ShantanuT01/DACTYL-Pretraining huggingface dataset:
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix, which can be non-unitary, in an efficient way. We also give both classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations, and the quantum complexities of them are almost the same as non-general circuits.
We aim to characterize the distribution and composition of circumstellar material around young massive stars, and to investigate exactly which physical structures in these objects are probed by long-baseline mid-infrared interferometric observations. We used the two-telescope interferometric instrument MIDI of the Very Large Telescope Interferometer of the European Southern Observatory to observe a sample of 24 intermediate- and high-mass young stellar objects in the N band (8-13 micron). We had successful fringe detections for 20 objects, and present spectrally-resolved correlated fluxes and visibility levels for projected baselines of up to 128 m. We fit the visibilities with geometric models to derive the sizes of the emitting regions, as well as the orientation and elongation of the circumstellar material. Fourteen objects in the sample show the 10 micron silicate feature in absorption in the total and correlated flux spectra. For 13 of these objects, we were able to fit the correlated flux spectra with a simple absorption model, allowing us to constrain the composition and absorptive properties of the circumstellar material. Nearly all of the massive young stellar objects observed show significant deviations from spherical symmetry at mid-infrared wavelengths. In general, the mid-infrared emission can trace both disks and outflows, and in many cases it may be difficult to disentangle these components on the basis of interferometric data alone, because of the sparse spatial frequency coverage normally provided by current long-baseline interferometers. For the majority of the objects in this sample, the absorption occurs on spatial scales larger than those probed by MIDI. Finally, the physical extent of the mid-infrared emission around these sources is correlated with the total luminosity, albeit with significant scatter.
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
A k-quantum nonlinear Jaynes-Cummings model for two trapped ions interacting with laser beams resonant to k-th red side-band of center-of-mass mode, far from Lamb-Dicke regime, has been obtained. The exact analytic solution showed the existence of quantum collapses and revivals of the occupation of two atoms.
The epitaxial growth of the polar GaP(100) on the nonpolar Si(100) substrate suffers from inevitable defects at the antiphase domain boundaries, resulting from mono-atomic steps on the Si(100) surface. Stabilization of Si(100) substrate surfaces with arsenic is a promising technological step enabling the preparation of Si substrates with double atomic steps and reduced density of the APDs. In this paper, 4-50 nm thick GaP epitaxial films were grown on As-terminated Si(100) substrates with different types of doping, miscuts, and As-surface termination by metalorganic vapor phase epitaxy. The GaP(As)/Si(100) heterostructures were investigated by X-ray photoelectron spectroscopy (XPS) combined with gas cluster ion beam (GCIB) sputtering and by hard X-ray photoelectron spectroscopy (HAXPES). We found residuals of arsenic atoms in the GaP lattice (0.2-0.3 at.%) and a localization of As atoms at the GaP(As)/Si(100) interface (1 at.%). Deconvolution of core level peaks revealed interface core level shifts. In As core levels, chemical shifts between 0.5-0.8 eV were measured and identified by angle-resolved XPS measurements. Similar valence band offset (VBO) values of 0.6 eV were obtained, regardless of the doping type of Si substrate, Si substrate miscut or type of As-terminated Si substrate surface. The band alignment diagram of the heterostructure was deduced.
We evaluate the electric dipole absorption in small metal particles in a longitudinal electric field taking into account the Fermi-Thomas screening. When either the level broadening or the frequency of the field are larger than the mean energy-level spacing, the main contribution to absorption is classical, with quantum corrections. When both the broadening and the frequency are smaller than the mean level spacing, the absorption is manifestly quantum and can be understood in terms of the two-level system.
A new phenomenological model is proposed to describe the evolution of the Fermi surface (FS) in a wide range of dopings. It reproduces the key features of the cuprates in the underdoped phase above the superconducting temperature $T_c$. It is shown that the explicit accounting of strong electron correlation in the framework of the $t-J$ model taken in complementary to the translational symmetry breaking induced by the charge density wave (CDW) gives rise to the Fermi surface reconstruction (FSR) into small electron pockets. While the strong Coulomb repulsion leads to an emergence of the arc-like Fermi surface in the pseudogap (PG) phase, the Bragg reflection on the boundaries of the reduced Brillouin zone (BZ) opens up a possibility to close the quasiparticle orbits. Direct calculation of the FS properties allows us to unveil the scenario of the experimentally observed transition to the CDW phase that sets in at the doping level $\delta\approx0.08$ and is accompanied by a divergence of the carriers effective mass and the sign reversals of the Hall and Seebeck coefficients.
The multplicative order of an integer g modulo a prime p, with p coprime to g, is defined to be the smallest positive integer k such that g^k is congruent to 1 modulo p. For fixed integers g and d the distribution of this order over residue classes mod d is considered as p runs over the primes.   An overview is given of the most significant of my results on this problem obtained (mainly) in the three part series of papers `On the distribution of the order and index of g (modulo p) over residue classes' I-III (appeared in the Journal of Number Theory, also available from the ArXiv).
Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespectively of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.
Boundary-engineering in nanostructures has the potential to dramatically impact the development of materials for high-efficiency conversion of thermal energy directly into electricity. In particular, nanostructuring of semiconductors can lead to strong suppression of heat transport with little degradation of electrical conductivity. Although this combination of material properties is promising for thermoelectric materials, it remains largely unexplored. In this work, we introduce a novel concept, the directional phonon suppression function, to unravel boundary-dominated heat transport in unprecedented detail. Using a combination of density functional theory and the Boltzmann transport equation, we compute this quantity for nanoporous silicon materials. We first compute the thermal conductivity for the case with aligned circular pores, confirming a significant thermal transport degradation with respect to the bulk. Then, by analyzing the information on the directionality of phonon suppression in this system, we identify a new structure of rectangular pores with the same porosity that enables a four-fold decrease in thermal transport with respect to the circular pores. Our results illustrate the utility of the directional phonon suppression function, enabling new avenues for systematic thermal conductivity minimization and potentially accelerating the engineering of next-generation thermoelectric devices.
The optimal measurement configuration, i.e., the optimal input quantum state and measurement in the form of a POVM with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined as the contracting directions of the channel with an arbitrary fixed basis of Pauli- matrices. In the qubit Pauli channel case with known channel directions it is shown that the optimal configuration that maximizes the Fisher information of the estimated parameters consists of three von Neumann measurements together with pure input states directed to the appropriate channel directions. Extensions of these results for generalized Pauli channels are also given. Furthermore, a computationally efficient estimation method is proposed for estimating the channel directions in the qubit Pauli channel case. The efficiency of this method is illustrated by simulations: it is shown that its variance is of order 1/N, where N is the number of used measurements.
We consider a fractional Schr\"{o}dinger-Poisson system with a general nonlinearity in subcritical and critical case. The Ambrosetti-Rabinowitz condition is not required. By using a perturbation approach, we prove the existence of positive solutions. Moreover, we study the asymptotics of solutions for a vanishing parameter.
Let (A,L) be a principally polarized abelian surface of type (1,3). The linear system |L| defines a 6:1 covering of A onto P2, branched along a curve B of degree 18 in P2. The main result of the paper is that for general (A,L) the curve B irreducible, admits 72 cusps, 36 nodes or tacnodes, each tacnode counting as two nodes, 72 flexes and 36 bitangents. The main idea of the proof is to use the fact that for a general (A,L) of type (1,3) the closure of the Severi variety V in |L| is dual to the curve B in the sense of projective geometry. We investigate V and B via degeneration to a special abelian surface.
We present results of large N-body-hydrodynamic simulations of galaxy formation. Our simulations follow the formation of galaxies in cubic volumes of side 100Mpc, in two versions of the cold dark matter (CDM) cosmogony: the standard, Omega=1 SCDM model and the flat, Omega=0.3 LCDM model. Over 2000 galaxies form in each of these simulations. We examine the rate at which gas cools and condenses into dark matter halos. This roughly tracks the cosmic star formation rate inferred from observations at various redshifts. Galaxies in the simulations form gradually over time in the hierarchical fashion characteristic of the CDM cosmogony. In the LCDM model, substantial galaxies first appear at z=5 and the population builds up rapidly until z=1 after which the rate of galaxy formation declines as cold gas is consumed and the cooling time of hot gas increases. In both cosmologies, the present-day K-band luminosity function of the simulated galaxies resembles observations. The galaxy autocorrelation functions differ significantly from those of the dark matter. At the present epoch there is little bias in either model between galaxies and dark matter on large scales, but a significant anti-bias on scales of 1Mpc/h and a positive bias on scales of 100kpc/h. The galaxy correlation function evolves little with redshift in the range z=0-3, and depends on the luminosity of the galaxy sample. The projected pairwise velocity dispersion of the galaxies is much lower than that of the dark matter on scales less than 2Mpc/h. Applying a virial mass estimator to the largest galaxy clusters recovers the cluster virial masses in an unbiased way. (Abridged)
Investigation of materials that exhibit quantum phase transition provides valuable insights into fundamental problems in physics. We present neutron scattering under pressure in a triangular-lattice antiferromagnet which has a quantum disorder in the low-pressure phase and a noncollinear structure in the high-pressure phase. The neutron spectrum continuously evolves through the critical pressure; a single mode in the disordered state becomes soft with the pressure, and it splits into gapless and gapped modes in the ordered phase. Extended spin-wave theory reveals that the longitudinal and transverse fluctuations of spins are hybridized in the modes because of the noncollinearity, and novel magnetic excitations are formed. We report a new hybridization of the phase and amplitude fluctuations of the order parameter in a spontaneously symmetry-broken state.
Two-dimensional ferromagnetic materials with strong ferromagnetism and high Curie temperature are significantly desired for the applications of nanoscale devices. Here, based on first-principles computations, we report hydrogenated/oxygenated Mn2C monolayer is a such material with strong room-temperature ferromagnetism. The bare Mn2C monolayer is an antiferromagnetic metal with the local magnetic moment of Mn ~ 3{\mu}B. However, the antiferromagnetic coupling of Mn atoms can transform into the ferromagnetic order under hydrogenation/oxygenation. Especially, the magnetic moments in hydrogenated/oxygenated Mn2C monolayer can be as large as 6 {\mu}B per unit cell, and the Curie temperatures are above 290K. Beside the potential applications in spintronic devices, our work suggests that Mn2C monolayer is also promising to be used in hydrogen/oxygen detection and removal devices.
We use the formalism of noisy Gaussian channels to derive explicit transformation laws describing how an arbitrary multimode Gaussian state of a scalar quantum field is perceived by a number of accelerating observers, each having access to at least one of the modes. Our work, which generalizes earlier results of Ahmadi, et al., Phys. Rev. D 93, 124031 (2016), is the next step torwards a better understanding of the effect of gravity on the states of quantum fields.
We study linear perturbations to a Lema{\^\i}tre-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities. We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, \zeta_{SMTP}, which is conserved on all scales. We then briefly extend our discussion to the Lema{\^\i}tre spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime.
A facial unique-maximum coloring of a plane graph is a proper coloring of the vertices using positive integers such that each face has a unique vertex that receives the maximum color in that face. Fabrici and G\"{o}ring (2016) proposed a strengthening of the Four Color Theorem conjecturing that all plane graphs have a facial unique-maximum coloring using four colors. This conjecture has been disproven for general plane graphs and it was shown that five colors suffice. In this paper we show that plane graphs, where vertices of degree at least four induce a star forest, are facially unique-maximum 4-colorable. This improves a previous result for subcubic plane graphs by Andova, Lidick\'y, Lu\v{z}ar, and \v{S}krekovski (2018). We conclude the paper by proposing some problems.
We bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G \wr S_n for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the hyperoctahedral group Z_2 \wr S_n, the generalized symmetric group Z_m \wr S_n, and S_m \wr S_n. These results provide benchmarks to which many other random walks, modeling a wide range of phenomena, may be compared using the comparison technique, thereby yielding bounds on the rates of convergence to uniformity for previously intractable random walks.
The internal shocks scenario in relativistic jets is used to explain the variability of the blazar emission. Recent studies have shown that the magnetic field significantly alters the shell collision dynamics, producing a variety of spectral energy distributions and light-curves patterns. However, the role played by magnetization in such emission processes is still not entirely understood. In this work we numerically solve the magnetohydodynamic evolution of the magnetized shells collision, and determine the influence of the magnetization on the observed radiation. Our procedure consists in systematically varying the shell Lorentz factor, relative velocity, and viewing angle. The calculations needed to produce the whole broadband spectral energy distributions and light-curves are computationally expensive, and are achieved using a high-performance parallel code.
We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's degeneration embeds into projective space, our algorithm is a special case of a general toric two-step homotopy algorithm. When Anderson's degeneration is embedded in a weighted projective space, we explain how to lift to a projective space and construct an appropriate modification of the toric homotopy. Our algorithms are illustrated on several examples using Macaulay2.
Strong lensing provides a powerful means of investigating the nature of dark matter as it probes dark matter structure on sub-galactic scales. We present an extension of a forward modeling framework that uses flux ratios from quadruply imaged quasars (quads) to measure the shape and amplitude of the halo mass function, including line of sight (LOS) halos and main deflector subhalos. We apply this machinery to 50 mock lenses --- roughly the number of known quads --- with warm dark matter (WDM) mass functions exhibiting free-streaming cutoffs parameterized by the half-mode mass $m_{\rm{hm}}$. Assuming cold dark matter (CDM), we forecast bounds on $m_{\rm{hm}}$ and the corresponding thermal relic particle masses over a range of tidal destruction severity, assuming a particular WDM mass function and mass-concentration relation. With significant tidal destruction, at $2 \sigma$ we constrain $m_{\rm{hm}}<10^{7.9} \left(10^{8.4}\right) M_{\odot}$, or a 4.4 (3.1) keV thermal relic, with image flux uncertainties from measurements and lens modeling of $2\% \left(6\%\right)$. With less severe tidal destruction we constrain $m_{\rm{hm}}<10^{7} \left(10^{7.4}\right) M_{\odot}$, or an 8.2 (6.2) keV thermal relic. If dark matter is warm, with $m_{\rm{hm}} = 10^{7.7} M_{\odot}$ (5.1 keV), we would favor WDM with $m_{\rm{hm}} > 10^{7.7} M_{\odot}$ over CDM with relative likelihoods of 22:1 and 8:1 with flux uncertainties of $2\%$ and $6\%$, respectively. These bounds improve over those obtained by modeling only main deflector subhalos because LOS objects produce additional flux perturbations, especially for high redshift systems. These results indicate that $\sim 50$ quads can conclusively differentiate between warm and cold dark matter.
The M{\o}lmer-S{\o}rensen gate is a state-of-the-art entangling gate in the ion trap quantum computing where the gate fidelity can exceed 99\%. Here we propose an analogous implementation in the setting of cavity QED. The cavity photon mode acts as the bosonic degree of freedom in the gate in contrast of that played by a phonon mode in ion traps. This is made possible by utilising cavity assisted Raman transitions interconnecting the logical qubit states embedded in a four-level energy structure, making the "anti-Jaynes-Cummings" (AJC) term available under the rotating-wave approximation. We identify practical sources of infidelity and discuss their effects on the gate performance. Our proposal not only demonstrates an alternative entangling gate scheme but also sheds new light on the relationship between ion traps and cavity QED, in the sense that many techniques developed in the former are transferable to the latter through our framework.
The unbound nucleus $^{12}$Li is evaluated by studying three-neutron one-proton excitations within the multistep shell model in the complex energy plane. It is found that the ground state of this system consists of an antibound $2^-$ state. A number of narrow states at low energy are found which ensue from the coupling of resonances in $^{11}$Li to continuum states close to threshold.
Observed variations in the IMF are reviewed with an emphasis on environmental density. The remote field IMF studied in the LMC by several authors is clearly steeper than most cluster IMFs, which have slopes close to the Salpeter value. Local field regions of star formation, like Taurus, may have relatively steep IMFs too. Very dense and massive clusters, like super star clusters, could have flatter IMFs, or inner-truncated IMFs. We propose that these variations are the result of three distinct processes during star formation that affect the mass function in different ways depending on mass range. At solar to intermediate stellar masses, gas processes involving thermal pressure and supersonic turbulence determine the basic scale for stellar mass, starting with the observed pre-stellar condensations, and they define the mass function from several tenths to several solar masses. Brown dwarfs require extraordinarily high pressures for fragmentation from the gas, and presumably form inside the pre-stellar condensations during mutual collisions, secondary fragmentations, or in disks. High mass stars form in excess of the numbers expected from pure turbulent fragmentation as pre-stellar condensations coalesce and accrete with an enhanced gravitational cross section. Variations in the interaction rate, interaction strength, and accretion rate among the primary fragments formed by turbulence lead to variations in the relative proportions of brown dwarfs, solar to intermediate mass stars, and high mass stars.
We have studied the effect of tidal deformability constraint given by the binary neutron star merger event GW170817 on the equations of state (EOS) of hybrid stars. The EOS are constructed by matching the hadronic EOS described by relativistic mean field (RMF) model and parameter sets NL3, TM1 and NL3$\omega\rho$ with the quark matter EOS described by modified MIT bag model, via Gibbs' construction. It is found that the tidal deformability constraints along with the lower bound on maximum mass ($M_{\rm max}=2.01\pm0.04M_\odot$) significantly limit the bag model parameter space ($B_{\rm eff}^{1/4}$, $a_4$). We also obtain upper limits on the radius of $1.4M_\odot$ and $1.6M_\odot$ stars as $R_{1.4}\leq13.2-13.5$ km and $R_{1.6}\leq13.2-13.4$ km, respectively for different hadronic EOS considered here.
We develop a new formalism to treat nuclear many-body systems using bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays important role in nuclear many-body systems due to the role of the pion in strongly interacting system. We take the antisymmetrized molecular dynamics (AMD) as a basic framework and add a tensor correlation operator acting on the AMD wave function using the concept of the tensor-optimized shell model (TOSM). We demonstrate a systematical and straightforward formulation utilizing the Gaussian integration and differentiation method and the antisymmetrization technique to calculate all the matrix elements of the many-body Hamiltonian. We can include the three-body interaction naturally and calculate the matrix elements systematically in the progressive order of the tensor correlation operator. We call the new formalism "tensor-optimized antisymmetrized molecular dynamics".