistic radiative transfer calculations of the emission from evolving ejecta from black hole systems, with proper accounting for differential arrival times of photons emitted from the plasmoids, and determine the emission lightcurves of plasmoids when they are in orbit and when they break free from their magnetic confinement. The implications for interpreting time-dependent spectroscopic observations of flaring emission from accreting black holes are discussed.
Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized volume of the convex hull of their union. Under these conditions the problem of computing mixed volume of several polytopes can be transformed into a volume computation problem for a single polytope in the same dimension. We demonstrate through problems from real world applications that substantial reduction in computational costs can be achieved via this transformation in situations where the convex hull of the union of the polytopes has less complex geometry than the original polytopes. We also discuss the important implications of this result in the polyhedral homotopy method for solving polynomial systems.
We define a three parameter family of Bell pseudo-involutions in the Riordan group. The defining sequences have generating functions that are expressible as continued fractions. We indicate that the Hankel transforms of the defining sequences, and of the $A$ sequences of the corresponding Riordan arrays, can be associated with Somos $4$ sequence. We give examples where these sequences can be associated with elliptic curves, and we exhibit instances where elliptic curves can give rise to associated Riordan pseudo-involutions. In the case of a particular one parameter family of elliptic curves, we show how we can associate to each such curve a unique Bell pseudo-involution.
Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic solution to the Einstein equations with cosmological constant. However, as discussed here, it is not the most general, locally isotropic solution. One can construct an infinite family of such solutions, designer de Sitter spacetimes, which are everywhere locally isometric to a region of de Sitter spacetime. However, the global dynamics of these designer cosmologies is very different than that of de Sitter spacetime itself. The construction and dynamics of these designer de Sitter spacetimes is detailed along with some comments about their implications for the structure of our universe.
Spin-crossover (SCO) molecules are versatile magnetic switches with applications in molecular electronics and spintronics. Downscaling devices to the single-molecule level remains, however, a challenging task since the switching mechanism in bulk is mediated by cooperative intermolecular interactions. Here, we report on electron transport through individual Fe-SCO molecules coupled to few-layer graphene electrodes \textit{via} $\pi - \pi$ stacking. We observe a distinct bistability in the conductance of the molecule and a careful comparison with density functional theory (DFT) calculations allows to associate the bistability with a SCO-induced orbital reconfiguration of the molecule. We find long spin-state lifetimes that are caused by the specific coordination of the magnetic core and the absence of intermolecular interactions according to our calculations. In contrast with bulk samples, the SCO transition is not triggered by temperature but induced by small perturbations in the molecule at any temperature. We propose plausible mechanisms that could trigger the SCO at the single-molecule level.
We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. In the case of deterministic and non-negative integrands, our estimates involve only the third moment of integrand in addition to a variance term using a square norm of the integrand. As a consequence, we are able to observe a "third moment phenomenon" in which the vanishing of the first cumulant can lead to faster convergence rates. Our results are also applied to compound Hawkes processes, and improve on the current literature where estimates may not converge to zero in large time, or have been obtained only for specific kernels such as the exponential or Erlang kernels.
We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a classical continuous-time Markov chain. The quantum jump method is well known in the quantum optics community and has also been applied to simulate open quantum walks in discrete time. This method however, is well-suited to continuous-time problems. It is shown here that a continuous-time hitting problem is amenable to analysis via quantum jumps: The hitting time can be defined as the time of the first jump. Using this fact, we derive the distribution of hitting times and explicit exressions for its statistical moments. Simple examples are considered to illustrate the final results. We then show that the hitting statistics obtained via quantum jumps is consistent with a previous definition for a measured walk in discrete time [Phys.~Rev.~A~{\bf 73}, 032341 (2006)] (when generalised to allow for non-unitary evolution and in the limit of small time steps). A caveat of the quantum-jump approach is that it relies on the final state (the state which we want to hit) to share only incoherent edges with other vertices in the graph. We propose a simple remedy to restore the applicability of quantum jumps when this is not the case and show that the hitting-time statistics will again converge to that obtained from the measured discrete walk in appropriate limits.
Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zerm\'elo's paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the {\it irreversible} Second Law of Thermodynamics (Loschmidt's) as well as {\it periodic} in the time (Zerm\'elo's, illustrating Poincar\'e recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems.   The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals' information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here. We review our investigations presented in Budapest in 1997 and end with presentday questions posed as the Snook Prize Problems in 2020 and 2021.
This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the properties of this random walk concerning strong approximations, local times and range. We give a survey of these results together with some further problems.
We prove continuity up to the boundary of the minimizer of an obstacle problem and higher integrability of its gradient under generalized Orlicz growth. The result recovers similar results obtained in the special cases of polynomial growth, variable exponent growth and produces new results for Orlicz and double phase growth.
Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property. For the first time, we investigate the quantitative uniqueness of higher order elliptic equations and show the vanishing order of solutions. Furthermore, strong unique continuation is established for higher order elliptic equations using this variant of frequency function.
We present a geometric characterization of the ferrotoroidic moment in terms of a set of Abelian Berry phases. We also introduce a fundamental complex quantity which provides an alternative way to calculate the ferrotoroidic moment and its moments, and is derived from a second order tensor. This geometric framework defines a natural computational approach for density functional and many-body theories.
After operations at the LHC and e^+e^- Linear Colliders it may be found that a Standard-Model-like scenario is realized. In this scenario no new particle will be discovered, except a single Higgs boson having partial widths or coupling constants squared with fundamental particles close, within anticipated experimental uncertainty, to those of the SM. Experiments at a Photon Collider can resolve whether the SM model or e.g. the Two Higgs Doublet Model is realized in Nature.   For the SM-like version of the 2HDM (II) we study the loop couplings of the Higgs boson with \gamma\gamma and Z \gamma, and also with gluons. The deviation of the two-photon width from its SM value is generally higher than the expected inaccuracy in the measurement of \Gamma_{\gamma \gamma} at a Photon Collider. The result is sensitive to the parameters of the Higgs self interaction.
An overview of the Pondicherry interpretation of quantum mechanics is presented. This interpretation proceeds from the recognition that the fundamental theoretical framework of physics is a probability algorithm, which serves to describe an objective fuzziness (the literal meaning of Heisenberg's term "Unschaerfe," usually mistranslated as "uncertainty") by assigning objective probabilities to the possible outcomes of unperformed measurements. Although it rejects attempts to construe quantum states as evolving ontological states, it arrives at an objective description of the quantum world that owes nothing to observers or the goings-on in physics laboratories. In fact, unless such attempts are rejected, quantum theory's true ontological implications cannot be seen. Among these are the radically relational nature of space, the numerical identity of the corresponding relata, the incomplete spatiotemporal differentiation of the physical world, and the consequent top-down structure of reality, which defies attempts to model it from the bottom up, whether on the basis of an intrinsically differentiated spacetime manifold or out of a multitude of individual building blocks.