In low-resource framework development (e.g., HarmonyOS), large language models (LLMs) often lack sufficient pre-training exposure, resulting in poor code generation performance. Although they generally preserve programming logic across languages, they frequently fail on framework-specific APIs and syntax, revealing a gap between learned algorithmic knowledge and unfamiliar framework conventions. Consequently, even advanced models such as GPT-4o struggle to produce correct code without prior exposure. Inspired by these challenges, we propose APIKG4Syn, a framework that leverages API knowledge graphs to synthesize API-oriented question-code pairs without requiring executable environments. It incorporates both single-API and multi-API information, with the latter guided by uncertainty estimation (UE) and Monte Carlo Tree Search (MCTS), to construct high-quality fine-tuning data. For evaluation, we select HarmonyOS as a case study due to its accessible documentation and growing ecosystem, and build the first benchmark for its code generation. Experimental results show that fine-tuning Qwen2.5-Coder-7B with APIKG4Syn achieves a pass@1 of 25.00%, outperforming untuned GPT-4o (17.59%). We further observe that larger volumes of data generated by APIKG4Syn consistently lead to better fine-tuning performance, and that the optimal Single-API to Multi-API ratio is 8:2. Ablation studies also confirm the necessity and effectiveness of each component in our framework. These findings highlight the effectiveness of API-oriented data in enhancing LLM performance for low-resource software development scenarios.

The top-quark mass is measured using top-quark decays producing an isolated lepton and $J/ψ$ meson reconstructed in its $μ^+μ^-$ decay mode. The data sample was recorded with the ATLAS detector in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb$^{-1}$. The measurement is based on the invariant mass $m(\ell μ^+μ^-)$ of the system made of the isolated lepton $\ell$ from the $W$ boson decay and the non-isolated $μ^+μ^-$ pair from a $J/ψ$ decay of a $b$-hadron, exploiting its sensitivity to the top-quark mass. An unbinned maximum-likelihood fit to the $m(\ell μ^+μ^-)$ distribution is performed to extract the top-quark mass. The top-quark mass is measured to be $m_{top} = 172.17 \pm 0.80 (stat) \pm 0.81 (syst) \pm 1.07 (recoil)$ GeV, with a total uncertainty of 1.56 GeV. The third uncertainty arises from changing the dipole parton shower gluon-recoil scheme used in top-quark decays.

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of standard quantum mechanics based on the concept of stochastic trajectories in the configuration space of a quantum system. For particle systems, configuration space is made up out of their coordinates and, if relevant, their orientation. Quantum analytical mechanics derives equations of motion for these variables which allow a description of the measurement process as a dynamical physical process. After all, it is exactly these variables experiments are designed to interact with. The theory is not a replacement of Hilbert space quantum mechanics but a mathematical completion enriching our toolset for the description of quantum phenomena.

A search for final states characterised by at least one isolated high transverse-momentum photon, jets and large missing transverse momentum is presented. Such a final state might occur in gauge-mediated supersymmetric models where a pair of binos and higgsinos mix to form neutralinos, one of which decays into a photon plus a gravitino while the other decays into a Higgs boson, a Z boson or a photon, plus a gravitino. The search is performed using the full Run-2 data sample of 140 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collisions collected by the ATLAS detector at the Large Hadron Collider. No significant excess of events is observed above the Standard Model prediction and model-dependent exclusion limits at the 95% confidence level are set. These limits are interpreted in terms of the masses of gauginos, which are excluded up to 1.2 TeV depending on their branching ratios, and on their branching ratios as a function of their mass.

We consider the optical appearance of a non-singular, spherically symmetric black hole from Eddington-inspired Born-Infeld gravity coupled to anisotropic fluids. Such a black hole has a single (external) horizon located very near the Schwarzschild radius, $r_h=2M$, while its surface of unstable bound geodesics (photon sphere) is located at a moderately shortened radius than its Schwarzschild counterpart. Relying on a geometrically and optically thin accretion disk with a monochromatic emission described by suitable adaptations of Standard Unbound profiles previously employed in the literature, we generate images of this solution, which displays relevant modifications to the typical photon ring and central brightness depression features found in black hole images. In this sense, we fit the width of the two first photon rings in order to reconstruct the Lyapunov exponent of nearly-bound geodesics characterizing the theoretical ratio of successive rings. Such an exponent is tightly attached to observational features of photon rings such as their relative intensities in time-averaged images and the time-scale of hot-spots. Our results point out that non-singular black holes of this type are hard to distinguish from their Schwarzschild counterparts using this method alone, since the theoretical, numerical, disk-modeling, and observational uncertainties are too entangled with one another to allowing a neat distinction of such an exponent. It also points out to the need of incorporating dynamical settings such as hot-spots or quasi-normal modes from gravitational wave ringdowns as a way to circumvent such difficulties.

Let $G$ be a finite group. A finite collection of elements from $G$, where the order is disregarded and repetitions are allowed, is said to be a product-one sequence if its elements can be ordered such that their product in $G$ equals the identity element of $G$. Then, the Gao's constant $\mathsf E (G)$ of $G$ is the smallest integer $\ell$ such that every sequence of length at least $\ell$ has a product-one subsequence of length $|G|$. For a positive integer $n$, we denote by $C_n$ a cyclic group of order $n$. Let $G = C_n \rtimes_s C_2$ with $s^2\equiv 1\pmod n$ be a metacyclic group. The direct and inverse problems of $\mathsf E (G)$ were settled recently, except for the case that $G=C_{3n_2}\rtimes_s C_2$ with $n_2\neq 1$, $\gcd(n_2,6)=1$, $s\equiv -1 \pmod 3$, and $s\equiv 1\pmod {n_2}$. In this paper, we complete the remaining case and hence for all metacyclic groups of the form $G=C_n \rtimes C_2$, the Gao's constant and the associated inverse problem are now fully settled (see Theorem 1.2).

We reanalyze cosmological constraints from Hyper Suprime-Cam (HSC) Y3 shear-shear correlation function using new calibration of the tomographic redshift distribution via the clustering redshifts method with DESI spectroscopy presented in Choppin de Janvry et al. (2025a). We present both importance sampling of the original MCMC chains by HSC, applying the weights of our newly calibrated $Δz$ priors, as well as full MCMC analysis with new photometric redshift distributions, finding consistent results between the two. We obtain the growth of structure parameter $S_8\equivσ_8\sqrt{Ω_m/0.3}=0.805\pm{0.018}$, compared to previous HSC Y3 result of $S_8=0.769^{+0.031}_{-0.034}$, which is a 1.8 reduction of error due to the improved clustering redshift calibrations, with the central value shifting considerably higher towards Planck cosmology. With the new photometric redshift calibration, HSC Y3 has comparable constraining power to the recent KIDS Legacy and DES Y6 results.

We present a randomized polynomial-time simplex algorithm with higher probability and tighter bounds for linear programming by applying improved quasi-convex properties, a logarithmic rounding on a given polytope and its logarithmic perturbation. We base our work on the first randomized polynomial-time simplex method by Jonathan A. Kelner and Daniel A. Spielman [KS06]. We obtain stronger bounds for the expected number of edges in the projection of a perturbed polytope onto a two-dimensional shadow plane. In the $k$-round case, we obtain a bound of $16 \sqrt{2} πk (1 + λH_n) \sqrt{d} n / 3 λ$. In the non-$k$-round case, we obtain a bound of $26 πt (1 + λH_n) \sqrt{d} n / λρ$. To achieve this, we provide a slightly lower bound of $3 \sqrt{2} λ/ (16 n \sqrt{d})$ on the expected edge length that appears in the shadow. Another tool we employ is a tighter bound for $1$-quasi-concave minimization and $1$-quasi-convex maximization. In the $k$-round case, we obtain a quasi-convex bound of $(d - 2) ε^2 / 2$. In the non-$k$-round case, we obtain a quasi-convex bound of $3.4 ε^2 / ρ^2$. We propose a modification of the Kelner and Spielman randomized simplex algorithm (STOC'06) [KS06] that achieves a higher success probability. To accomplish this, we apply our tighter bounds with a new expected value of $λ= c \log n$ for independent exponentially distributed random variables and with $\log(k)$-rounding. The desired properties resulting from the construction of an artificial vertex during initialization hold with a higher probability of at least $1 - (d + 2), e^{-\log n}$. The pivot rule of the randomized simplex modification holds with a probability of at least $3/4$.

We study Einstein-Maxwell (non-null) sourcefree configurations that can be extended to any conformally invariant non-linear electrodynamics (CINLE) by a constant rescaling of the electromagnetic field. We first obtain a criterion which characterizes such extendable solutions in terms either of the electromagnetic invariants, or (equivalently) of the canonical Newman-Penrose form of the self-dual Maxwell field. This is then used to argue that all static configurations are extendable (more generally, all configurations admitting a non-null twistfree Killing vector field). One can thus draw from the extensive literature to straightforwardly extend to CINLE various known exact solutions, whereby the duality invariance of the Einstein-Maxwell theory allows for dyonic solutions even in more general theories. This is illustrated by a few explicit examples, including the homogeneous $Λ<0$ universe of Ozsváth, a black hole in the universe of Levi-Civita, Bertotti and Robinson, a generalization of the charged $C$-metric, and non-expanding gravitational waves in the Bonnor-Melvin background.

We apply the methodology of our recent paper 'The Dynamics of the Hubbard Model through Stochastic Calculus and Girsanov Transformation' [1] to thermodynamic correlation functions in the Fermi-Hubbard model. They can be obtained from a stochastic differential equation (SDE) system. To this SDE system, a Girsanov transformation can be applied. This has the effect that the usual determinant or pfaffian which shows up in a pfaffian quantum Monte Carlo (PfQMC) representation [2] basically gets absorbed into the new integration variables and information from that pfaffian moves into the drift part of the transformed SDE system. While the PfQMC representation depends heavily on the choice of how the quartic interaction has been factorized into quadratic quantities in the beginning, the Girsanov transformed formula has the very remarkable property that it is nearly independent of that choice, the drift part of the transformed SDE system as well as a remaining exponential which has the obvious meaning of energy are always the same and do not depend on the Hubbard-Stratonovich details. The resulting formula may serve as a starting point for further theoretical or numerical investigations. Here we consider the spin-spin correlation at half-filling on a bipartite lattice and obtain an analytical proof that the signs of these correlations have to be of antiferromagnetic type, at arbitrary temperatures. Also, by checking against available benchmark data [3], we find that approximate ground state energies can be obtained from an ODE system. This may even hold for exact ground state energies, but future work would be required to prove or disprove this. As in [1], the methodology is generic and can be applied to arbitrary quantum many body or quantum field theoretical models.

The interaction between free electrons and optical modes underlies a variety of quantum and nanoscale light-matter phenomena, yet the associated momentum exchange with the sample largely remained overlooked. Here, we experimentally demonstrate the momentum transfer from free electrons to planar samples during optical mode excitation using momentum-resolved electron energy-loss spectroscopy. The momentum transfer to the sample modifies the apparent dispersion relation which is significant when the planner sample is tilted. Under specific conditions, the sample receives momentum opposite to the electron beam direction.

Digital platforms increasingly face a common challenge in the age of artificial intelligence (AI): how to elicit richer and more useful user-generated content (UGC) without fully automating content production. We study this question in the context of online reviews by examining Yelp's introduction of an AI-enabled topic nudging tool in 2023, which provides real-time prompts to guide reviewers in addressing key dimensions of the dining experience as they write. Using more than 1.5 million Yelp reviews and a differences-in-differences design, we find that AI-enabled topic nudges significantly reshape review generation. The nudges expand topical coverage, especially for underrepresented aspects such as service and ambiance, and lead to longer reviews, but they also reduce overall review volume. In addition, reviews become more textually complex and less readable, and receive fewer helpfulness votes on average. Further analysis shows that the decline in perceived helpfulness is mitigated when review content remains concentrated on a dominant dimension, highlighting the importance of informational focus. We also find heterogeneous effects: less experienced users expand topical coverage and review length more strongly, whereas experienced users exhibit greater complexity and larger declines in perceived helpfulness. Our findings extend research on AI and UGC by highlighting a distinct mode of AI deployment-guiding human contributions rather than generating content on users' behalf-and by revealing its benefits and unintended consequences for platform design.

This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We extend the time-varying barrier function framework to address time-varying safety constraints and explicitly account for control-dependent nonlinearities at the plant input. Guaranteed bounds on the input-output behavior of these nonlinearities are provided through pointwise-in-time quadratic constraints. The result is a class of robust time-varying control barrier functions that define a safety filter. This filter ensures robust safety for all admissible nonlinearities while minimally modifying the command generated by a baseline controller. We derive a second-order cone program (SOCP) to compute this safety filter online and provide novel feasibility conditions for ball-constrained inputs. The proposed approach is demonstrated on a spacecraft docking maneuver.

The Exact Factorization (EF) theory aims at the separation of the nuclear and electronic degrees of freedom in the many-body (MB) quantum mechanical problem. Being formally equivalent to the solution of the MB Schrödinger equation, EF sets up a strategy for the construction of efficient approximations in the theory of the correlated electronic-nuclear motion. Here we extend the EF formalism to incorporate the case of a system under the action of an electromagnetic field. An important interplay between the physical magnetic and the Berry-curvature fields is revealed and discussed within the fully non-adiabatic theory. In particular, it is a known property of the Born-Oppenheimer approximation that, for a neutral atom in a uniform magnetic field, the latter is compensated by the Berry-curvature field in the nuclear equation of motion (\citet{Yin-92}). From an intuitive argument that the atom must not be deflected by the Lorentz force from a straight line trajectory, it has been conjectured that the same compensation should occur within the EF theory as well. We give a rigorous proof of this property.

Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have emerged as a research hotspot due to their ability to express interactions among multiple nodes. This study proposes an iterative generation model for higher-order fractal networks. The iteration is controlled by three parameters: the dimension K of the simplicial complex, the multiplier m, and the iteration count t. The constructed network is a pure simplicial complex. Theoretical analysis using the similarity dimension and experimental verification using the box-counting dimension demonstrate that the generated networks exhibit fractal characteristics. When the multiplier m is large, the generalized degree distribution of the generated networks is characterized by its scale-free nature.

In most particle acceleration or propagation theories, the characteristic features of the cosmic ray spectra due to acceleration limits or propagation phase changes are charge dependent. Alternatively, the interaction scenario would expect mass dependent spectral features in general. The observational verification of which relation takes effect in nature is still lack due to the difficulty of measuring the spectra of individual particles up to very high energies. Here we report direct measurements of the carbon, oxygen, and iron spectra from ~20 gigavolts to ~100 teravolts (~60 teravolts for iron) with 9 years of on-orbit data collected by the Dark Matter Particle Explorer. Distinct spectral softenings have been directly detected in these spectra for the first time. Combined with the updated proton and helium spectra, the spectral softening appears universally at a rigidity of ~15 teravolts. A nuclei mass dependent softening is rejected at a confidence level of >99.999%. Possible interpretations of these results, including a nearby cosmic ray source and other models such as the propagation effect, are discussed.

The bimodule KMS symmetry of a bimodule quantum Markov semigroup extends the classical KMS symmetry of a quantum Markov semigroup. Compared with (bimodule) GNS symmetry, the (bimodule) KMS symmetry retains significantly more of the underlying noncommutativity. In this paper, we study bimodule KMS symmetric quantum Markov semigroups and introduce directional matrices for such semigroups, which reduce to diagonal matrices in the GNS symmetric setting. Using these directional matrices, we establish a corresponding gradient-flow structure. As a consequence, we obtain both a modified logarithmic Sobolev inequality and a Talagrand inequality for bimodule KMS symmetric quantum Markov semigroups.

In this note, we investigate the sharpness of existing bounds for various types of bi-parameter paraproducts acting between product Hardy spaces in the dyadic setting. We show that these bounds are sharp in most cases but fail to be so in one particular instance.

A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the clusters. It is shown that thermal diffusion emerges in the collective description as a significant factor even if it is negligible when transport of the original molecular species is considered. Analytical expressions for the effective diffusion and thermal diffusion coefficients at temperature, pressure, and chemical composition gradients have been derived. The theory has been applied to a technology of H2S conversion in a centrifugal plasma-chemical reactor and has made it possible to account for sulfur clusters in numerical process modeling.

It is known that listeners lose the ability to discriminate the direction of motion of a revolving sound (clockwise vs. counterclockwise) beyond a critical velocity ("the upper limit"), likely due to degraded front-back discrimination. Little is known about how this ability is affected by simultaneously present distractor sounds, despite the real-life importance of tracking moving sounds in the presence of distractors. We hypothesized that the presence of a static distractor sound would impair the perception of moving target sounds and reduce the upper limit, and show that this is indeed the case. A distractor on the right was as effective as a distractor at the front in reducing the upper limit despite the likely importance of resolving front-back confusions. By manipulating the spectral content of both the target and distractor, we found that the upper limit was reduced if and only if the distractor spectrally overlaps with the target in the frequency range relevant for front/back discrimination. Our findings form the first steps toward a better understanding of the tracking of multiple sounds in the presence of distractors.

Ultralight scalar dark matter may couple to the Standard Model through dimension-five operators that contain the field-strength tensors of the gauge interactions. Recent progress in nuclear clocks is projected to increase the sensitivity to such couplings by several orders of magnitude. Future experimental constraints may even have Planck-scale sensitivity, calling for a study of such couplings in a framework that includes quantum gravity. We take a first step towards providing the theoretical constraints on such couplings that arise in asymptotically safe gravity. We find evidence that such couplings vanish in asymptotically safe gravity and are also not generated in a perturbative quantum-gravity regime that describes quantum gravity as an effective field theory.

Multiensemble superradiance extends Dicke superradiance to multiple ensembles and supports dark states whose properties depend on the initial state. In the large-\(N\) limit, we derive analytical covariance matrices for these dark states, revealing inter-ensemble entanglement that enhances quantum metrology. The minimum eigenvalue, determined by the curvature of the superradiance potential, corresponds to the optimal multiparameter spin-squeezing coefficient, which is given by the \emph{Rayleigh quotient} of the spin-squeezing matrix, linking metrological sensitivity to the geometric structure of the underlying dynamics. The multiparameter squeezing coefficient provides a variational framework for optimizing metrological performance. These results enable optimal estimation of arbitrary linear combinations of multiple parameters, offering a concrete protocol for distributed quantum sensing and a promising route toward multimode quantum interferometry.

Flatbands (FB) with compact localized eigenstates (CLS) fall into three main categories, controlled by the algebraic properties of the CLS set: orthogonal, linearly independent, linearly dependent (singular). A CLS parametrization allows us to continuously tune a linearly independent FB into a limiting orthogonal or a linearly dependent (singular) one. We derive the asymptotic real space decay of the flat band projectors for each category. The linearly independent FB is characterized by an exponentially decaying projector and a corresponding localization length $ξ$, all dressed by an algebraic prefactor. In the orthogonal limit, the localization length is $ξ=0$, and the projector is compact. The singular FB limit corresponds to $ξ\rightarrow \infty$ with an emerging power law decay of the projector. We obtain analytical estimates for the localization length and the algebraic power law exponents depending on the dimension of the lattice and the number of bands involved. Numerical results are in excellent agreement with the analytics. Our results are of relevance for the understanding of the details of the FB quantum metric discussed in the context of FB superconductivity, the impact of disorder, and the response to local driving.

Computing-in-Memory (CIM) macros have gained popularity for deep learning acceleration due to their highly parallel computation and low power consumption. However, limited macro size and ADC precision introduce throughput and accuracy bottlenecks. This paper proposes a two-stage CIM-aware model adaptation process. The first stage compresses the model and reallocates resources based on layer importance and macro size constraints, reducing model weight loading latency while improving resource utilization and maintaining accuracy. The second stage performs quantization-aware training, incorporating partial sum quantization and ADC precision to mitigate quantization errors in inference. The proposed approach enhances CIM array utilization to 90\%, enables concurrent activation of up to 256 word lines, and achieves up to 93\% compression, all while preserving accuracy comparable to previous methods.

Flying focus techniques produce laser pulses whose focal points travel at arbitrary, controllable velocities. While this flexibility can enhance a broad range of laser-based applications, existing techniques constrain the motion of the focal point to the propagation direction of the pulse. Here, we introduce a flying focus configuration that decouples the motion of the focus from the propagation direction. A chirped laser pulse focused and diffracted by a diffractive lens and grating creates a focal point that can move both along and transverse to the propagation direction. The focal length of the lens, grating period, and chirp can be tuned to control the direction and velocity of the focus. Simulations demonstrate this control for a holographic configuration suited to high-power pulses, in which two off-axis pump beams with different focal lengths encode the equivalent phase of a chromatic lens and grating in a gas or plasma. For low-power pulses, conventional solid-state or adaptive optics can be used instead. Multi-dimensional control over the focal trajectory enables new configurations for applications, including laser wakefield acceleration of ions, nonlinear Thomson scattering, and surface-plasmon emission of THz radiation.

While architecture is recognized as key to the performance of deep neural networks, its precise effect on training dynamics has been unclear due to the confounding influence of data and loss functions. This paper proposed an analytic framework based on the geometric control theory to characterize the dynamical properties intrinsic to a model's parameterization. We prove that the Structural Invariant Manifolds (SIMs) of an analytic model $F(\mathbfθ)(\mathbf{x})$--submanifolds that confine gradient flow trajectories independent of data and loss--are unions of orbits of the vector field family $\{\nabla_{\mathbfθ} F(\cdot)(\mathbf{x})\mid\mathbf{x}\in\mathbb{R}^d\}$. We then prove that a model's symmetry, e.g., permutation symmetry for neural networks, induces SIMs. Applying this, we characterize the hierarchy of symmetry-induced SIMs in fully-connected networks, where dynamics exhibit neuron condensation and equivalence to reduced-width networks. For two-layer networks, we prove all SIMs are symmetry-induced, closing the gap between known symmetries and all possible invariants. Overall, by establishing the framework for analyzing SIMs induced by architecture, our work paves the way for a deeper analysis of neural network training dynamics and generalization in the near future.

Channel Charting (CC) has emerged as a promising framework for data-driven radio localization, yet existing approaches often struggle to scale globally and to handle the distortions introduced by non-line-of-sight (NLoS) conditions. In this work, we propose a novel CC method that leverages Channel Impulse Response (CIR) data enriched with practical features such as Time Difference of Arrival (TDoA) and Transmission Reception Point (TRP) locations, enabling a self-supervised localization function on a global scale. The proposed framework is further enhanced with short-interval User Equipment (UE) displacement measurements, which improve the continuity and robustness of the learned positioning function. Our algorithm incorporates a mechanism to identify and mask NLoS-induced noisy measurements, leading to significant performance gains. We present the evaluations of our proposed models in a real 5G testbed and benchmarked against centimeter-accurate Real-Time Kinematic (RTK) positioning, in an O-RAN--based 5G network by OpenAirInterface (OAI) software at EURECOM. It demonstrated outperforming results against the state-of-the-art semi-supervised and self-supervised CC approaches in a real-world scenario. The results show localization accuracies of 2-4 meters in 90% of cases, across a range of NLoS ratios. Furthermore, we provide public datasets of CIR recordings, along with the true position labels used in this paper's evaluation.

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is $\#\textsf{BQP}$-complete in the worst case. In this work, we introduce QFAMES (Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

A robust definition of quantum runtime is essential for assessing the performance of quantum algorithms and claims of quantum advantage. While for most classical hardware the total runtime is well approximated by computation plus a weakly varying constant, on current quantum hardware a clean experimental separation between "pure computation" and "overhead" is often not justified. Consequently, conventional quantum runtime analyses excluding substantial system-level overheads can lead to biased performance assessments. In this work we introduce experimentally grounded, end-to-end definitions of quantum runtime for digital and analogue quantum computers, together with a methodology for selecting strong classical baselines for quantum-classical runtime comparisons. Within this framework, we evaluate recent claims of quantum advantage in annealing and gate-based algorithms. We examine three representative case studies. First, we revisit annealing for approximate QUBO problems PRL 134, 160601 (2025), which employs a well-motivated time-to-$ε$ metric but effectively uses annealing time as a proxy for runtime. Second, we analyze a restricted implementation of Simon's problem PRX 15, 021082 (2025), where the favorable scaling in oracle calls is undisputed; however, we show that the estimated runtime of the quantum experiment is approximately two orders of magnitude slower than a tuned classical baseline at the tested sizes. Finally, we find that the runtime advantage of the BF-DCQO hybrid algorithm arXiv:2505.08663 is not observed under more comprehensive benchmarking. Therefore, on current NISQ hardware, runtime-based quantum advantage has not yet been demonstrated under experimentally grounded performance metrics, and credible claims require careful time accounting, appropriate performance measures, and properly chosen classical reference implementations, as discussed in this work.

We present a novel implementation for the quadratic maximum likelihood (QML) power spectrum estimator for multiple correlated scalar fields on the sphere. Our estimator supports arbitrary binning in redshift and multipoles $\ell$ and includes cross-correlations of redshift bins. It implements a fully optimal analysis with a pixel-wise covariance model. We implement a number of optimizations which make the estimator and associated covariance matrix computationally tractable for a low-$\ell$ analysis, suitable for example for kSZ velocity reconstruction or primordial non-Gaussianity from scale-dependent bias analyses. We validate our estimator extensively on simulations and compare its features and precision with the common pseudo-$C_\ell$ method, showing significant gains at large scales. We make our code publicly available. In a companion paper, we apply the estimator to kSZ velocity reconstruction using data from ACT and DESI Legacy Survey and construct full set of QML estimators on 40 correlated fields up to $N_{\text{side}}= 32$ in timescale of an hour on a single 24-core CPU requiring $<256\ \mathrm{Gb}$ RAM, demonstrating the performance of the code.