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The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the model approaches the learned state by approximating a minimal sufficient statistics. In this paper we extend this tool to the domain of quantum learning models. In a second step, we study how the insight on how much the model compresses the input data (provided by the information plane) can be used to improve a learning algorithm. Specifically, we consider two ways to do so: via a multiplicative regularization of the loss function, or with a compression-gnostic scheduler of the learning rate (for algorithms based on gradient descent). Both ways turn out to be equivalent in our implementation. Finally, we benchmark the proposed learning algorithms on several classification and regression tasks using variational quantum circuits. The results demonstrate an improvement in test accuracy and convergence speed for both synthetic and real-world datasets. Additionally, with one example we analyzed the impact of the proposed modifications on the performances of neural networks in a classification task.

We report the observation of the electro-optic effect in Bi$_2$Se$_3$ crystals induced by an intense single-cycle terahertz pulse. The effect reveals itself as a transient change of the polarization state of a femtosecond laser pulse reflected from the crystal that is exposed to the terahertz electric field. The corresponding experimental signal is apparently instantaneous with respect to the field and contains a linear (Pockels) and a quadratic (Kerr) components of comparable magnitude. The latter does not depend on the crystal orientation, while the former demonstrates three-fold rotational symmetry in agreement with the trigonal symmetry of the crystal surface. The electro-optic effect vanishes upon phase transition to the non-topological metal state induced by indium doping and also can be quenched by a femtosecond pre-pulse. We associate this effect with surface Dirac electronic states of Bi$_2$Se$_3$ and discuss its possible mechanisms., Comment: 9 pages, 9 figures

In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are subject to, and in algorithm design, a large effort is underway to provide scalable error correction or mitigation techniques. Yet some previous work has indicated that certain classes of quantum algorithms, such as quantum machine learning, may, in fact, be intrinsically robust to or even benefit from the presence of a small amount of noise. Here, we demonstrate that noise levels in quantum hardware can be effectively tuned to enhance the ability of quantum neural networks to generalize data, acting akin to regularisation in classical neural networks. As an example, we consider a medical regression task, where, by tuning the noise level in the circuit, we improved the mean squared error loss by 8%., Comment: 11 pages, 6 figures, 2 tables

This paper describes the STCON system for the CHiME-8 Challenge Task 1 (DASR) aimed at distant automatic speech transcription and diarization with multiple recording devices. Our main attention was paid to carefully trained and tuned diarization pipeline and speaker counting. This allowed to significantly reduce diarization error rate (DER) and obtain more reliable segments for speech separation and recognition. To improve source separation, we designed a Guided Target speaker Extraction (G-TSE) model and used it in conjunction with the traditional Guided Source Separation (GSS) method. To train various parts of our pipeline, we investigated several data augmentation and generation techniques, which helped us to improve the overall system quality.

Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local decoherence affecting its physical carriers. TQFT states' inherent nonlocality, redundancy, and entanglement position them as natural error-correcting codes. We demonstrate that information recovery protocols can be derived from the principle that protected information must be uniformly distributed across the system and from interpreting correlations in terms of space connectivity. Specifically, we employ a topological framework to devise erasure error correction protocols, showing that information can be successfully recovered even when parts of the system are corrupted., Comment: 24 pages, 3 figures, color diagrams

We present the high-precision result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. At this perturbative order, the soft function is the last missing ingredient required for the computation of a hadronic colour singlet production or a colour singlet decay into two jets using the zero-jettiness variable as the slicing parameter. Furthermore, the knowledge of the N3LO soft function enables the re-summed description of the thrust distribution in the process $e^+ e^- \to \textrm{hadrons}$ through next-to-next-to-next-to-leading logarithmic order, which is important for the extraction of the strong coupling constant using this shape variable. On the methodological side, the complexity of the zero-jettiness variable forced us to develop a new semi-analytic method for phase-space integration in the presence of constraints parameterized through Heaviside functions which, hopefully, will be useful for further development of the $N$-jettiness slicing scheme., Comment: 6 pages, attached results in computer readable form

Consensus plays a crucial role in distributed ledger systems, impacting both scalability and decentralization. Many blockchain systems use a weighted lottery based on a scarce resource such as a stake, storage, memory, or computing power to select a committee whose members drive the consensus and are responsible for adding new information to the ledger. Therefore, ensuring a robust and fair committee selection process is essential for maintaining security, efficiency, and decentralization. There are two main approaches to randomized committee selection. In one approach, each validator candidate locally checks whether they are elected to the committee and reveals their proof during the consensus phase. In contrast, in the second approach, a sortition algorithm decides a fixed-sized committee that is globally verified. This paper focuses on the latter approach, with cryptographic sortition as a method for fair committee selection that guarantees a constant committee size. Our goal is to develop deterministic guarantees that strengthen decentralization. We introduce novel methods that provide deterministic bounds on the influence of adversaries within the committee, as evidenced by numerical experiments. This approach overcomes the limitations of existing protocols that only offer probabilistic guarantees, often providing large committees that are impractical for many quorum-based applications like atomic broadcast and randomness beacon protocols.

We find that the double-threshold voltage-current characteristics in the insulating regime in the ultra-clean two-valley two-dimensional electron system in SiGe/Si/SiGe quantum wells are promoted by perpendicular magnetic fields, persisting to an order of magnitude lower voltages and considerably higher electron densities compared to the zero-field case. This observation indicates the perpendicular-magnetic-field stabilization of the quantum electron solid.

The abstract theory of risk measures is well-developed for certain classes of solid subspaces of $L^{0}$. We provide an example to illustrate that this framework is insufficient to deal with the subtleties of incomplete markets. To remedy this problem, we consider risk measures on the subspace generated by a closed, absolutely convex, and bounded subset $K\subset L^{0}$, which represents the attainable securities. In this context, we introduce the equicontinuous Fatou property. Under the existence of a certain topology $\tau$ on $\mathrm{span}(K)$, interpreted as a generalized weak-star topology, we obtain an equivalence between the equicontinuous Fatou property, and lower semicontinuity with respect to $\tau$. As a corollary, we obtain tractable dual representations for such risk measures, which subsumes essentially all known results on weak-star representations of risk measures. This dual representation allows one to prove that all risk measures of this form extend, in a maximal way, to the ideal generated by $\mathrm{span}(K)$ while preserving a Fatou-like property.

Given a bounded sequence $\{X^{n}\}_{n}$ of semimartingales on a time interval $[0,T]$, we find a sequence of convex combinations $\{Y^{n}\}_{n}$ and a limiting semimartingale $Y$ such that $\{Y^{n}\}_{n}$ converges to $Y$ in a $\sigma$-localized modification of the \'Emery topology. More precisely, $\{Y^{n}\}_{n}$ converges to $Y$ in the \'Emery topology on an increasing sequence $\{D_{n}\}_{n}$ of predictable sets covering $\Omega\times[0,T]$. We also prove some technical variants of this theorem, including a version where the complement of $\{D_{n}\}_{n}$ forms a disjoint sequence. Applications include a complete characterization of sequences admitting convex combinations converging in the \'Emery topology, and a supermartingale counterpart of Helly's selection theorem., Comment: Revision from reviewer comments

We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo integration (RQMC) methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that RQMC approaches based on scrambled Sobol' sequences can yield smaller bias and root mean square error than MC methods for risk-averse optimization., Comment: 19 pages

We consider top quark production and decay in the narrow width approximation and study if the polarisation effects, that manifest themselves in correlations of angular distributions of particles from top quark decays and final state jets in the production sub-process, are affected by linear power corrections. We find that, in general, the answer to this question is affirmative. We also discuss how these non-perturbative corrections affect polarisation observables used to study single top production at the LHC. Finally, we point out that generic kinematic distributions of leptons from top quark decays are affected by linear power corrections, which may have implications for proposals to extract the top quark mass from such leptonic observables. On the other hand, we demonstrate that the distribution of the ``out-of-collision-plane'' component of the positron momentum is free from linear power corrections, making it an interesting candidate for the top quark mass measurement., Comment: 40 pages, 2 figures

Given a computably locally compact Polish space $M$, we show that its 1-point compactification $M^*$ is computably compact. Then, for a computably locally compact group $G$, we show that the Chabauty space $\mathcal S(G)$ of closed subgroups of $G$ has a canonical effectively-closed (i.e., $\Pi^0_1$) presentation as a subspace of the hyperspace $\mathcal K(G^*)$ of closed sets of $G^*$. We construct a computable discrete abelian group $H$ such that $\mathcal S(H)$ is not computably closed in $\mathcal K(H^*)$; in fact, the only computable points of $\mathcal S(H)$ are the trivial group and $H$ itself, while $\mathcal S(H)$ is uncountable. In the case that a computably locally compact group $G$ is also totally disconnected, we provide a further algorithmic characterization of $\mathcal S(G)$ in terms of the countable meet groupoid of $G$ introduced recently by the authors (arXiv: 2204.09878). We apply our results and techniques to show that the index set of the computable locally compact abelian groups that contain a closed subgroup isomorphic to $(\mathbb{R},+)$ is arithmetical.

We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems. Leveraging techniques for metric entropy bounds, we derive non-asymptotic Monte Carlo-type convergence rates for the ensemble-based solutions. Our theoretical framework is validated through numerical simulations on a harmonic oscillator problem and a vaccination scheduling problem for epidemic control under model parameter uncertainty.

We study QCD corrections to the process where a Higgs boson is produced in weak boson fusion and then decays into a pair of massive $b$ quarks. We find that typical experimental criteria used to identify $b$ jets in this process affect QCD corrections to the decay, making it necessary to account for them in the proper description of this process. Indeed, if corrections to the production and decay are combined, the fiducial cross section of the weak boson fusion process $p p \to H(\to b \bar{b}) j j$ is reduced by about $40\%$ relative to leading-order predictions, compared to just about $8\%$ if only corrections to the production process are considered. We investigate the origin of these large corrections through next-to-next-to-leading-order and conclude that they appear because a number of independent moderately-large effects conspire to significantly reduce the fiducial cross section for this process., Comment: 12 pages, 4 figures

We examine the physical significance of torsion co-cycles in the cohomology of a projective Calabi-Yau three-fold for the (2,2) superconformal field theory (SCFT) associated to the non-linear sigma model with such a manifold as a target space. There are two independent torsion subgroups in the cohomology. While one is associated to an orbifold construction of the SCFT, the other encodes the possibility of turning on a topologically non-trivial flat gerbe for the NS-NS B-field. Inclusion of these data enriches mirror symmetry by providing a refinement of the familiar structures and points to a generalization of the duality symmetry, where the topology of the flat gerbe enters on the same footing as the topology of the underlying manifold., Comment: 46 pages; tikz figures and diagrams; v2 typos fixed, K-theory mistake in section 2.3 corrected

We have developed a technique that dramatically reduces the contact resistances and depletes a shunting channel between the contacts outside the Hall bar in ultra-high mobility SiGe/Si/SiGe heterostructures. It involves the creation of three overlapping independent gates deposited on top of the structure and allows transport measurements to be performed at millikelvin temperatures in the strongly interacting limit at low electron densities, where the energy of the electron-electron interactions dominates all other energy scales. This design allows one to observe the two-threshold voltage-current characteristics that are a signature for the collective depinning and sliding of the electron solid.

Resonant states underlie a variety of metastructures that exhibit remarkable capabilities for effective control of acoustic waves at subwavelength scales. The development of metamaterials relies on the rigorous mode engineering providing the implementation of the desired properties. At the same time, the application of metamaterials is still limited as their building blocks are frequently characterized by complicated geometry and can't be tuned easily. In this work, we consider a simple system of coupled Helmholtz resonators and study their properties associated with the tuning of coupling strength and symmetry breaking. We numerically and experimentally demonstrate the excitation of quasi-bound state in the continuum in the resonators placed in a free space and in a rectangular cavity. It is also shown that tuning the intrinsic losses via introducing porous inserts can lead to spectral splitting or merging of quasi-\textit{bound states in the continuum} and occurrence of \textit{exceptional points}. The obtained results will open new opportunities for the development of simple and easy-tunable metastructures based on Helmholtz resonances.

The origin of multiple peaks in lightcurves of various wavelengths remains illusive during flares. Here we discuss the flare of SOL2023-05-09T03:54M6.5 with six flux peaks as recorded by a tandem of new microwave and Hard X-ray instruments. According to its microwave spectra, the flare represents a high-turnover frequency (>15 GHz) event. The rather-complete microwave and HXR spectral coverage provides a rare opportunity to uncover the origin of such event together with simultaneous EUV images. We concluded that (1) the microwave sources originates around the top section of the flaring loops with a trend of source spatial dispersion with frequency;(2) the visible movement of the microwave source from peak to peak originates from the process of new flaring loops appearing sequentially along the magnetic neutral line; 3) the optically-thin microwave spectra are hard with the indices varying from -1.2 to -0.4, and the turnover frequency always exceeds 15 GHz; 4) higher turnover/peak frequency corresponds to stronger peak intensity and harder optically-thin spectra. Using the Fokker-Planck and GX simulator codes we obtained a good fit to the observed microwave spectra and spatial distribution of the sources at all peaks, if assuming the radiating energetic electrons have the same spatial distribution and single-power-law spectra but with the number density varying in a range of 30%. We conclude that the particle acceleration in this flare happens in a compact region nearing the looptop. These results provide new constraints on the acceleration of energetic electrons and the underlying flare intermittent reconnection process., Comment: 23 pages, 11 figures

In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an eigenvalue/eigenvector search, this algorithm features wide applicability. Operationally, power iterations consist of performing repeated matrix-to-vector multiplications (or MatVec) followed by a renormilization step in order to converge to the dominant eigenvalue/eigenvector. However, classical realizations, including novel tensor network based approaches, necessitate an exponential scaling for the algorithm's run-time. In this paper, we propose a quantum realiziation to circumvent this pitfall. Our methodology involves casting low-rank representations; Matrix Product Operators (MPO) for matrices and Matrix Product States (MPS) for vectors, into quantum circuits. Specifically, we recover a unitary approximation by variationally minimizing the Frobenius distance between a target MPO and an MPO ansatz wherein the tensor cores are constrained to unitaries. Such an unitary MPO can easily be implemented as a quantum circuit with the addition of ancillary qubits. Thereafter, with appropriate initialization and post-selection on the ancillary space, we realize a single iteration of the classical algorithm. With our proposed methodology, power iterations can be realized entirely on a quantum computer via repeated, static circuit blocks; therefore, a run-time advantage can indeed be guaranteed. Moreover, by exploiting Riemannian optimization and cross-approximation techniques, our methodology becomes instance agnostic and thus allows one to address black-box optimization within the framework of quantum computing., Comment: 15 pages, 6 figures

Let $E$ be a Banach space such that $E'$ has the Radon-Nikod\'ym property. The aim of this work is to connect relative weak compactness in the $E$-valued martingale Hardy space $H^{1}(\mu,E)$ to a convex compactness criterion in a weaker topology, such as the topology of uniform convergence on compacts in measure. These results represent a dynamic version of the deep result of Diestel, Ruess, and Schachermayer on relative weak compactness in $L^{1}(\mu,E)$. In the reflexive case, we obtain a Kadec-Pe{\l}czy\'nski dichotomy for $H^{1}(\mu,E)$-bounded sequences, which decomposes a subsequence into a relatively weakly compact part, a pointwise weakly convexly convergent part, and a null part converging to zero uniformly on compacts in measure. As a corollary, we investigate a parameterized version of the vector-valued Koml\'os theorem without the assumption of $H^{1}(\mu,E)$-boundedness., Comment: Revision from reviewer comments

The presence of quantum vortices determines the electromagnetic response of superconducting materials and devices. Controlling the vortex motion, their pinning on intrinsic and artificial defects is therefore essential for superconducting electronics. Here we take advantage of the attractive force between a magnetic cantilever of the Magnetic Force Microscope and a single quantum vortex to spatially map the pinning force inside 50-240 nm thick magnetron-sputtered Nb-films, commonly used in advanced superconducting electronics. The revealed pinning nano-network is related to the thickness-dependent granular structure of the films as well as to the characteristic microscopic scales of superconductivity. Our approach is general, and can be directly applied to other type II granular superconducting materials and nanodevices., Comment: 14 pages, 3 figures, 108 references

In these notes we review the calculation of Jones polynomials using a matrix representation of the braid group and Temperley-Lieb algebra. The pseudounitary representation that we consider allows constructing ``states'' from the group/algebra matrices and compute the knot invariants as matrix elements, rather than traces. In comparison with a more standard way of computing the invariants through traces, the matrix element method is more interesting and complete from the point of view of applications. As a byproduct of the discussion we prove a general formula for pretzel knots., Comment: lecture notes, 9 pages, some typos fixed and some references added in this version

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully demonstrated a quantum advantage due to the ease with which the results can be adequately replicated on classical computers through the use of tensor network algorithms. Additionally, it remains unclear even in theory where exactly these advantages are rooted within quantum systems because the logarithmic complexity commonly associated with quantum algorithms is also present in algorithms based on tensor networks. In this article, we propose a novel approach called Tensor Quantum Programming, which leverages tensor networks for hybrid quantum computing. Our key insight is that the primary challenge of algorithms based on tensor networks lies in their high ranks (bond dimensions). Quantum computing offers a potential solution to this challenge, as an ideal quantum computer can represent tensors with arbitrarily high ranks in contrast to classical counterparts, which indicates the way towards quantum advantage. While tensor-based vector-encoding and state-readout are known procedures, the matrix-encoding required for performing matrix-vector multiplications directly on quantum devices remained unsolved. Here, we developed an algorithm that encodes Matrix Product Operators into quantum circuits with a depth that depends linearly on the number of qubits. It demonstrates effectiveness on up to 50 qubits for several matrices frequently encountered in differential equations, optimization problems, and quantum chemistry. We view this work as an initial stride towards the creation of genuinely practical quantum algorithms., Comment: 17 pages, 13 figures

We derive a compact representation of the renormalized $N$-jettiness soft function that is free of infrared and collinear divergences through next-to-next-to-leading order in perturbative QCD. The number of hard partons $N$ is a parameter in the formula for the finite remainder. Cancellation of all infrared and collinear singularities between the bare soft function and its renormalization matrix in color space is demonstrated analytically., Comment: 46 pages, 4 appendices

Let $M$ be a $W^{\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\mathscr{B}(H)$ factors through an $\mathfrak{L}_{\infty}$-space only if $M$ is a finite type $\mathrm{I}$ algebra.

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.

There is still a limited number of high-redshift ($z>3$) active galactic nuclei (AGN) whose jet kinematics have been studied with very long baseline interferometry (VLBI). Without a dedicated proper motion survey, regularly conducted astrometric VLBI observations of bright radio-emitting AGN with sensitive arrays can be utilized to follow changes in the jets, by means of high-resolution imaging and brightness distribution modeling. Here we present a first-time VLBI jet kinematic study of NVSS~J080518$+$614423 ($z = 3.033$) and NVSS~J165844$-$073918 ($z = 3.742$), two flat-spectrum radio quasars that display milliarcsecond-scale jet morphology. Archival astrometric observations carried out mainly with the Very Long Baseline Array, supplemented by recent data taken with the European VLBI Network, allowed us to monitor changes in their radio structure in the $7.6-8.6$~GHz frequency band, covering almost two decades. By identifying individual jet components at each epoch, we were able to determine the apparent proper motion for multiple features in both sources. Apparent superluminal motions range between $(1-14)\,c$, and are found to be consistent with studies of other high-redshift AGN targets. Using the physical parameters derived from the brightness distribution modeling, we estimate the Doppler-boosting factors ($\delta \approx 11.2$ and $\delta \approx 2.7$), the Lorentz factors ($\Gamma \approx 7.4$ and $\Gamma \approx 36.6$) and the jet viewing angles ($\theta \approx 4\fdg4$ and $\theta \approx 8\fdg0$), for NVSS~J080518$+$614423 and NVSS~J165844$-$073918, respectively. The data revealed a stationary jet component with negligible apparent proper motion in NVSS~J165844$-$073918., Comment: Supplementary tables can also be found at the end of the main tex file

We analyze a space-time algebra of BPS states that emerges in the infinite distance limit in the moduli space of the nine-dimensional CHL string as the theory decompactifies to the ten-dimensional $\text{E}_8 \times \text{E}_8$ heterotic string. We find an affine algebra as expected from the heterotic case, but in a twisted version., Comment: 18 pages

We introduce TQCompressor, a novel method for neural network model compression with improved tensor decompositions. We explore the challenges posed by the computational and storage demands of pre-trained language models in NLP tasks and propose a permutation-based enhancement to Kronecker decomposition. This enhancement makes it possible to reduce loss in model expressivity which is usually associated with factorization. We demonstrate this method applied to the GPT-2$_{small}$. The result of the compression is TQCompressedGPT-2 model, featuring 81 mln. parameters compared to 124 mln. in the GPT-2$_{small}$. We make TQCompressedGPT-2 publicly available. We further enhance the performance of the TQCompressedGPT-2 through a training strategy involving multi-step knowledge distillation, using only a 3.1% of the OpenWebText. TQCompressedGPT-2 surpasses DistilGPT-2 and KnGPT-2 in comparative evaluations, marking an advancement in the efficient and effective deployment of models in resource-constrained environments.

We present an analytic calculation of the one-loop correction to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark soft final-state partons. We explain all the relevant steps of the computation including the reduction of phase-space integrals to master integrals in the presence of Heaviside functions, and the methods we employed to compute them., Comment: 33 pages, results attached, v2: Normalization fixed, matches published version

The drug design process currently requires considerable time and resources to develop each new compound that enters the market. This work develops an application of hybrid quantum generative models based on the integration of parametrized quantum circuits into known molecular generative adversarial networks, and proposes quantum cycle architectures that improve model performance and stability during training. Through extensive experimentation on benchmark drug design datasets, QM9 and PC9, the introduced models are shown to outperform the previously achieved scores. Most prominently, the new scores indicate an increase of up to 30% in the quantitative estimation of druglikeness. The new hybrid quantum machine learning algorithms, as well as the achieved scores of pharmacokinetic properties, contribute to the development of fast and accurate drug discovery processes., Comment: 16 pages, 8 figures, 4 tables

We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of states in Chern-Simons with properties similar to those of holographic states. While the holographic states are dual to classical geometries, these connectome states represent classical topologies, which satisfy a discrete analog of the Ryu-Takayanagi formula and characteristic inequalities for the entanglement entropy. Generic states are linear combinations of connectomes, and the theory also has nonperturbative states which are global spacetime defects formed by a large number of quantum fluctuations. Topological presentation of quantum states and emergence of topology from entanglement may be useful for building a generalization to geomentry, that is quantum gravity. Thinking of further quantum gravity comparisons we discuss replica wormholes and conclude that similar objects exist beyond gravitational theories. The topological theory perspective suggests that the sum over all wormholes is always factorizable, even though the individual ones might not be., Comment: 22 pages, 3 figures

Predicting solar panel power output is crucial for advancing the energy transition but is complicated by the variable and non-linear nature of solar energy. This is influenced by numerous meteorological factors, geographical positioning, and photovoltaic cell properties, posing significant challenges to forecasting accuracy and grid stability. Our study introduces a suite of solutions centered around hybrid quantum neural networks designed to tackle these complexities. The first proposed model, the Hybrid Quantum Long Short-Term Memory, surpasses all tested models by over 40% lower mean absolute and mean squared errors. The second proposed model, Hybrid Quantum Sequence-to-Sequence neural network, once trained, predicts photovoltaic power with 16% lower mean absolute error for arbitrary time intervals without the need for prior meteorological data, highlighting its versatility. Moreover, our hybrid models perform better even when trained on limited datasets, underlining their potential utility in data-scarce scenarios. These findings represent a stride towards resolving time series prediction challenges in energy power forecasting through hybrid quantum models, showcasing the transformative potential of quantum machine learning in catalyzing the renewable energy transition., Comment: 12 pages, 4 figures, 1 table

We investigate the interrelation between topology and Narain T-duality of heterotic flux vacua. We present evidence that all 5 and 4-dimensional Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in the moduli space with a T-dual description in terms of a compactification on the product of a K3 surface with a circle or a torus. A test of this equivalence is provided by calculating the new supersymmetric index on both sides of the duality. We examine the implications of these dualities for CHL-like orbifolds that reduce the rank of the gauge group, as well as those that lead to minimal supersymmetry in 4 dimensions. We also discuss properties of flux vacua that preserve minimal supersymmetry in 4 dimensions that cannot be related to conventional compactifications by Narain T-duality. Along the way we point out a number of properties of these vacua, including the role played by non-trivial flat gerbes, the appearance of rational worldsheet CFTs in decompactification limits, and the role of attractive K3 surfaces in backgrounds with minimal supersymmetry. Finally, we discuss the dual pairs from the perspective of M-theory/heterotic duality., Comment: 69 pages; typos fixed, comments added