The release of ChatGPT in 2022 triggered a rapid surge in generative artificial intelligence mobile apps (Gen-AI apps). Despite widespread adoption, little is known about how end users perceive and evaluate these Gen-AI functionalities. We conduct a user-centered analysis of 1,035,342 reviews from 171 Gen-AI apps from the Google Play Store. We propose SARA (Selection, Acquisition, Refinement, and Analysis), a four-phase framework that leverages prompt-based LLMs for large-scale review analysis. We validate the reliability of LLM-based topic extraction and assignment using 4,353 manually evaluated reviews, achieving 91% accuracy with five-shot prompting and filtering of non-informative reviews. We identify the top ten topics (e.g., AI Performance and Emotional Connection) and perform a cross-platform comparison with Apple App Store reviews. Through qualitative analysis of 762 reviews, we uncover three opportunities (AI for Accessibility and Wellbeing, AI as a Collaborative Creative Tool, and AI Versatility) and three challenges (Managing User Expectations and AI Limitations, Balancing Content Moderation and Creative Freedom, and Strategic Integration of Gen-AI Features). Finally, we analyze temporal trends, revealing how user concerns shift as users mature. Our findings enable researchers and developers to better leverage the capabilities of Gen-AI apps and address potential challenges.

Fast Fourier Transform (FFT) libraries are widely used for evaluating discrete convolutions. Most FFT implementations follow some variant of the Cooley-Tukey framework, in which the transform is decomposed into butterfly operations and index-reversal permutations. While butterfly operations dominate the floating-point operation count, the memory access patterns induced by index-reversal permutations significantly degrade the FFT's arithmetic intensity. When performing discrete convolution, the three sets of index-reversal permutations which occur in FFT-based implementations using Cooley-Tukey frameworks cancel out, thus paving the way to implementations free of any permutation. To the best of our knowledge, such permutation-free variants of FFT-based discrete convolution are not commonly used in practice, making such kernels worth investigating. Here, we look into such permutation-avoiding convolution procedures for multi-dimensional cases within a general radix Cooley-Tukey framework. We perform numerical experiments to benchmark the algorithms presented against state-of-the-art FFT-based convolution implementations. Our results suggest that developers of FFT libraries should consider supporting permutation-avoiding convolution kernels.

In this paper, we determine the asymptotic dimension for all surface braid groups -- including those associated with non-orientable and infinite-type surfaces -- as well as for torsion-free poly-finitely generated surface groups. We demonstrate that for both classes, the virtual cohomological dimension and the asymptotic dimension coincide. For poly-finitely generated surface groups and braid groups of finite-type surfaces, our approach establishes that these groups are virtual duality groups in the sense of Bieri-Eckmann. In the case of infinite-type surfaces, the argument is based on the fact that their braid groups are countable and normally poly-free.

We provide an exact formula for the mean first-passage time (MFPT) to a target at the origin for a single particle diffusing on a $d$-dimensional hypercubic {\em lattice} starting from a fixed initial position $\vec R_0$ and resetting to $\vec R_0$ with a rate $r$. Previously known results in the continuous space are recovered in the scaling limit $r\to 0$, $R_0=|\vec R_0|\to \infty$ with the product $\sqrt{r}\, R_0$ fixed. However, our formula is valid for any $r$ and any $\vec R_0$ that enables us to explore a much wider region of the parameter space that is inaccessible in the continuum limit. For example, we have shown that the MFPT, as a function of $r$ for fixed $\vec R_0$, diverges in the two opposite limits $r\to 0$ and $r\to \infty$ with a unique minimum in between, provided the starting point is not a nearest neighbour of the target. In this case, the MFPT diverges as a power law $\sim r^ϕ$ as $r\to \infty$, but very interestingly with an exponent $ϕ= (|m_1|+|m_2|+\ldots +|m_d|)-1$ that depends on the starting point $\vec R_0= a\, (m_1,m_2,\ldots, m_d)$ where $a$ is the lattice spacing and $m_i$'s are integers. If, on the other hand, the starting point happens to be a nearest neighbour of the target, then the MFPT decreases monotonically with increasing $r$, approaching a universal limiting value $1$ as $r\to \infty$, indicating that the optimal resetting rate in this case is infinity. We provide a simple physical reason and a simple Markov-chain explanation behind this somewhat unexpected universal result. Our analytical predictions are verified in numerical simulations on lattices up to $50$ dimensions. Finally, in the absence of a target, we also compute exactly the position distribution of the walker in the nonequlibrium stationary state that also displays interesting lattice effects not captured by the continuum theory.

The XY-mixer has widespread utilization in modern quantum computing, including in variational quantum algorithms, such as Quantum Alternating Operator Ansatz (QAOA). The XY ansatz is particularly useful for solving Cardinality Constrained Optimization tasks, a large class of important NP-hard problems. First, we give explicit decompositions of the dynamical Lie algebras (DLAs) associated with a variety of $XY$-mixer topologies. When these DLAs admit simple Lie algebra decompositions, they are efficiently trainable. An example of this scenario is a ring $XY$-mixer with arbitrary $R_Z$ gates. Conversely, when we allow for all-to-all $XY$-mixers or include $R_{ZZ}$ gates, the DLAs grow exponentially and are no longer efficiently trainable. We provide numerical simulations showcasing these concepts on Portfolio Optimization, Sparsest $k$-Subgraph, and Graph Partitioning problems. These problems correspond to exponentially-large DLAs and we are able to warm-start these optimizations by pre-training on polynomial-sized DLAs by restricting the gate generators. This results in improved convergence to high quality optima of the original task, providing dramatic performance benefits in terms of solution sampling and approximation ratio on optimization tasks for both shared angle and multi-angle QAOA.

Astrometry, the precise measurement of stellar positions and velocities, offers a promising approach to probing the low-frequency stochastic gravitational wave background (SGWB). Notably, astrometric vector sky maps are sensitive to parity-violating SGWB signals, which cannot be distinguished using pulsar timing array observations in an isotropic SGWB. We present the first astrometric constraints on parity-violating SGWB using quasar catalogs from Gaia DR3 and VLBA data. By analyzing the $EB$ correlation in the two-point correlation function of the proper motions of the quasars, we find 2$σ$ constraints on the parity-violating SGWB amplitude $h_{70}^2Ω_{V} = -0.020 \pm 0.025$ from Gaia DR3 and $h_{70}^2Ω_{V} = -0.004 \pm 0.010$ from VLBA. These constraints are valid in the frequency range $4.2 \times 10^{-18}\,{\rm Hz} < f < 1.1 \times 10^{-8}\,{\rm Hz}$. Although not currently a tight constraint on theoretical models, this first attempt lays the groundwork for future investigations using more precise astrometric data.

The integration of large language models (LLMs) into a wide range of applications has highlighted the critical role of well-crafted system prompts, which require extensive testing and domain expertise. These prompts enhance task performance but may also encode sensitive information and filtering criteria, posing security risks if exposed. Recent research shows that system prompts are vulnerable to extraction attacks, while existing defenses are either easily bypassed or require constant updates to address new threats. In this work, we introduce ProxyPrompt, a novel defense mechanism that prevents prompt leakage by replacing the original prompt with a proxy. This proxy maintains the original task's utility while obfuscating the extracted prompt, ensuring attackers cannot reproduce the task or access sensitive information. Comprehensive evaluations on 264 LLM and system prompt pairs show that ProxyPrompt protects 94.70% of prompts from extraction attacks, outperforming the next-best defense, which only achieves 42.80%.

Weihrauch reducibility is a notion of reducibility between computational problems that is useful to calibrate the uniform computational strength of a multivalued function. It complements the analysis of mathematical theorems done in reverse mathematics, as multi-valued functions on represented spaces can be considered as realizers of theorems in a natural way. Despite the rich literature and the relevance of the applications of category theory in logic and realizability, actually there are just a few works starting to study the Weihrauch reducibility from a categorical point of view. The main purpose of this work is to provide a full categorical account to the notion of extended Weihrauch reducibility introduced by A. Bauer, which generalizes the original notion of Weihrauch reducibility. In particular, we present a tripos and a topos for extended Weihrauch degrees. We start by defining a new tripos, abstracting the notion of extended Weihrauch degrees, and then we apply the tripos-to-topos construction to obtain the desired topos. Then we show that the Kleene-Vesley topos is a topos of $j$-sheaves for a certain Lawvere-Tierney topology over the topos of extended Weihrauch degrees.

The rapid progress in quantum hardware is expected to make them viable tools for the study of quantum algorithms in the near term. The timeline to useful algorithmic experimentation can be accelerated by techniques that use many noisy shots to produce an accurate estimate of the observable of interest. One such technique is to encode the quantum circuit using an error detection code and discard the samples for which an error has been detected. An underexplored property of error-detecting codes is the flexibility in the circuit encoding and fault-tolerant gadgets, which enables their co-optimization with the algorthmic circuit. However, standard circuit optimization tools cannot be used to exploit this flexibility as optimization must preserve the fault-tolerance of the gadget. In this work, we focus on the $[[k+2, k, 2]]$ Iceberg quantum error detection code, which is tailored to trapped-ion quantum processors. We design new flexible fault-tolerant gadgets for the Iceberg code, which we then co-optimize with the algorithmic circuit for the quantum approximate optimization algorithm (QAOA) using tree search. By co-optimizing the QAOA circuit and the Iceberg gadgets, we achieve an improvement in QAOA success probability from $44\%$ to $65\%$ and an increase in post-selection rate from $4\%$ to $33\%$ at 22 algorithmic qubits, utilizing 330 algorithmic two-qubit gates and 744 physical two-qubit gates on the Quantinuum H2-1 quantum computer, compared to the previous state-of-the-art hardware demonstration. Furthermore, we demonstrate better-than-unencoded performance for up to 34 algorithmic qubits, employing 510 algorithmic two-qubit gates and 1140 physical two-qubit gates.

Ensuring that an AI system behaves reliably and as intended, especially in the presence of unexpected faults or adversarial conditions, is a complex challenge. Inspired by the field of Byzantine Fault Tolerance (BFT) from distributed computing, we explore a fault tolerance architecture for AI safety. By drawing an analogy between unreliable, corrupt, misbehaving or malicious AI artifacts and Byzantine nodes in a distributed system, we propose an architecture that leverages consensus mechanisms to enhance AI safety and reliability.

Integrated green light sources are essential for telecommunications and quantum applications, while the performance of current on-chip green light generation is still limited in power and tunability. In this work, we demonstrate green light generation in silicon nitride microresonators using photo-induced second-order nonlinearities, achieving up to 3.5 mW green power via second-harmonic generation and densely tunable over a 29 nm range. In addition, we report milliwatt-level all-optical poling (AOP) threshold, allowing for amplifier-free continuous-wave AOP. Furthermore, we demonstrate non-cascaded sum-frequency generation, leveraging the combination of AOP and simultaneous coherent frequency combs generation at 1 $μ$m. Such comb-assisted AOP enables switching of the green light generation over an 11 nm range while maintaining the pump within a single resonance. The combination of such highly efficient photo-induced nonlinearity and multi-wavelength AOP enables the realization of low-threshold, high-power, widely-tunable on-chip green sources.

Precision measurements of Higgs boson differential production cross sections are a key tool to probe the properties of the Higgs boson and test the standard model. New physics can affect both Higgs boson production and decay, leading to deviations from the distributions that are expected in the standard model. In this paper, combined measurements of differential spectra in a fiducial region matching the experimental selections are performed, based on analyses of four Higgs boson decay channels ($γγ$, ZZ$^{(*)}$, WW$^{(*)}$, and $ττ$) using proton-proton collision data recorded with the CMS detector at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The differential measurements are extrapolated to the full phase space and combined to provide the differential spectra. A measurement of the total Higgs boson production cross section is also performed using the $γγ$ and ZZ decay channels, with a result of 53.4 $^{+2.9}_{-2.9}$ (stat) $^{+1.9}_{-1.8}$ (syst) pb, consistent with the standard model prediction of 55.6 $\pm$ 2.5 pb. The fiducial measurements are used to compute limits on Higgs boson couplings using the $κ$-framework and the SM effective field theory.

The conditions for forming quasicrystals and their approximants are stringent, normally requiring multiple length scales to stabilize the quasicrystalline order. Here we report an unexpected finding that the approximants and motifs of dodecagonal quasicrystals can be spontaneously formed in the simplest system of identical hard disks, utilizing the unstable feature of the initial square packing subject to mechanical perturbations. Because there is only one length scale involved, this finding challenges existing theories of quasicrystals and their approximants. By applying the same approach to a system known to form a dodecagonal quasicrystal, we develop decent quasicrystalline order in a purely mechanical manner. With the aid of thermal treatment, we achieve a significantly better quasicrystalline order than that from the direct self-assembly of the liquid state within the same period of time. In sufficiently low temperatures where the self-assembly of a liquid is significantly hindered, our approach still promotes the formation of quasicrystals. Our study thus opens a venue for high-efficiency search and formation of quasicrystals, and may have broader implications for the design and synthesis of quasicrystalline materials.

In this paper, we propose a novel method for frequency modulated continuous wave (FMCW) radar mutual interference mitigation (IM) based on the discrete fractional Fourier transform (DFrFT). Interference chirps are detected and mitigated by compression and zeroing in the fractional domain. We provide an efficient implementation that can deal with multiple interferers, where we perform consecutive DFrFTs utilizing its angle-additivity property. For that purpose, we generalize and reduce the computational complexity of the multi-angle centered discrete fractional Fourier transform [1]. Our algorithm is designed to be simple and fast such that it can be implemented in hardware. We evaluate our algorithm on a synthetic I/Q-modulated dataset and outperform reference methods in terms of the mean squared error, signal-to-interference-plus-noise ratio, error vector magnitude, true positive rate, false alarm rate and F1-score.

Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same time, finding a new category of graphs that allows a "common denominator" functor unifying the covariant and contravariant constructions is a fundamental problem. Herein, we solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. Although we focus on Leavitt path algebras and graph C*-algebras, on the way we unravel functors to k-Alg given by path algebras, Cohn path algebras and Toeplitz graph C*-algebras from suitable subcategories of RG. Better still, we illustrate relation morphisms of graphs by naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls.

Starting in the 2024/25 season, the Union of European Football Associations (UEFA) has fundamentally changed the format of its club competitions: the group stage has been replaced by a league phase played by 36 teams in an incomplete round robin format. This makes ranking the teams based on their results challenging because teams play against different sets of opponents, whose strengths vary. In this research note, we apply several well-known ranking methods for incomplete round robin tournaments to the 2024/25 UEFA Champions League league phase in order to check the robustness of the official ranking, as well as to call the attention of organizers to the non-trivial issue of ranking in these competitions. Our results show that it is doubtful whether the currently used point-based system provides the best ranking of the teams.

It is well-known that a function on an open set in $\mathbb R^d$ is smooth if and only if it is arc-smooth, i.e., its composites with all smooth curves are smooth. In recent work, we extended this and related results (for instance, a real analytic version) to suitable closed sets, notably, sets with Hölder boundary and fat subanalytic sets satisfying a necessary topological condition. In this paper, we prove that the resulting set-theoretic identities of function spaces are bornological isomorphisms with respect to their natural locally convex topologies. Extending the results to maps with values in convenient vector spaces, we obtain corresponding exponential laws. Additionally, we show analogous results for special ultradifferentiable Braun-Meise-Taylor classes.

Quantum information scrambling (QIS) describes the rapid spread of initially localized information across an entire quantum many-body system through entanglement generation. Once scrambled, the original local information becomes encoded globally, inaccessible from any single subsystem. In this work, we introduce a circuit-based decoding protocol. By utilizing the concept of postselected closed timelike curves (PCTCs), we demonstrate how postselection allows us to interpret an ordinary quantum experiment as an example of a paradox-free trajectory, simulating a consistent time loop and reliable information recovery. Specifically, when conditioned on a final postselected outcome, this experiment can be interpreted as decoding the scrambled information even before the original information is generated. Furthermore, the success probability of the PCTC is governed by out-of-time-ordered correlations, which is a standard measure of QIS. We experimentally implement our protocol on cloud-based Quantinuum and IBM quantum processors. Our approach illuminates a unique quantum task under postselection: the causally consistent simulation of future-to-past scrambled information retrieval.

We investigate the time modulation of weak nuclear decays as a method to probe axion dark matter. To this end, we develop a theoretical framework to compute the $θ$-dependence of weak nuclear decays, including electron capture and $β$ decay, which enables us to predict the time variation of weak radioactivity in response to an oscillating axion dark matter background. As an application, we recast old data sets, from the weak nuclear decays of ${^{40}\text{K}}$ and ${^{137}\text{Cs}}$ taken at the underground Gran Sasso Laboratory, in order to set constraints on the axion decay constant, specifically in the axion mass range from few $10^{-23}\;$eV up to $10^{-19}\;$eV. We finally propose a new measurement at the Gran Sasso Laboratory, based on the weak nuclear decay of ${^{40}\text{K}}$ via electron capture, in order to explore even shorter timescales, thus reaching sensitivities to axion masses up to $10^{-9}\;$eV.

This is the text of a talk given by the first author at the Harish-Chandra centenary meeting held in Allahabad in October 2023. It reviews Harish-Chandra's isomorphism and its many applications to representation theory and mathematical physics. It also announces the existence and uniqueness of nonsymmetric shift operators for an arbitrary root system. These are differential-reflection operators with a transmutation property relative to Dunkl-Cherednik operators: they shift the parameter k of these operators by 1, and restrict on symmetric functions to the hypergeometric shift operators introduced by the first author.

We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the regularization parameter shrinks with the sample size; this regime is largely unexplored in the prior statistical literature, where $ε$ is typically held fixed. Additionally, we show that a rescaling of the barycentric projection of the empirical entropic optimal self-transport plans converges to the score function, a central object for diffusion models, and characterize the asymptotic fluctuations both pointwise and in $L^2$. Finally, we describe under what conditions the methods used enable to derive (pointwise) limiting distribution results for the empirical entropic optimal transport potentials in the case of two different measures and appropriately chosen shrinking regularization parameter. This endeavour requires a better understanding of the composition of Sinkhorn operators in the small $\eps$-limit, a result of independent interest.

We use the Monte Carlo For AGN (active galactic nucleus) Channel Testing and Simulation (McFACTS, https://www.github.com/mcfacts/mcfacts) code to study the effect of AGN disk and nuclear star cluster parameters on predicted mass distributions for LIGO-Virgo-KAGRA (LVK) compact binaries forming in AGN disks. The assumptions we vary include the black hole (BH) initial mass function, disk model, disk size, disk lifetime, and the prograde-to-retrograde fraction of newly formed black hole binaries. Broadly we find that dense, moderately short-lived AGN disks are preferred for producing a $(q,χ_{\rm eff})$ anti-correlation like those identified from existing gravitational wave (GW) observations. Additionally, a BH initial mass function (MF $\propto M^{-2}$) is preferred over a more top-heavy MF ($M^{-1}$). The preferred fraction of prograde-to-retrograde is $>90\%$, to produce results consistent with observations.

A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed using regular orthogonal matrices of level 2, which has relevance for Haemers' conjecture. We present two new switching methods and several combinatorial and geometrical reformulations of existing switching operations of level 2. We also introduce the concept of reducibility and use it to classify all irreducible switching methods that correspond to a conjugation with a regular orthogonal matrix of level 2 with one nontrivial indecomposable block, up to switching sets of size 12, extending previous results.

The stability theory of compact metric spaces with positive topological dimension is a well-established area in Dynamical Systems. A central result, attributed to Walters, connects the concepts of topological stability and the shadowing property in invertible dynamics. In contrast, zero-dimensional stability theory is a developing field, with an analogue of Walters' theorem for Cantor spaces being fully established only in 2019 by Kawaguchi. In this paper, we investigate the shadowing and stability properties of non-invertible dynamics in zero-dimensional spaces, focusing on the $p$-adic integers $\mathbb{Z}_{p} $ and the $p$-adic numbers $\mathbb{Q}_{p}$, where $p \geq 2$ is a prime number. The main result provides sufficient conditions under which the following families of maps exhibit strong shadowing and stability properties: 1) $p$-adic dynamical systems that are right-invertible through contractions, and 2) left-invertible contractions. Consequently, new examples of stable $p$-adic dynamics are presented.

We show that a locally finite, connected graph has a coarse embedding into a Hilbert space if and only if there exist bond percolations with arbitrarily large marginals and two-point function vanishing at infinity. We further show that the decay of the two-point function is stretched exponential with stretching exponent $α\in[0,1]$ if and only if the $L^1$-compression exponent of the graph is at least $α$, leading to a probabilistic characterization of this exponent. These results are new even in the particular setting of Cayley graphs of finitely generated groups. The proofs build on new probabilistic methods introduced recently by the authors to study group-invariant percolation on Cayley graphs [28,29], which are now extended to the general, non-symmetric situation of graphs to study their coarse embeddability and $L^1$-compression exponents.

While a physical theory should be independent of the coordinate frame chosen by any observer, the observations themselves in fact depend on the choice of coordinates. In particular, different coordinate frames reflect different symmetries seen by a local observer. In this work, we discuss the applicability of different coordinate choices and the resulting line elements for static axisymmetric vacuum spacetimes. We find that the effective potential experienced by a local observer in the low-velocity limit is highly dependent on the form of the line element and thus on the coordinates chosen in the description. For example, this affects the form of a rotation curve expected by such an observer. We thus conclude that it is important to review the choices of local (coordinate frame of the observer) and global symmetries carefully to understand observations from a generally relativistic point of view.

In this note, (rational) Betti numbers of homotopy colimits for toric diagrams and their classifying spaces are described in terms of sheaf cohomology over CW posets. We prove for any $T$-diagram $D$ over any CW poset that Cohen-Macaulayness (over $\mathbb{Q}$) of the $T$-action on $hocolim\ D$ is equivalent to acyclicity for a certain sheaf. The ordinary and bigraded Betti numbers are computed for skeletons of equivariantly formal spaces from this class (in particular, of compact smooth toric manifolds).

We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-abelian anyon condensation, which is a gauging operation for topological lines with non-group-like i.e. non-invertible fusion rules. We find that, generically, dualities involve such non-invertible anyon condensation and that this unifies a variety of exceptional phenomena in topological field theories and their associated boundary rational conformal field theories, including conformal embeddings, and Maverick cosets (those where standard algorithms for constructing a coset model fail.) We illustrate our discussion in a variety of isolated examples as well as new infinite series of dualities involving non-abelian anyon condensation including: i) a new description of the parafermion theory as $(SU(N)_{2} \times Spin(N)_{-4})/\mathcal{A}_{N},$ ii) a new presentation of a series of points on the orbifold branch of $c=1$ conformal field theories as $(Spin(2N)_{2} \times Spin(N)_{-2} \times Spin(N)_{-2})/\mathcal{B}_{N}$, and iii) a new dual form of $SU(2)_{N}$ as $(USp(2N)_{1} \times SO(N)_{-4})/\mathcal{C}_{N}$ arising from conformal embeddings, where $\mathcal{A}_{N}, \mathcal{B}_{N},$ and $\mathcal{C}_{N}$ are appropriate collections of gauged non-invertible bosons.

The field of nuclear science has considerably advanced since its beginning just over a century ago. Today, the science of rare isotopes is on the cusp of a new era with theoretical and computing advances complementing experimental capabilities at new facilities internationally. In this article we present a vision for the science of rare isotope beams (RIBs). We do not attempt to cover the full breadth of the field, but rather provide a perspective and address a selection of topics that reflect our own interests and expertise. We focus in particular on systems near the drip lines, where one often finds nuclei that are referred to as "exotic," and where the role of the "nuclear continuum" is only just starting to be explored. An important aspect of this article is the attempt to highlight the crucial connections between nuclear structure and nuclear reactions required to fully interpret and leverage the rich data to be collected in the next years at RIB facilities. Further, we connect the efforts in structure and reactions to key questions of nuclear astrophysics.

Transmon qubits arise from the quantization of nonlinear resonators, systems that are prone to the buildup of strong, possibly chaotic, fluctuations. Such instabilities will likely affect fast gate operations which involve the transient population of higher excited states outside the computational subspace. Here we show that a statistical analysis of the instantaneous eigenphases of the time evolution operator, in particular of their curvatures, allows for identifying the subspace affected by chaotic fluctuations. Our analysis shows that fast entangling gates, operating at speeds close to the so-called quantum speed limit, contain transient regimes where the dynamics indeed becomes partially chaotic for just two transmons.