ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates, where T is the single-qubit 45-degree phase shift. We assume that the circuit outputs a bit string x obtained by measuring some subset of w qubits. Two simulation tasks are considered: (1) computing the probability of a given output x, and (2) sampling x from the output probability distribution. It is shown that these tasks can be solved on a classical computer in time $poly(n,m)+2^{0.5 t} t^3$ and $poly(n,m)+2^{0.23 t} t^3 w^3$ respectively, where t is the number of T-gates, m is the total number of gates, and n is the number of qubits. The proposed simulation algorithms may serve as a verification tool for medium-size quantum computations that are dominated by Clifford gates. The main ingredient of both algorithms is a subroutine for approximating the norm of an n-qubit state which is given as a linear combination of $\chi$ stabilizer states. The subroutine runs in time $\chi n^3 \epsilon^{-2}$, where $\epsilon$ is the relative error. We also develop techniques for approximating tensor products of "magic states" by linear combinations of stabilizer states. To demonstrate the power of the new simulation methods, we performed a classical simulation of a hidden shift quantum algorithm with 40 qubits, a few hundred Clifford gates, and nearly 50 T-gates.
Weyl semimetals (WSM) have been discovered in time-reversal symmetric materials, featuring monopoles of Berry's curvature in momentum space. WSM have been distinguished between Type-I and II where the velocity tilting of the cone in the later ensures a finite area Fermi surface. To date it has not been clear whether the two types results in any qualitatively new phenomena. Here we focus on the shift-current response ($\sigma_{shift}(\omega)$), a second order optical effect generating photocurrents. Surprisingly we find that up to an order unity constant, $\sigma_{shift}(\omega)\sim \frac{e^3}{h^2}\frac{1}{\omega}$ in Type-II WSM, diverging in the low frequency $\omega\rightarrow 0$ limit. This is in stark contrast to the vanishing behavior ($\sigma_{shift}(\omega)\propto \omega$) in Type-I WSM. In addition, in both Type-I and Type-II WSM, a nonzero chemical potential $\mu$ relative to nodes leads to a large peak of shift-current response with a width $\sim |\mu|/\hbar$ and a height $\sim \frac{e^3}{h}\frac{1}{|\mu|}$, the latter diverging in the low doping limit. We show that the origin of these divergences is the singular Berry's connections and the Pauli-blocking mechanism. Similar results hold for the real part of the second harmonic generation, a closely related nonlinear optical response.
The emergence of active regions (ARs) leads to various dynamic activities. Using high-resolution and long-lasting H$\alpha$ observations from the New Vacuum Solar Telescope, we report the dynamics of NOAA AR 12700 in its emerging phase on 26 February 2018 in detail. In this AR, constant interchange reconnections between emerging fibrils and preexisting ones were detected. Driven by the flux emergence, small-scale fibrils observed in H$\alpha$ wavelength continuously emerged at the center of the AR and reconnected with the ambient preexisting fibrils, forming new longer fibrils. We investigate three scenarios of such interchange reconnection in two hours. Specially, the third scenario of reconnection resulted in the formation of longer fibrils that show pronounced rotation motion. To derive the evolution of the magnetic structure during the reconnections, we perform nonlinear force-free field extrapolations. The extrapolated three-dimensional magnetic fields clearly depict a set of almost potential emerging loops, two preexisting flux ropes at 03:00 UT before the second reconnection scenario, and a set of newly formed loops with less twist at 03:48 UT after the third reconnection scenario. All of these extrapolated structures are consistent with the fibrils detected in H$\alpha$ wavelength. The aforementioned observations and extrapolation results suggest that the constant interchange reconnections resulted in that the magnetic twist was redistributed from preexisting flux ropes towards the newly-formed system with longer magnetic structure and weaker twist.
We give a path integral derivation of the annulus diagram in a supersymmetric theory of open and closed strings with Dbranes. We compute the pair correlation function of Wilson loops in the generic weakly coupled supersymmetric flat spacetime background with Dbranes. We obtain a -u^4/r^9 potential between heavy nonrelativistic sources in a supersymmetric gauge theory at short distances.
We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise'' and ``delay''. We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay.
By using totally isotropic subspaces in an orthogonal space Omega^{+}(2i,2), several infinite families of packings of 2^k-dimensional subspaces of real 2^i-dimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with Barnes-Wall lattices, Kerdock sets and quantum-error-correcting codes.
We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.
Since Convolutional Neural Networks (CNNs) have become the leading learning paradigm in visual recognition, Naive Bayes Nearest Neighbour (NBNN)-based classifiers have lost momentum in the community. This is because (1) such algorithms cannot use CNN activations as input features; (2) they cannot be used as final layer of CNN architectures for end-to-end training , and (3) they are generally not scalable and hence cannot handle big data. This paper proposes a framework that addresses all these issues, thus bringing back NBNNs on the map. We solve the first by extracting CNN activations from local patches at multiple scale levels, similarly to [1]. We address simultaneously the second and third by proposing a scalable version of Naive Bayes Non-linear Learning (NBNL, [2]). Results obtained using pre-trained CNNs on standard scene and domain adaptation databases show the strength of our approach, opening a new season for NBNNs.
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability distribution. In this way we find that galaxy distribution in these samples is characterized by large amplitude fluctuations with a large spatial extension, whose size is only limited by the sample's boundaries. These fluctuations are quite typical and persistent in the sample's volumes, and they are detected in two independent regions in the northern and southern galactic caps. We discuss the relation of the scale-length method to several statistical quantities, such as counts of galaxies as a function of redshift and apparent magnitude. We confirm previous results, which have determined by magnitude and redshift counts that there are fluctuations of about 30% between the southern and the northern galactic caps and we relate explicitly these counts to structures in redshift space. We show that the estimation of fluctuation amplitude normalized to the sample density is biased by systematic effects, which we discuss in detail. We consider the type of fluctuations predicted by standard cosmological models of structure formation in the linear regime and, to study nonlinear clustering, we analyze several samples of mock-galaxy catalogs generated from the distribution of dark matter in cosmological N-body simulations. In this way we conclude that the galaxy fluctuations present in these samples are too large in amplitude and too extended in space to be compatible with the predictions of the standard models of structure formation.
We analyze the dynamics of entanglement due to decoherence in a system of two identical fermions with spin $3/2$ interacting with a global bosonic environment. We resort to an appropriate measure of the so-called fermionic entanglement to quantify the fermionic correlations, and compare its dynamics with that of a pair of distinguishable qubits immersed in the same environment. According to the system's initial state, three types of qualitatively different dynamics are identified: i) \textit{invariant regime}, corresponding to initial states that belong to a decoherence free subspace (DFS), which maintain invariant their entanglement and coherence throughout the evolution; ii) \textit{exponential decay}, corresponding to initial states orthogonal to the DFS, and evolve towards states whose entanglement and coherence decrease exponentially; iii) \textit{entanglement sudden death}, corresponding to initial states that have some overlap with the DFS and exhibit a richer dynamics leading, in particular, to the sudden death of the fermionic entanglement, while the coherence decays exponentially. Our analysis offers insights into the dynamics of entanglement in open systems of identical particles, into its comparison with the distinguishable-party case, and into the existence of decoherence free subspaces and entanglement sudden death in indistinguishable-fermion systems.
We consider a lattice gas in spaces of dimensionality $\mathcal{D}=1,2,3$. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in $\mathcal{D}=3$, a logarithmic potential in $\mathcal{D}=2$, and a distance-independent force in $\mathcal{D}=1$. Under mild additional assumptions regarding symmetry and fluctuations we investigate equilibrium states of self-gravitating material clusters, in particular radial density profiles for closed and open systems. We present exact analytic results in several instances and high-precision numerical data in others. The density profile of a cluster with finite mass is found to exhibit exponential decay in $\mathcal{D}=1$ and power-law decay in $\mathcal{D}=2$ with temperature-dependent exponents in both cases. In $\mathcal{D}=2$ the gas evaporates in a continuous transition at a nonzero critical temperature. We describe clusters of infinite mass in $\mathcal{D}=3$ with a density profile consisting of three layers (core, shell, halo) and an algebraic large-distance asymptotic decay. In $\mathcal{D}=3$ a cluster of finite mass can be stabilized at $T>0$ via confinement to a sphere of finite radius. In some parameter regime, the gas thus enclosed undergoes a discontinuous transition between distinct density profiles. For the free energy needed to identify the equilibrium state we introduce a construction of gravitational self-energy that works in all $\mathcal{D}$ for the lattice gas. The decay rate of the density profile of an open cluster is shown to transform via a stretched exponential for $1<\mathcal{D}<2$ whereas it crosses over from one power-law at intermediate distances to a different power-law at larger distances for $2<\mathcal{D}<3$.
A sufficient condition for entanglement in two-mode continuous systems is constructed based on interference visibility and the uncertainty of the total particle number. The observables to be measured (particle numbers and particle number variances) are relatively easily accessible experimentally. The method may be used to detect entanglement in light fields or in Bose-Einstein condensates. In contrast to the standard approach based on entanglement witnesses, the condition is expressed in terms of an inequality which is nonlinear in expectation values.
We present N-body simulations for generic non-Gaussian initial conditions with the aim of exploring and modelling the scale-dependent halo bias. This effect is evident at very large scales requiring large simulation boxes. In addition, the previously available prescription to implement generic non-Gaussian initial conditions has been improved to keep under control higher-order terms which were spoiling the power spectrum on large scales. We pay particular attention to the differences between physical, inflation-motivated primordial bispectra and their factorizable templates, and to the operational definition of the non-Gaussian halo bias (which has both a scale-dependent and an approximately scale-independent contributions). We find that analytic predictions for both the non-Gaussian halo mass function and halo bias work well once a calibration factor (which was introduced before) is calibrated on simulations. The halo bias remains therefore an extremely promising tool to probe primordial non-Gaussianity and thus to give insights into the physical mechanism that generated the primordial perturbations. The simulation outputs and tables of the analytic predictions will be made publicly available via the non-Gaussian comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html
It is shown that the three-body non-Borromean halo nuclei like ^{12}Be, ^{18}C, ^{20}C have p-wave virtual states with energy of about 1.6 times the corresponding neutron-core binding energy. We use a renormalizable model that guarantees the general validity of our results in the context of short range interactions.
The recently discovered dynamical phase transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this paper we extend the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if $T>0$. This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density.
The baryon asymmetry, together with a dark matter asymmetry, may be produced during a first order phase transition in a generative sector. We study the possibility of a gravitational wave signal in a model realising such a scenario. We identify areas of parameter space with strong phase transitions which can be probed by future, space based, gravitational wave detectors. Other signals of this scenario include collider signatures of a $Z'$, DM self interactions, a contribution to $\Delta N_{\rm eff}$ and nuclear recoils at direct detection experiments.
The quantum dynamics of a bulk-boundary theory is closely examined by the use of the background field method. As an example we take the Mirabelli-Peskin model, which is composed of 5D super Yang-Mills (bulk) and 4D Wess-Zumino (boundary). Singular interaction terms play an important role of canceling the divergences coming from the KK-mode sum. Some new regularization of the momentum integral is proposed. An interesting background configuration of scalar fields is found. It is a localized solution of the field equation. In this process of the vacuum search, we present a new treatment of the vacuum with respect to the extra coordinate. The "supersymmetric" effective potential is obtained at the 1-loop full (w.r.t. the coupling) level. This is the bulk-boundary generalization of the Coleman-Weinberg's case. Renormalization group analysis is done where the correct 4d result is reproduced. The Casimir energy is calculated and is compared with the case of the Kaluza-Klein model.
The Sun's atmosphere is frequently disrupted by coronal mass ejections (CMEs), coupled with flares and energetic particles. In the standard picture, the coupling is explained by magnetic reconnection at a vertical current sheet connecting the flare loops and the CME, with the latter embedding a helical magnetic structure known as flux rope. As it jumps upward due to instabilities or loss of equilibrium, the flux rope stretches the overlying coronal loops so that oppositely directed field is brought together underneath, creating the current sheet. However, both the origin of flux ropes and their nascent paths toward eruption remain elusive. Here we present an observation of how a stellar-sized CME bubble evolves continuously from plasmoids, mini flux ropes that are barely resolved, within half an hour. The eruption initiates when plasmoids springing from a vertical current sheet merge into a leading plasmoid occupying the upper tip of the current sheet. Rising at increasing speed to stretch the overlying loops, this leading plasmoid then expands impulsively into the CME bubble, in tandem with hard X-ray bursts. This observation illuminates for the first time a complete CME evolutionary path that has the capacity to accommodate a wide variety of plasma phenomena by bridging the gap between micro-scale dynamics and macro-scale activities.
The diffuse plasma inside clusters of galaxies has X-ray emitting temperatures of a few keV. The physical mechanisms that heat this intracluster medium (ICM) to such temperatures include the accretion shock at the periphery of a galaxy cluster, the shocks driven by merger events, as well as a somewhat overlooked mechanism -- the dissipation of intracluster turbulent motions. We study the relative role of these heating mechanisms using galaxy clusters in Lagrangian tracer particle re-simulations of the Omega500 cosmological simulation. We adopt a novel analysis method of decomposing the temperature increase at each time step into the contribution from dissipative heating and that from adiabatic heating. In the high-resolution spatial-temporal map of these heating rates, merger tracks are clearly visible, demonstrating the dominant role of merger events in heating the ICM. The dissipative heating contributed by each merger event is extended in time and also occurs in the rarefaction regions, suggesting the importance of heating by the dissipation of merger-induced turbulence. Quantitative analysis shows that turbulence heating, rather than direct heating at merger shocks, dominates the temperature increase of the ICM, especially at inner radii $r < r_{\rm 500c}$. In addition, we find that many merger shocks can propagate with almost constant velocity to very large radii $r \gg r_{\rm 500c}$, some even reach and join with the accretion shock and becoming the outer boundary of the ICM. Altogether, these results suggest that the ICM is heated more in an `inside-out' fashion rather than `outside-in' as depicted in the classical smooth accretion picture.
We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that the set of all possible distributions of intrinsic location functionals for periodic stationary processes is the convex hull generated by a specific group of distributions. We then focus on two special subclasses of these random locations. For the first subclass, the density has a uniform lower bound; for the second subclass, the possible distributions are closely related to the concept of joint mixability.
We introduce a new, very deep neutral hydrogen (HI) survey being performed with the Westerbork Synthesis Radio Telescope (WSRT). The Westerbork Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) Survey is producing an archive of some of the most sensitive HI observations available, on the angular scales which are most useful for studying faint, diffuse gas in and around nearby galaxies. The survey data are being used to perform careful modeling of the galaxies, characterizing their gas content, morphology, and kinematics, with the primary goal of revealing the global characteristics of cold gas accretion onto spiral galaxies in the local Universe. In this paper, we describe the survey sample selection, the data acquisition, reduction, and analysis, and present the data products obtained during our pilot program, which consists of UGC 2082, NGC 672, NGC 925, and NGC 4565. The observations reveal a first glimpse of the picture that the full HALOGAS project aims to illuminate: the properties of accreting HI in different types of spirals, and across a range of galactic environments. None of the pilot survey galaxies hosts an HI halo of the scale of NGC 891, but all show varying indications of halo gas features. We compare the properties of detected features in the pilot survey galaxies with their global characteristics, and discuss similarities and differences with NGC 891 and NGC 2403.
It is well known that mode coupling theory (MCT) leads to a two step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic theory developed in the Fundamental Theory of Statistical Particle Dynamics (arXiv:0905.4904). We show how the power-law exponents can be computed in the second-order approximation where we treat hard-sphere fluids with statics described by the Percus-Yevick solution.
We show that a semi-classical polymerization of the interior of Schwarzschild black holes gives rise to a tantalizing candidate for a non-singular, single horizon black hole spacetime. The exterior has non-zero quantum stress energy but closely approximates the classical spacetime for macroscopic black holes. The interior exhibits a bounce at a microscopic scale and then expands indefinitely to a Kantowski-Sachs spacetime. Polymerization therefore removes the singularity and produces a scenario reminiscent of past proposals for universe creation via quantum effects inside a black hole.
The behavior of charge density wave (CDW) in an external magnetic field is dictated by both orbital and Pauli (Zeeman) effects. A quasi-one-dimensional (Q1D) system features Q1D Fermi surfaces that allow these effects to be distinguished, which in turn can provide sensitive probe to the underlying electronic states. Here we studied the field dependence of an incommensurate CDW in a transition-metal chalcogenide Ta2NiSe7 with a Q1D chain structure. The angle-dependent magnetoresistance (MR) is found to be very sensitive to the relative orientation between the magnetic field and the chain direction. With an applied current fixed along the b axis (the chain direction), the angle-dependent MR shows a striking change of the symmetry below T_CDW only for a rotating magnetic field in the ac plane. In contrast, the symmetry axis remains unchanged for other configurations (H in ab and bc plane). The orbital effect conforms to the lattice symmetry, while Pauli effect in the form of {\mu}B B / v_F can be responsible for such symmetry change, provided that the Fermi velocity v_F is significantly anisotropic and the nesting vector changes in a magnetic field, which is corroborated by our first-principles calculations. Our results show that the angle-dependent MR is a sensitive transport probe of CDW and can be useful for the study of low-dimensional systems in general.