Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of both code distance and encoding rate. However, despite its powerful algebraic formulation, the physical mechanism for assembling a general product code from its constituents remains unclear. In this letter, we show that the tensor and balanced product codes admit an intuitive coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. Our framework accommodates both classical or quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes.

Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small error, as occurs for local quantum dynamics on the lattice. A priori, approximate QCAs could exhibit genuinely new behavior, failing to be well-approximated by any exact QCA. We show this does not occur in one dimension: every approximate QCA on a finite circle can be rounded to a strict QCA with approximately the same action on local operators, so these systems are classified by the same index as in the exact case. Previous work considered the case of the infinite line, by using global methods not amenable to finite systems. Our new approach proceeds locally and now applies to finite systems, including circles or homomorphisms from sub-intervals. We extract exact local boundary algebras from the approximate QCA restricted to local patches, then glue these to form a strict QCA. The key technical ingredient is a robust notion of the intersection of two subalgebras: when the projections onto two subalgebras approximately commute, we construct an exact subalgebra that serves as a stable proxy for their intersection. This construction uses a recent theorem of Kitaev on the rigidity of approximate $C^*$-algebras.

Context. Ultra fast outflows (UFOs) from active galactic nuclei (AGN) are expected to lead to the formation of sub-relativistic strong shocks expanding in a dense circumnuclear medium, and thus have the potential for being efficient particle accelerators, and to be proficient sources of gamma rays and neutrinos. Aims. We investigate the detectability of a sample of nearby identified UFOs in gamma rays and neutrinos with current and next- generation instruments. Methods. We model the acceleration of particles at the strong shocks of UFOs, and estimate the associated gamma-ray and neutrino signal. We adopt our model to investigate the prospects for detection with current and next-generation observatories. Results. We find that several UFOs could be detectable in the very-high-energy (VHE) domain - for example, by the Cherenkov Telescope Array Observatory (CTAO)- even if they remain undetected by Fermi-LAT in the high-energy range. Detectability is favored for hard proton spectra (spectral index α \lessim 3.9), high acceleration efficiencies, and amplified magnetic fields. Our results suggest that next-generation VHE observatories could detect the first gamma-ray signatures of AGN UFOs, providing a new probe of particle acceleration in sub-relativistic shocks

The large overhead imposed by quantum error correction is a critical challenge to the realization of quantum computers, and motivates searching for alternative error correcting codes and fault-tolerant circuit constructions. Postselection is a powerful tool that builds large programs out of probabilistically generated sub-circuits, and has been shown to increase the threshold of quantum error correction based on fusing fixed-size resource states or concatenated codes. In this work, we present an approach to lower the overhead of quantum computing using scalable postselection, based on directly postselecting sub-circuits with a size extensive in the code distance using decoder soft information. We introduce a metric, the partial gap, that estimates what the logical gap of a resource state will be after it is consumed, and show that postselection based on the partial gap leads to scalable improvements in the logical error rate. In the specific context of implementing logical gates via teleportation through a cluster state, we demonstrate that scalable postselection provides a $4\times$ reduction in the overhead per logical gate, at the same logical error probability.

We derive new constraints on light CP-even scalars using old gamma-ray observations in the direction of SN1987A by the Solar Maximum Mission (SMM) satellite. Light scalars can be abundantly produced in the supernova core via the nucleon bremsstrahlung process, can stream out of the supernova-environment and decay into photons -- either primary photons or secondary photons from lepton-antilepton pairs -- thus leading to a gamma-ray signal. From the non-observation of excess photon flux by SMM after the detection of the neutrino burst from SN1987A, we set new constraints on the mixing angle of the CP-even scalar with the Standard Model Higgs boson.

We study the superradiant phase transition of a mesoscopic Fermi gas comprising between a few tens and a few thousand $^6$Li atoms in a high-finesse cavity across a wide range of densities. We observe a non-monotonic variation of the superradiant threshold as a function of density, with a minimum reached when the Fermi and recoil wavevectors are comparable. The minimum corresponds to a crossover between Fermi pressure-assisted ordering and Pauli blocking of photon scattering, in good agreement with theory. This interpretation is confirmed by a study of the atom-number dependence of the ordering threshold and photon number scaling. Lastly, we demonstrate the operation of our mesoscopic system in a regime where light-induced forces are opposite for the two spin components, leading to an ordered phase with a spin-density-wave character. Our system opens the perspective of studying few-fermion systems with strong and coherent light-matter coupling.

We investigate several aspects of the thermodynamic geometry for a quantum fluid with square-well interactions using a third-order perturbation theory framework based on the path-integral-necklace analogy. A comparison is made between the thermodynamic and geometric properties of the quantum fluid and its classical counterpart for the interaction ranges $λ^{*}= 1.3$, 1.5, and 1.7. In particular, we analyze the scalar curvature behavior, criticality, and the corresponding Widom lines derived from curvature and several thermodynamic response functions. Quantum effects are shown to smooth supercritical anomalies of the scalar curvature and to shift its extrema for short-range interactions, while leaving the critical exponents of both the curvature and its heat capacity consistent with mean-field predictions. Widom lines associated with temperature-dependent response functions and with the curvature scalar exhibit pronounced classical-quantum differences for short interaction ranges; in contrast, those derived from the isothermal compressibility exhibit only minor variations. Overall, these results highlight the sensitivity of geometric information of thermodynamic systems due to quantum effects and the crucial role of the interaction range in shaping supercritical thermodynamic behavior.

Nonlinear interactions between vibrational modes play a crucial role in understanding the dynamical response of nanomechanical resonators. Here, we report the experimental observation and theoretical modeling of nonlinear mode coupling in a high-stress square silicon nitride membrane resonator. We quantify frequency shifts of the fundamental mode arising from tension-mediated geometric nonlinearity by increasing the amplitude of the fundamental mode and higher-order flexural modes. A quantitative theoretical framework based on Kirchhoff-Love plate theory is developed, which incorporates both intrinsic Duffing nonlinearity and nonlinear intermodal coupling and shows good agreement with experimental measurements for the (1,1)-(2,1) and (1,1)-(2,2) mode pairs. We further compute the nonlinear coupling matrix across mode families, revealing the role of mode symmetry and spatial overlap in governing intermodal interactions. These results establish nonlinear mode coupling as a controllable resource for multimode frequency tuning and mechanical transduction.

The strongly correlated spin-triplet superconductor UTe2 hosts an unusual landscape of magnetic-field-sensitive charge density wave (CDW) phases, positioning it as a compelling system for studying intertwined electronic orders. A central challenge is determining whether the observed charge modulations arise from a triplet pair density wave (PDW) order and, if so, how the anisotropic magnetic field response of triplet superconductivity is manifested in the CDW response. Here, using a scanning tunneling microscope equipped with a vector magnetic field, we systematically investigate the evolution and interrelation of distinct CDW orders. Complementing the previously identified incommensurate CDW peaks (qi=1,2,3), we resolve an additional set of nondispersive modulations (pi=1,2,3 and h1,2) with distinct temperature and magnetic field dependencies. The pi CDW peaks vanish near Tc, while the qi peaks survive well above Tc but are progressively suppressed by magnetic field in an anisotropic manner. The critical fields of the qi peaks mirror the directional hierarchy of Hc2, which suggests a PDW is present above the bulk Tc. This is consistent with a Landau free-energy picture where PDWs with wavevectors pi form above the bulk Tc, leading to composite CDW orders with wavevector qi. Below Tc, the coupling of PDWs and uniform superconductivity leads to the pi CDWs. Together, these findings establish UTe2 as a rare platform where both the parent PDW and descendant orders are directly resolved, enabling access to both the fundamental and emergent manifestations of PDW physics.

In this paper, we derive general bright-dark soliton solutions to the coupled Sasa-Satsuma (CSS) equation using the Kadomtsev-Petviashvili (KP) reduction method. Since the CSS equation is a special case of the four-component Hirota equation, our approach begins with the construction of two-bright-two-dark soliton solutions for the four-component Hirota equation. By imposing specific parameter constraints, these solutions are subsequently reduced to the bright-dark soliton solutions of the CSS equation. Finally, the dynamical behaviors of the one- and two-bright-dark soliton solutions are thoroughly analyzed and illustrated.

The fragmented landscape of quantum computer benchmarks, characterized by system-specific tools and inconsistent evaluation methodologies, hinders reliable cross-platform performance assessment. We introduce Metriq, an open-source collaborative platform for reproducible cross-platform quantum benchmarking that integrates benchmark definition and execution, data collection, and public presentation into a unified workflow. The Metriq benchmark suite spans both system-level metrics that characterize fundamental device properties such as entanglement quality, gate performance, and circuit speed, as well as application-inspired protocols that assess performance on quantum machine learning, optimization, and quantum simulation tasks. Benchmarks are chosen to scale with processor size, and the framework incorporates cost and resource estimation to support practical evaluation. Using Metriq, we collect and publicly release results from more than ten quantum computers across multiple hardware vendors, enabling systematic cross-platform comparison. The resulting curated dataset also reveals the practical strengths and limitations of individual benchmarks, creating a feedback loop that informs the ongoing refinement of the suite. To summarize performance across the benchmark suite, we introduce the Metriq Score, a composite index aggregating benchmark outcomes. We further present cross-benchmark analyses enabled by the shared dataset and their correlations with hardware calibration metrics. Through open development and data sharing, Metriq provides a practical foundation for reproducible benchmarking of quantum computers as hardware and benchmarking methods continue to evolve.

Rydberg atom electrometry offers traceable electric field measurements over many decades of radio frequencies in a single device. Miniaturization of these sensors is primarily limited by requirements of the lasers used. Here we demonstrate a three-photon sensing scheme using a J-shaped energy level coupling that can be achieved using external cavity diode lasers, without the need for a doubling crystal or tapered amplifier. In the low laser power regime, we demonstrate a full-width at half-maximum linewidth of 1.3 MHz. We demonstrate that for RF field electrometry using conventional heterodyne techniques, we can detect 4.7 GHz at a sensitivity of 27 μV m-1 Hz-1/2, comparable to that of two-photon detection schemes which require the use of a tapered amplifier. We also investigate a modified scheme where the probe laser is locked to a different hyperfine state, thus measuring the two-photon electromagnetically induced transparency in the other two lasers via the change in population of this separate state due to repumping. In this scheme we find the sensitivity for a 4.7 GHz field to be 39 μV m-1 Hz-1/2, and demonstrate that the amplitude scaling with probe power offers a different saturation profile than the linked J-scheme counterpart.

Optical metasurfaces, comprised of subwavelength nanostructures, hold a great promise to high-power laser optics but also a limited pertinence due to their currently limited aperture size, throughput and durability. Here, an alternative approach is presented, reliant on laser-controlled self-organizing mask formation followed by ion etching which results in an all-fused-silica-glass metasurface. Two 1 mm diameter optical elements (an axicon lens and a shadower) are fabricated and their optical performance is validated at 532 nm wavelength with an extremely low broadband reflection (<0.15%) - a result of the unique metasurface elements shape. The self-organizing working principle enables producing large amounts of nano-elements at-once, thus a path for aperture scaleup. It also enables generation of sub-100 nm nanoelements, thus a path to short wavelengths operation. Two key advancements towards viability are presented: a laser scan with in-situ transmission feedback enables patterning the etching mask to a prescribed nanoparticle distribution, and a crafted beyond-mask-erosion-point etching of the mask enables increasing the metasurface phase difference to at least pi, while keeping extremely low reflection across it. This paves a path to high-power lasers optics, requiring large aperture, high throughput and laser light durability.

We show that cosmological wavefunction coefficients associated with $n$-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of $A_{2n{-}2}$ and $B_{2n{-}1}$ cluster variables, respectively, and satisfy the associated cluster adjacency properties. The key step in proving this is identifying a precise connection between graph "tubings" that appear in the kinematic flow equation and polygon "triangulations" that encode the combinatorics of cluster compatibility. Our results imply that cosmological wavefunction coefficients in a general power-law FRW cosmology satisfy cluster adjacency to all orders in the $ε$ expansion. We use this information as bootstrap input to show that de Sitter symbols for $n \leq 4$ are uniquely determined by simple physical constraints.

In the forthcoming years the LHC experiments are going to be upgraded to benefit from the substantial increase of the LHC instantaneous luminosity, which will lead to larger, denser events, and, consequently, greater complexity in reconstructing charged particle tracks, motivating frontier research in new technologies. Quantum machine learning models are being investigated as potential new approaches to high energy physics (HEP) tasks. We characterize and upgrade a quantum graph neural network (QGNN) architecture for charged particle track reconstruction on a simulated high luminosity dataset. The model operates on a set of event graphs, each built from the hits generated in tracking detector layers by particles produced in proton collisions, performing a classification of the possible hit connections between adjacent layers. In this approach the QGNN is designed as a hybrid architecture, interleaving classical feedforward networks with parametrized quantum circuits. We characterize the interplay between the classical and quantum components. We report on the principal upgrades to the original design, and present new evidence of improved training behavior, specifically in terms of convergence toward the final trained configuration.

We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a Lévy flight random walk. For such system, the step-length distribution can be modeled as $P(\ell)\sim \ell^{-1-α(\ell)}$, with the Lévy index $α(\ell)$ varying smoothly with the step length. Moreover, the walkers alternate between two distinct distributions depending on the occurrence of collisions between atoms in the light scattering. We obtain the Lévy index from transmission measurements for different system sizes and atomic densities. The measured Lévy index is determined by the system size $α=α(\ell=L)$. Simulations are made for walkers alternating between two Lévy like step-length

Molecular hydrogen (H$_2$) and hydrogen deuteride (HD) are key coolants in primordial gas and regulate the formation of the first stars and proto-galaxies. Recent results from the James Webb Space Telescope provide striking insights into galaxies detected at high redshifts, which are found to be significantly more abundant and luminous than expected from galaxy formation models, thus suggesting a gap in our understanding of the early Universe. Standard pathways for H$_2$ formation in the early Universe proceed through the H$^-$ and H$_2^+$ intermediates, both of which are strongly suppressed at high redshift by the cosmic microwave background. We propose an additional pathway for H2 and HD formation that could be active as early as the end of the epoch of recombination and could enable the formation of the first stars earlier than the current prediction at redshift z ~ 30 - 20. The proposed pathway relies on the manifestation of Jahn-Teller dynamical coupling between electronic states of H$_3^+$. This coupling induces transient three-body recombination in H$^+$, H and H, and charge exchange within the charged atom-dimer complex that directly creates ground-state H$_2$ (and HD), bypassing the fragile intermediates that limit the standard primordial pathways. Our analysis shows that this mechanism could occur under the thermodynamic conditions of the post-recombination epoch, also suggesting that it might be playing a role in the active galactic nuclei feedback processes, regulating the formation rates of the first stars and the accretion rates of the first black holes. Though the global impact on galaxy formation and black-hole growth is not yet determined and will require quantitative assessment in future modeling, the mechanism offers an additional chemical route for H$_2$ and HD formation, with substantial cosmological relevance for primordial chemistry and early structure formation.

The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of spatial patterns. Dating back to Turing, pattern formation has been suggested to arise in tissues via spontaneous symmetry breaking instabilities in the concentration field of chemical morphogens. Within the vertex model of tissue mechanics, we show that spontaneous symmetry breaking may also arise via a mechanical instability in the strain field of a deformed tissue, leading to a patterned coexistence of fluid and solid regions, with a strong localisation of the strain into shear bands. The nature of the bands differs between tissues in which internal cell-cell dissipation dominates external drag against a substrate, and vice versa.

Black holes are the most efficient scramblers in nature. By mapping the instantaneous mass and angular momentum of two spinless black holes in a quasi-circular binary onto those of an effective Kerr black hole, we demonstrate that the final state of the merger remnant corresponds with remarkable accuracy to the configuration that renders null geodesics unstable at the highest possible rate. This suggests a deep connection between the properties of black holes resulting from binary mergers and their unstable null orbits.

We give the first and lowest order examples of 3-regular 3-edge-colored graphs that demonstrate the non-factorization of tensor model invariants in the large N limit of Gaussian random tensors, as proven on general grounds in [Gurau R., Joos F. and Sudakov B., Lett. Math. Phys., 115 (2025), arXiv:2506.15362 [math-ph]]. This non-factorization is in stark contrast to the well-known large N factorization for random matrices.

We investigate the geodesic structure of realistic static and spherically symmetric spacetimes embedding neutron stars in metric $f(R)$ gravity, focusing on the quadratic Starobinsky model $f(R)=aR^2$ with $a<0$. Neutron-star solutions are obtained by numerically solving the modified Tolman-Oppenheimer-Volkoff system for several realistic equations of state. Such solutions are then matched consistently to the exterior vacuum geometry by enforcing the full set of junction conditions required in metric $f(R)$ theories. Using an effective potential approach, we show that stable circular orbits appear in discrete radial bands separated by forbidden regions, with a dominant principal band of stability that depends sensitively on the stellar central pressure, the equation of state, and the magnitude of the parameter $|a|$. Outside the stable bands, massive particles can have bound but unstable precessing trajectories as well as unbounded motions. On the other hand, for null geodesics, we find no evidence for photon spheres outside the neutron star within the parameter range studied.

One of the main targets for space-borne gravitational wave detectors is the detection of Extreme Mass Ratio Inspirals (EMRIs). The data analysis of EMRIs requires waveform models that are both accurate and fast. The major challenge for the fast generation of such waveforms is the generation of the Teukolsky amplitudes for generic (eccentric and inclined) Kerr orbits. The requirement for the modeling of $\sim10^5$ harmonic modes across a four-dimensional parameter space makes traditional approaches, including direct computation or dense interpolation, computationally prohibitive. To overcome this issue, we introduce a convolutional encoder-decoder architecture for a fast and end-to-end global fitting of the Teukolsky amplitudes. We also adopt a transfer learning strategy to reduce the size of the training dataset, and the model is trained gradually from the simplest Schwarzschild circular orbits to generic Kerr orbits step by step. Within this framework, we obtain a surrogate model based on a semi-analytical Post-Newtonian dataset, and the full harmonic amplitudes can be generated within milliseconds, while the median mode-distribution error for generic orbits is approximately $\sim10^{-3}$. This result indicates that the framework is viable for constructing efficient waveform models for EMRIs.

In this article, we will compute the expectation value of observables (which appear as Wilson loops) in $\mathrm{U}(1)^n$ Chern-Simons theory for closed oriented $3$-manifolds. We will show how the various topological sectors of the observable affect the expectation value and confirm that it is a topological invariant. We will also exhibit in this case as well a form of the CS duality introduced in previous works. Finally, to complete the treatment of this theory, we will compute its zero modes and the equations of motion.

We develop a multi-reference perturbation theory for electronic structure calculations based on symmetries of the Hamiltonian. The reference Hamiltonian in the symmetry-based perturbation theory (SBPT) is chosen such that it possesses more symmetries than the original Hamiltonian, leading to a larger reduction of computational resources in terms of both the number of configurations in the configuration interaction expansion and the number of required qubits in quantum computing applications. We provide approximate, scalable solutions for the second-order correction, as well as an application to selected configuration interaction. We show that SBPT is an extension of other existing multi-reference perturbation theories and that it can give better results for some molecular systems in a robust way.

A proper-time method for constructing models of dynamic gravitational-wave fields is presented. Using the proper-time method, analytical (not numerical) models of secondary gravitational waves are constructed as perturbative solutions of linearized field equations against the background of the exact wave solution of Einstein's equations for the vacuum in the Bianchi VI universe in a privileged wave coordinate system. Relations for the proper time of test particles against the background of a strong gravitational wave are used. The analytical form of the metric components for secondary gravitational waves is found from compatibility conditions for the field equations. From the field equations, an explicit form of ordinary differential equations and their solutions is obtained for functions included in small corrections to the metric for secondary gravitational waves. It is shown that there exists a continuum of gravitational wave parameters for which the perturbative solutions are stable.

We derive an explicit formula for the ADM mass of asymptotically locally Euclidean (ALE) almost Kähler manifolds. The formula expresses the mass in terms of the total Hermitian scalar curvature and topological data associated with the underlying almost complex structure, extending a result of Hein and LeBrun in the Kähler ALE case. Our approach is based on a spin$^\mathbb {C}$ adaptation of Witten's proof of the positive mass conjecture in the spin case and is therefore distinct from previous complex-geometric methods. In dimension $4$, we prove a positive mass theorem and a Penrose-type inequality for asymptotically Euclidean (AE) almost Kähler manifolds. We also study rigidity phenomena of almost Kähler ALE manifolds. We prove that an almost Kähler-Einstein ALE manifold with nonnegative scalar curvature and certain decay assumptions is necessarily Kähler-Einstein. In particular, any four dimensional Ricci-flat almost Kähler manifold with maximal volume growth and curvature in $L^2$ is Kähler, yielding new evidence towards the Bando--Kasue--Nakajima conjecture. We also discuss analogous rigidity results for asymptotically locally flat (ALF) manifolds.

We present an inverse seesaw model based on the $Δ(27)$ symmetry and Abelian discrete symmetries, which account for the mass hierarchies and, through a specific pattern of symmetry breaking, leads to viable leptonic mixing angles according to the cobimaximal mixing pattern. In the model, leptogenesis successfully accounts for the observed baryon asymmetry of the Universe for a large range of the parameter space, only for the scenario of normal neutrino mass hierarchy.

Hyperpolarisation using Signal Amplification By Reversible Exchange (SABRE) is a convenient method for high repeatability studies. The core of this technique is polarisation transfer to the target substrate during an on-going chemical exchange process. Typically, polarisation transfer is achieved as fast as possible. In this study we employ NMR sequences that on contrary slow down the polarisation transfer and yet demonstrate improved performance. Simulations confirm that such methods can lead to high polarisation yield in SABRE system that exhibit higher magnetic inequivalence and lower chemical exchange rate.

We study bipartite spin-singlet correlations when rotational symmetry is described by a quantum group rather than an ordinary Lie group. We show that, even though the single-spin observables act as in the undeformed theory, the non-trivial coproduct reshapes the notion of "total" symmetry and leads to a deformed analogue of the Bell singlet state. We show that implementing local measurements with the conventional tensor-factor observables yields a striking effect: perfect anticorrelation is preserved, yet the one-site outcome statistics become deformation-dependent and biased. Using instead the symmetry-covariant, R-matrix-dressed embedding of local observables restores unbiased statistics while maintaining perfect anticorrelation. Our results demonstrate that, in a quantum group symmetry setting, strict tensor-factor locality is not stable under the symmetry and must be replaced by a braided notion of locality to formulate consistent local measurements.

This paper describes the implementation of the direct solution method (DSM) using radial spectral elements for the calculation of synthetic seismograms in self-gravitating, spherically symmetric, non-rotating, anelastic, and transversely isotropic Earth models. In contrast to previous implementations of the DSM that used a potential formulation within fluid regions, we use a displacement formulation throughout. It is this feature that allows us to extend the DSM to account fully for self-gravitation along with arbitrary fluid stratification. Our code, $\texttt{DSpecM1D}$, is benchmarked against the normal mode summation code $\texttt{MINEOS}$ as well as the direct radial integration code $\texttt{YSpec}$. Agreement between the codes is excellent for both elastic and anelastic models.