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A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has uncovered new codes and new code implementations. In this work, we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a unique solution to hardware design challenges and introducing flexibility in surface code realization. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of $\Lambda_{35,\text{hex}} = 2.15(2)$, $\Lambda_{35,\text{walk}} = 1.69(6)$, and $\Lambda_{35,\text{iSWAP}} = 1.56(2)$, achieving state-of-the-art error suppression for each. With detailed error budgeting, we explore their performance trade-offs and implications for hardware design. This work demonstrates that dynamic circuit approaches satisfy the demands for fault-tolerance and opens new alternative avenues for scalable hardware design., Comment: 11 pages, 5 figures, Supplementary Information

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $\Lambda_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create particles with local gates and simulate their quantum dynamics via a discretized time evolution. As the effective magnetic field is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent particle and string dynamics.

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Bars drive gas inflow. As the gas flows inwards, shocks and shear occur along the bar dust lanes. Such shocks and shear can affect the star formation and change the gas properties. For four barred galaxies, we present H{\alpha} velocity gradient maps that highlight bar-driven shocks and shear using data from the PHANGS-MUSE and PHANGS-ALMA surveys which allow us to study bar kinematics in unprecedented detail. Velocity gradients are enhanced along the bar dust lanes, where shocks and shear are shown to occur in numerical simulations. Velocity gradient maps also efficiently pick up expanding shells around HII regions. We put pseudo slits on the regions where velocity gradients are enhanced and find that H{\alpha} and CO velocities jump up to ~170 km/s, even after removing the effects of circular motions due to the galaxy rotation. Enhanced velocity gradients either coincide with the peak of CO intensity along the bar dust lanes or are slightly offset from CO intensity peaks, depending on the objects. Using the BPT diagnostic, we identify the source of ionization on each spaxel and find that star formation is inhibited in the high velocity gradient regions of the bar, and the majority of those regions are classified as LINER or composite. This implies that star formation is inhibited where bar-driven shear and shocks are strong. Our results are consistent with the results from the numerical simulations that show star formation is inhibited in the bar where shear force is strong., Comment: 26 pages, Accepted for publication in ApJ

One of the main challenges in simultaneous localization and mapping (SLAM) is real-time processing. High-computational loads linked to data acquisition and processing complicate this task. This article presents an efficient feature extraction approach for mapping structured environments. The proposed methodology, weighted conformal LiDAR-mapping (WCLM), is based on the extraction of polygonal profiles and propagation of uncertainties from raw measurement data. This is achieved using conformal M bius transformation. The algorithm has been validated experimentally using 2-D data obtained from a low-cost Light Detection and Ranging (LiDAR) range finder. The results obtained suggest that computational efficiency is significantly improved with reference to other state-of-the-art SLAM approaches.

Dwarf barred galaxies are the perfect candidates for hosting slowly-rotating bars. They are common in dense environments and they have a relatively shallow potential well, making them prone to heating by interactions. When an interaction induces bar formation, the bar should rotate slowly. They reside in massive and centrally-concentrated dark matter halos, which slow down the bar rotation through dynamical friction. While predictions suggest that slow bars should be common, measurements of bar pattern speed, using the Tremaine-Weinberg method, show that bars are mostly fast in the local Universe. We present a photometric and kinematic characterisation of bars hosted by two dwarf galaxies in the Virgo Cluster, NGC 4483 and NGC 4516. We derive the bar length and strength using the Next Generation Virgo Survey imaging and the circular velocity, bar pattern speed, and rotation rate using spectroscopy from the Multi Unit Spectroscopic Explorer. Including the previously studied galaxy IC 3167, we compare the bar properties of the three dwarf galaxies with those of their massive counterparts from literature. Bars in the dwarf galaxies are shorter and weaker, and rotate slightly slower with respect to those in massive galaxies. This could be due to a different bar formation mechanism and/or to a large dark matter fraction in the centre of dwarf galaxies. We show that it is possible to push the application of the Tremaine-Weinberg method to the galaxy low mass regime., Comment: Accepted for publication in MNRAS

The debate about the universality of the stellar initial mass function (IMF) revolves around two competing lines of evidence. While measurements in the Milky Way, an archetypal spiral galaxy, seem to support an invariant IMF, the observed properties of massive early-type galaxies (ETGs) favor an IMF somehow sensitive to the local star formation conditions. The fundamental methodological and physical differences between both approaches have hampered, however, a comprehensive understanding of IMF variations. We describe here an improved modelling scheme that allows for the first time consistent IMF measurements across stellar populations with different ages and complex star formation histories. Making use of the exquisite MUSE optical data from the TIMER survey and powered by the MILES stellar population models, we show the age, metallicity, [Mg/Fe], and IMF slope maps of the inner regions of NGC 3351, a spiral galaxy with a mass similar to that of the Milky Way. The measured IMF values in NGC3351 follow the expectations from a Milky Way-like IMF, although they simultaneously show systematic and spatially coherent variations, particularly for low-mass stars. In addition, our stellar population analysis reveals the presence of metal-poor and Mg-enhanced star-forming regions that appear to be predominantly enriched by the stellar ejecta of core-collapse supernovae. Our findings showcase therefore the potential of detailed studies of young stellar populations to better understand the early stages of galaxy evolution and, in particular, the origin of the observed IMF variations beyond and within the Milky Way., Comment: 16 pages, 11 figures. Accepted for publication in Astronomy and Astrophysics

We apply the barred Schwarzschild method developed by Tahmasebzadeh et al. (2022) to a barred S0 galaxy, NGC 4371, observed by IFU instruments from the TIMER and ATLAS3D projects. We construct the gravitational potential by combining a fixed black hole mass, a spherical dark matter halo, and stellar mass distribution deprojected from $3.6$ $\mu$m S$^4$G image considering an axisymmetric disk and a triaxial bar. We independently modelled kinematic data from TIMER and ATLAS3D. Both models fit the data remarkably well. We find a consistent bar pattern speed from the two sets of models with $\Omega_{\rm p} = 23.6 \pm 2.8 \hspace{.08cm} \mathrm{km \hspace{.04cm} s^{-1} \hspace{.04cm} kpc^{-1} }$ and $\Omega_{\rm p} = 22.4 \pm 3.5 \hspace{.08cm} \mathrm{km \hspace{.04cm} s^{-1} \hspace{.04cm} kpc^{-1} }$, respectively. The dimensionless bar rotation parameter is determined to be $ 1.88 \pm 0.37$, indicating a likely slow bar in NGC 4371. Additionally, our model predicts a high amount of dark matter within the bar region ($M_{\rm DM}/ M_{\rm total}$ $\sim 0.51 \pm 0.06$), which, aligned with the predictions of cosmological simulations, indicates that fast bars are generally found in baryon-dominated disks. Based on the best-fitting model, we further decompose the galaxy into multiple 3D orbital structures, including a BP/X bar, a classical bulge, a nuclear disk, and a main disk. The BP/X bar is not perfectly included in the input 3D density model, but BP/X-supporting orbits are picked through the fitting to the kinematic data. This is the first time a real barred galaxy has been modelled utilizing the Schwarzschild method including a 3D bar., Comment: 25 pages, 19 figures, Accepted for publication in MNRAS

Double bars make up a significant fraction of barred galaxies. We propose a new formation scenario for double bars that involves tidal interactions. We demonstrate the viability of this scenario using two examples of simulated galaxies from run TNG50-1 of the IllustrisTNG project. In the proposed scenario the inner bar forms first, either in isolation, via instabilities, or through previous tides. The outer bar forms later from the material that is tidally distorted by a strong interaction. The inner and outer bars formed this way rotate with different pattern speeds and can be mistaken for a single bar when their phases align. The double-barred structure is stable and can last for at least 3 Gyr. The inner bars of the tidally induced double bars can also have big sizes, which can possibly explain the origin of sizable inner bars recently found in some galaxies., Comment: 5 pages, 6 figures, submitted to MNRAS Letters

The innermost regions of most galaxies are characterised by the presence of extremely dense nuclear star clusters. Nevertheless, these clusters are not the only stellar component present in galactic nuclei, where larger stellar structures known as nuclear stellar discs, have also been found. Understanding the relation between nuclear star clusters and nuclear stellar discs is challenging due to the large distance towards other galaxies which limits their analysis to integrated light. The Milky Way's centre, at only 8 kpc, hosts a nuclear star cluster and a nuclear stellar disc, constituting a unique template to understand their relation and formation scenario. We aim to study the kinematics and stellar metallicity of stars from the Milky Way's nuclear star cluster and disc to shed light on the relation between these two Galactic centre components. We used publicly available photometric, proper motions, and spectroscopic catalogues to analyse a region of $\sim2.8'\times4.9'$ centred on the Milky Way's nuclear star cluster. We built colour magnitude diagrams, and applied colour cuts to analyse the kinematic and metallicity distributions of Milky Way's nuclear star cluster and disc stars with different extinction along the line of sight. We detect kinematics and metallicity gradients for the analysed stars along the line of sight towards the Milky Way's nuclear star cluster, suggesting a smooth transition between the nuclear stellar disc and cluster. We also find a bi-modal metallicity distribution for all the analysed colour bins, which is compatible with previous work on the bulk population of the nuclear stellar disc and cluster. Our results suggest that these two Galactic centre components might be part of the same structure with the Milky Way's nuclear stellar disc being the grown edge of the nuclear star cluster., Comment: Accepted for publication in A&A. 13 pages, 9 figures

When galactic discs settle and become massive enough, they are able to form stellar bars. These non-axisymmetric structures induce shocks in the gas, causing it to flow to the centre where nuclear structures, such as nuclear discs and rings, are formed. Previous theoretical and observational studies have hinted at the co-evolution of bars and nuclear discs, suggesting that nuclear discs grow "inside-out", thereby proposing that smaller discs live in younger bars. Nevertheless, it remains unclear how the bar and the nuclear structures form and evolve with time. The smallest nuclear discs discovered to date tend to be larger than $\sim200~\rm{pc}$, even though some theoretical studies find that when nuclear discs form they can be much smaller. Using MUSE archival data, we report for the first time two extragalactic nuclear discs with radius sizes below $100~\rm{pc}$. Additionally, our estimations reveal the youngest bars found to date. We estimate that the bars in these galaxies formed $4.50^{+1.60}_{-1.10}\rm{(sys)}^{+1.00}_{-0.75}\rm{(stat)}$ and $0.7^{+2.60}\rm{(sys)}^{+0.05}_{-0.05}\rm{(stat)}~\rm{Gyr}$ ago, for NGC\,289 and NGC\,1566, respectively. This suggests that at least some disc galaxies in the Local Universe may still be dynamically settling. By adding these results to previous findings in the literature, we retrieve a stronger correlation between nuclear disc size and bar length and we derive a tentative exponential growth scenario for nuclear discs., Comment: Accepted in A&A (in press), 13 pages, 5 figures, 2 tabels

We present photometric and morphological analyses of nuclear star clusters (NSCs) -- very dense, massive star clusters present in the central regions of most galaxies -- in a sample of 33 massive disk galaxies within 20 Mpc, part of the "Composite Bulges Survey." We use data from the Hubble Space Telescope including optical (F475W and F814W) and near-IR (F160W) images from the Wide Field Camera 3. We fit the images in 2D to take into account the full complexity of the inner regions of these galaxies (including the contributions of nuclear disks and bars), isolating the nuclear star cluster and bulge components. We derive NSC radii and magnitudes in all 3 bands, which we then use to estimate NSC masses. Our sample significantly expands the sample of massive late-type galaxies with measured NSC properties. We clearly identify nuclear star clusters in nearly 80% of our galaxies, putting a lower limit on the nucleation fraction in these galaxies that is higher than previous estimates. We find that the NSCs in our massive disk galaxies are consistent with previous NSC mass-NSC radius and Galaxy Mass-NSC Mass relations. However, we also find a large spread in NSC masses, with a handful of galaxies hosting very low-mass, compact clusters. Our NSCs are aligned in PA with their host galaxy disks but are less flattened. They show no correlations with bar or bulge properties. Finally, we find the ratio of NSC to BH mass in our massive disk galaxy sample spans a factor of $\sim$300., Comment: Accepted to The Astrophysical Journal

In arXiv:1911.08213 it was conjectured that the compactly supported cohomology of the $m$-th restricted contact locus of an isolated hypersurface singularity coincides, up to a shift, with the Floer cohomology of the $m$-th iterate of the monodromy of the Milnor fiber. In this paper we give an affirmative answer to this conjecture in the case of plane curves., Comment: 27 pages, 2 figures

The epoch in which galactic discs settle is a major benchmark to test models of galaxy formation and evolution but is as yet largely unknown. Once discs settle and become self-gravitating enough, stellar bars are able to form; therefore, determining the ages of bars can shed light on the epoch of disc settling, and on the onset of secular evolution. Nevertheless, until now, timing when the bar formed has proven challenging. In this work, we present a new methodology for obtaining the bar age, using the star formation history of nuclear discs. Nuclear discs are rotation-supported structures, built by gas pushed to the centre via bar-induced torques, and their formation is thus coincident with bar formation. In particular, we use integral field spectroscopic (IFS) data from the TIMER survey to disentangle the star formation history of the nuclear disc from that of the underlying main disc, which enables us to more accurately determine when the nuclear disc forms. We demonstrate the methodology on the galaxy NGC 1433 -- which we find to host an old bar that is $8.0^{+1.6}_{-1.1}\rm{(sys)}^{+0.2}_{-0.5}\rm{(stat)}$ Gyr old -- and describe a number of tests carried out on both the observational data and numerical simulations. In addition, we present evidence that the nuclear disc of NGC 1433 grows in accordance with an inside-out formation scenario. This methodology is applicable to high-resolution IFS data of barred galaxies with nuclear discs, making it ideally suited for the TIMER survey sample. In the future we will thus be able to determine the bar age for a large sample of galaxies, shedding light on the epoch of disc settling and bar formation., Comment: Accepted for Publication by A&A, 18 pages, 14 figures

The embedded Nash problem for a hypersurface in a smooth algebraic variety, is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface. We show that divisors on minimal models of the pair contribute with such families. We solve the problem for unibranch plane curve germs, in terms of the resolution graph. These are embedded analogs of known results for the classical Nash problem on singular varieties., Comment: v2: The main change is in the proof of Thm 7.4. To appear in Forum Math. Pi

The brain computer interface (BCI) is a nonstimulatory direct and occasionally bidirectional communication link between the brain and a computer or an external device. Classically, EEG-based BCI algorithms have relied on models such as support vector machines and linear discriminant analysis or multiclass common spatial patterns. During the last decade, however, more sophisticated machine learning architectures, such as convolutional neural networks, recurrent neural networks, long short-term memory networks and gated recurrent unit networks, have been extensively used to enhance discriminability in multiclass BCI tasks. Additionally, preprocessing and denoising of EEG signals has always been key in the successful decoding of brain activity, and the determination of an optimal and standardized EEG preprocessing activity is an active area of research. In this paper, we present a deep neural network architecture specifically engineered to a) provide state-of-the-art performance in multiclass motor imagery classification and b) remain robust to preprocessing to enable real-time processing of raw data as it streams from EEG and BCI equipment. It is based on the intertwined use of time-distributed fully connected (tdFC) and space-distributed 1D temporal convolutional layers (sdConv) and explicitly addresses the possibility that interaction of spatial and temporal features of the EEG signal occurs at all levels of complexity. Numerical experiments demonstrate that our architecture provides superior performance compared baselines based on a combination of 3D convolutions and recurrent neural networks in a six-class motor imagery network, with a subjectwise accuracy that reaches 99%. Importantly, these results remain unchanged when minimal or extensive preprocessing is applied, possibly paving the way for a more transversal and real-time use of deep learning architectures in EEG classification.