Papers

A quantum channel is called incompatibility-breaking if it always destroys the incompatibility of quantum measurements. On the other extreme are incompatibility-preserving channels, which never destroy incompatibility. This work studies both types of channels through the mathematical framework of zonotopes and zonoids, an approach that provides a complete characterization of compatibility for dichotomic measurements and is particularly powerful in the qubit setting. Using the language of zonoids, we present necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking, which are also sufficient for nonunital channels. As one of our main results, we demonstrate the superactivation phenomenon of two incompatibility-breaking qubit channels that are no longer incompatibility-breaking when used in parallel. Translating this result into the task of quantum steering, it says that two copies of a two-qubit Werner state can be steered at noise threshold $1/2$, even though this is impossible using just one copy. For the problem of incompatibility preservation, we prove that a quantum channel with matching input and output dimensions will preserve general incompatibility if and only if it is a unitary transformation. When the output dimension is larger, this result no longer holds, and we offer a conjectured form of a general incompatibility-preserving channel.

We investigate emission from polycyclic aromatic hydrocarbon (PAH) dust molecules in 224 MIRI-selected star-forming and quiescent galaxies at $z=0.5-0.8$ in the GOODS-South field using multi-wavelength data from the AstroSat/UVIT, JWST, HST, Herschel, and MUSE. We define an observed diagnostic parameter, f$_{\rm PAH}$, as the ratio of JWST/MIRI F1280W to the average of F770W and F2550W band fluxes, and demonstrate that it effectively traces the PAH mass fraction (q$_{\rm PAH}$) by capturing 7.7$\mu$m PAH emission at our targeted redshift. We observe a bimodal distribution of similar nature in both f$_{\rm PAH}$ and q$_{\rm PAH}$, suggesting that PAH enrichment in galaxies goes through a rapid transition phase from a PAH-poor to a PAH-rich system, at about 70% solar metallicity. For the star-forming galaxies (SFGs; i.e., $\sim$78% of the total sample), we find that f$_{\rm PAH}$ increases with stellar mass and rest-frame FUV luminosity, identifying massive, UV-bright galaxies to have higher PAH mass fraction. However, the majority of the massive quiescent galaxies (QGs) show lower PAH mass fraction relative to that of SFGs of similar mass, suggesting PAH and smaller dust grains are more susceptible to destruction during quenching processes. Among SFGs, we observe an anti-correlation between f$_{\rm PAH}$ and the O32 emission line ratio, suggesting PAH photo-dissociation in strongly ionized ISM. This anti-correlation, along with a correlation between f$_{\rm PAH}$ and gas-phase metallicity 12+log(O/H), indicates that low-mass, metal-poor SFGs, which are increasingly common at even higher redshifts, host more extreme conditions less favorable for PAH production and survival.

Galaxy richness maps provide a useful tracer of the stellar mass distribution in galaxy clusters, but identifying cluster members from multiband photometric data can be challenging. In this work, we investigate multiband imaging data obtained with the Super-Pressure Balloon-borne Imaging Telescope (SuperBIT) during its science flight in April 2023. Using spectroscopically identified cluster members across the SuperBIT cluster sample, we benchmark the performance of the three colors available from the three SuperBIT bands: $(u-b)$, $(b-g)$, and $(u-g)$. We quantify the performance of each color using the $1\,\sigma$ scatter of the spectroscopically identified members in color and the purity of our cluster-member identification algorithm. We find that $(b-g)$ consistently exhibits the smallest color scatter and highest purity across the sample and over the redshift range probed by SuperBIT. We therefore identify $(b-g)$ as the preferred color for red-sequence-based cluster-member identification, providing a basis for future analyses of the cluster galaxy population using SuperBIT multiband photometry.

The Brightest Cluster Galaxies (BCGs) in the most massive galaxy clusters of our Universe are, at present, mostly quiescent, elliptical, and red. However, their formation histories are unclear and likely different from those of massive ellipticals in lower-mass haloes. Simulations face the challenge of simultaneously requiring large volumes to sample massive clusters and sufficient resolution to model their stellar populations. Therefore, we make use of TNG-Cluster, one of the highest-resolution cosmological simulations of galaxy clusters, which returns 352 BCGs at $z=0$ with stellar masses $M_{*, <30 \mathrm{pkpc}} = 10^{11.6-12.9} ~\mathrm{M}_\odot$ and total halo masses $M_{\mathrm{200c}} = 10^{14.3-15.4}~\mathrm{M}_\odot$. 93 per cent of the BCGs are quenched at $z=0$, whereas at redshift $z>3$ all their main progenitors were still star forming. The star-formation histories of individual BCGs are complex, including multiple (re)quenching episodes. They rejuvenate on average $2.1 \pm 1.8$ times since $z=3$. BCGs quench for the first time $9.9^{+0.9}_{-1.4} ~\mathrm{Gyr}$ ago (10th-90th percentiles; $z=1.7^{+0.5}_{-0.5}$), while the last and final quenching event occurred $7.0^{+2.8}_{-5.0} ~\mathrm{Gyr}$ ago ($z=0.8^{+0.8}_{-0.6}$). We find a large scatter in the halo, stellar, and SMBH masses at both first and last quenching, suggesting no characteristic mass at which quenching occurs. Instead, BCGs quench for the first time when the cumulative kinetic energy injected by their SMBH equals the BCG binding energy, corresponding to a delay of $2.3^{+1.2}_{-1.2} ~ \mathrm{Gyr}$ after the first SMBH kinetic energy injection. Namely, TNG-Cluster BCGs quench when they experience significant gas expulsion. Our work shows that BCGs have complex and varied star-formation histories, with multiple rejuvenation episodes, but they ultimately quench due to SMBH feedback.

Interactions of very-high energy gamma-rays during their propagation through the intergalactic medium result in a delayed secondary “pair echo” signal. Detection of such pair echo can be used for measurements of intergalactic magnetic fields (IGMF) in the voids of the Large Scale Structure of the Universe. We notice that a combination of data of LHAASO and CTAO/LST-1 telescopes on the gamma-ray burst GRB 221009A is consistent with the pair echo model. The LST-1 measurement of the source signal 1.33 days after the burst can be interpreted as the pair echo produced by very-high-energy gamma-rays propagating through intergalactic medium with magnetic field of the strength log(B/G)=-16.2+/- 0.7, if its correlation length lambda_B is larger than 20 kpc. If the field correlation length is shorter than 20 kpc, the field strength estimate is modified upwards by a square root of (20 kpc / lambda_B). In the specific case of short correlation length IGMF that is relic from cosmological phase transitions, the pair echo model of the LST-1 signal implies the field strength in the 1e-14-1e-12 G range. Such magnetic field parameters are consistent with all known constraints on IGMF, including the lower bounds from gamma-ray observations of active galactic nuclei.

We present a phenomenological study of the longitudinal unpolarized structure function $F_{UU,L}$ in semi-inclusive deep inelastic scattering (SIDIS) and its ratio with the transverse structure function, $R_{\, \rm SIDIS}=F_{UU,L}/F_{UU,T}$. We study their transverse-momentum dependence, combining for the first time low- and high-transverse-momentum contributions across the kinematic range relevant to SIDIS measurements. At low transverse momentum, $F_{UU,L}$ is power suppressed, making it sensitive to next-to-next-to-leading-power dynamics in the unpolarized sector. We find that this contribution can be sizable, with $R_{\, \rm SIDIS}\simeq 0.3$ at low transverse momentum and hard scale, producing a correction of the order of $10\%$ to transverse-momentum-integrated observables. Although these estimates remain subject to theoretical uncertainties, our results indicate that accounting for $F_{UU,L}$ is likely to be important for the interpretation of SIDIS multiplicities and motivate dedicated measurements of $R_{\, \rm SIDIS}$ to better constrain the longitudinal contribution.

We investigate the real-time dynamics of the Riesz gas (RG), a paradigmatic system of particles with power-law interactions that encapsulates several many-body interacting classical systems. While the equilibrium properties of the system have been extensively studied the connection between microscopic dynamics, macroscopic evolution and thermalization has remained largely unexplored. Combining extensive large-scale Newtonian simulations with a hydrodynamic framework formulated in terms of three coarse grained fields – density, velocity, and temperature – we establish a direct and quantitative correspondence between the two descriptions. The hydrodynamic theory incorporates two phenomenological transport coefficients, the bulk viscosity $\xi$ and thermal conductivity $\kappa$, which encode dissipative effects at a macroscopic level. By analyzing representative classes of initial conditions, such as dome-like and Newton-cradle-type profiles, we find excellent agreement between microscopic and hydrodynamic evolution over a broad range of timescales, starting from relatively early all the way up to times at which steady state is attained. Notably, this agreement persists across a substantial window of $\xi$ and $\kappa$, demonstrating the robustness of the emergent hydrodynamic description. Our results provide a systematic validation of hydrodynamics in the RG and establish a concrete bridge between Newtonian dynamics and continuum theories in systems with power-law interactions, starting from first principles.

We prove stability of nonrelativistic fermionic matter in the presence of fixed nuclei \(\{R_j\}\) on an asymptotically Euclidean Riemannian manifold \((M,g)\). Upper and lower bounds on sectional curvatures are assumed, but no specific sign conditions on the curvature are imposed. The proof follows the route of Lieb-Thirring and electrostatic inequalities, the latter being proved by means of a Voronoi decomposition type argument which is however based on the Green functions \(\{G(\,\cdot\,,R_j)\}\) rather than the distance function.

Building on our earlier program-evolution workflow guided by large language models (LLMs), we study weight-five bivariate bicycle (BB) and perturbed bivariate bicycle (PBB) codes. The resulting catalogue contains 1,142 distinct code proposals, including 1,081 nonbaseline proposals attributable to LLM-generated programs. Across the catalogue, we certify connected Calderbank–Shor–Steane (CSS) realizations [[96,4,10]], [[140,6,10]], and [[180,4,14]]. A post-search comparison certifies seven imported Lin–Pryadko archive constructions. For leading parameter triples also represented in that archive, we provide exact distance evidence, explicit bivariate presentations, and verified component reductions. A basis-independent connectivity analysis identifies 409 of the 1,142 catalogue entries as disconnected and shows that 73.1% of the classes with exact distance certificates contain repeated connected components. Algebraic analysis organizes the connected CSS classes into order-3, order-7, and order-15 cyclotomic-kernel strata. The strongest exact connected PBB parameter point is [[216,4,10]], attained by two distinct component classes. Among the 936 distinct CSS proposals from the LLM-guided campaign with a recorded positive distance, 816 (87.18%) are certified at $d\geq5$. For comparison, three random-search controls each sample 6,444 CSS code proposals uniformly without replacement, using the same per-lattice and encoded-dimension sample counts as the LLM-guided campaign. In these controls, 4,672–4,785 proposals (72.50–74.26%) meet the same criterion. The LLM-guided campaign has the higher certified yield, while the random controls cover more connected classes. Together, these results extend LLM-guided discovery to a more constrained code family and provide a reproducible structural and exact-distance account of its strongest candidates.

GPU-based optimization faces two communication bottlenecks: coordinating frequent requests and delivering dense models that exceed device memory. We present a discrete simulated bifurcation (dSB) architecture that addresses both through NVIDIA DOCA GPUNetIO. For resident models, a persistent service receives field updates, executes each solve within one GPU thread block, and returns the result. Exact integer coupling sums, GPU work queues, and batched transmission keep the receive–solve–reply path on the device without a dedicated CPU data-path core. In comparisons with socket-based servers using the same solver, the largest latency gains occur under concurrent load. As the offered load increases from 400 to 800 thousand requests per second, median round-trip latency rises by only 6%. At the highest tested load, median and 99th-percentile latencies are 189 and 218~$\mu$s, compared with 288 and 609~$\mu$s for the tuned persistent CPU proxy across repeated runs. For models larger than device memory, a streaming solver retains dynamical state on the GPU and reuses incoming coupling tiles across replicas. It evaluates ten-million-variable dense binary matrices at approximately 307~Gb/s, consuming a 12.5-TB logical matrix through a 64-MiB packet buffer. Ground-state recovery on planted instances and agreement with reference executions verify the computation. Together, the two modes scale dSB to concurrent requests and dense models beyond GPU memory.

Global condition-number dependence can substantially overestimate the difficulty of preparing normalized quantum linear-system solutions. Many existing beyond-conditioning approaches are favorable when globally ill-conditioned directions have limited relevance to the target solution. Here we study a harder regime for time-evolution quantum Krylov linear solving (QKS), where a vanishing eigenvalue remains solution-relevant and must be retained. We identify a QKS regime in which the solution-relevant spectrum is compressed into a compact reduced space where the ill-conditioning is concentrated along a soft direction aligned with the solution, so that normalization removes the divergent amplification along that direction and leaves only a bounded transverse response. Consequently, the normalized-state complexity need not inherit the divergence of the global condition number. Our contributions are threefold: (1) We show that the solution-relevant information admits a compact and stable QKS representation, with bounded subspace dimension, evolution time, and reconstruction overhead as the relevant eigenvalue vanishes. (2) We show that normalized-state difficulty is governed by whether inverse amplification changes the solution direction, rather than by the small eigenvalue alone; even an arbitrarily ill-conditioned reduced system can remain directionally stable when the amplification is solution-aligned. (3) We prove that this stability persists under finite projected-system errors and transfers to the actual QKS output, yielding an end-to-end complexity bound without inverse dependence on the retained small eigenvalue. An explicit separation family further shows that a full inverse-amplification criterion can diverge while the corresponding QKS quantities remain bounded.

Characterizing the frequencies of resonant modes is critical to a wide variety of experimental applications. In this work we demonstrate a heterodyne-enhanced sensing scheme capable of precisely measuring the frequency spacing between longitudinal modes of a 19 m optical cavity. The technique utilizes two resonant lasers to sense the differential phase accumulated between them as they propagate through the cavity by measuring their interference beatnote before their injection to the cavity and in transmission of it. With these measurements we were able to mitigate the effects of noise in our control loops in post-processing by up to a factor of 30 in the frequency range from 1 mHz to 100 Hz while suppressing injected calibration signals by over two orders of magnitude.

The hopping expansion is an important approximation of the quark propagator in lattice quantum chromodynamics, but it diverges for light quarks, which limits the scope of strong-coupling and finite-density simulations. We present an artificial scientific discovery framework using gauge-equivariant neural networks in the Clifford basis to extract interpretable approximations. Our approach yields improved low-order approximations that outperform the hopping expansion at identical computational cost. In the parameter regime where the hopping expansion fails, our approach identifies convergent behavior, thus suggesting a novel series expansion. The discovered approximations generalize to unseen gauge fields and volumes, enabling immediate implementation as plug-in replacements and a new theoretical understanding of quark-propagator expansions.

We present a discrete analogue of geometric quantization over finite fields which, when applied to certain classical error-correcting codes, yields quantum error-correcting codes. This provides a physical interpretation for a previously known quantum-classical correspondence in coding theory.

Estimating the logical error rate (LER) of a quantum error-correcting (QEC) code by Monte Carlo sampling takes $O(p^{-\lceil d/2 \rceil}/\varepsilon^2)$ samples at physical error rate $p$, code distance $d$ and relative error $\varepsilon$, which becomes intractable at large distances and low error rates, and especially for concatenated codes, whose distance grows as $d^{\ell}$ with the number of levels $\ell$. The fail fast method reduces this cost by sampling the failures of each weight separately, but it only works for unconcatenated codes, and does not model the soft information that the levels of a concatenated code pass to each other. We propose a predictor that takes the stabilizers, the minimum-weight logical operators and, for odd $d$, the logical operators of weight $d + 1$ of a code, and computes, without sampling, the leading monomial $c\,p^{o}$ of the LER when expressed as a polynomial in $p$, at every level of concatenation, in time polynomial in the code parameters and linear in $\ell$ for fixed budgets. We prove that our prediction is exact for any unconcatenated stabilizer code, for every logical observable and arbitrary per-qubit error rates, whenever no budget is exhausted. Furthermore, for concatenated codes, we construct a recursive approach that computes the leading monomial exactly in exponential time, and our predictor approximates this approach. Our predictions match exact enumeration at level 1 on every code we evaluate, and up to three levels for the iceberg code. Using our predictor, we evaluate and compare $37$ code configurations under four noise biases in $48$ core-hours, where Monte Carlo sampling would need more than $10^{12}$ shots at $p = 10^{-3}$ for $113$ of these $148$ cases.

Information causality (IC) was introduced as a physical principle that imposes constraints on the non-local correlations between two parties (Alice and Bob) in a Bell scenario. Specifically, it states that the information that Bob can gain about an $n$-bit database held by Alice is bounded by the information she communicates to him. To date, the question whether IC for any $n \in \mathbb{N}$ singles out the set of quantum correlations remains open, meaning that it is unknown whether for any number of inputs $m$ and outputs $d$ of the two parties the set of correlations that satisfy IC exactly coincides with the quantum correlations. In this work, we answer this question in the negative. Firstly, we show that for any finite database length $n \geq 2$, there is a bipartite set of correlations that satisfies IC for all compatible protocols and that exhibits post-quantum correlations in the Bell scenario with $n+1$ inputs and $2$ outcomes per party. This result relies on constructing an entropic proof of IC for GPTs that may be of independent interest. We further show that in the Bell scenario with $n+1$ inputs and $2$ outcomes per party, our constructed sets of correlations lead to neither a superset nor a subset of the quantum correlations. Secondly, we construct a set of correlations in the Bell scenario with $3$ inputs and $2$ outputs per party that satisfies IC (for all database sizes $n \in \mathbb{N}$) and that includes post-quantum points. Consequently, all known formulations of information causality fail to fully characterize the bipartite set of quantum correlations, already in the $3$-input, $2$-outcome Bell scenario.

We demonstrate on a network testbed a Digital Twin-aided multi-agent LLM for autonomous class-aware optical network management. The system detects soft failures and autonomously adapts modulation format per service class requirements, ensuring continuous, marginless channel quality with minimal human intervention. {\copyright}2026 The

The differences between the energy spectra reported by the Pierre Auger Observatory and the Telescope Array Collaboration are well-known. In an effort to understand these differences, we have studied the residuals of the fluxes measured in early work at AGASA, Volcano Ranch and Haverah Park with reference to the spectrum reported by the Auger Collaboration. After an empirical adjustment to the energies in the region before the ankle, where fluxes from the two hemispheres are expected to be the same, it is found that historic data are in good agreement with measurements made at the Pierre Auger Observatory above 30 EeV. Thus, the tensions between the spectra measured by the Telescope Array and the Auger Observatory remain.

Increasing capacity can induce a machine learning model to generalize worse until it perfectly interpolates the training data, and better once it moves beyond interpolation. This inversion, known as double descent, is well understood for independent features. For correlated features, its shape is governed by the spectrum of the feature covariance, but existing analyses typically yield only implicit equations. We first close this gap for classical linear regression, analytically characterizing the entire risk curve through two quantities, namely the condition number of the feature population covariance and a spectral measure of correlation strength. Then, we apply this theory on quantum models, focusing on quantum extreme learning machines (QELMs). We show that three tunable design knobs, i.e., encoding strength, input reuploads, and measurement shots, each regularize the QELM output covariance, and derive conditions under which the interpolation threshold remains stable. Finite measurement shot noise can be leveraged to guarantee this stability. Numerical experiments confirm each prediction, yielding concrete design principles for QELMs that generalize well beyond interpolation.

Geometry optimization is a major cost in many quantum-chemical workflows: each optimization step requires one force evaluation, and at the density-functional level that evaluation dominates the wall time. Research in this area has produced a broad range of optimization methods, and we ask whether a language model can improve on the best of them through autoresearch. An agent rewrites the optimizer itself to minimize force-call counts, restrained by two admission gates that reject premature stopping and improvements that do not generalize to unseen molecules. Starting from Sella, the fastest open-source optimizer available, the search produces AutoSella, a family of two optimizers. Both of them deliver consistent force-call reductions relative to Sella across held-out molecular benchmarks and potentials not used during the search. Most notably, at the r2SCAN-3c DFT level, the best variant requires only 40.2-77.2% of Sella's force calls while achieving the same energy reduction, even though agent used no DFT gradients.

We introduce contraction tree boundary matrix product states (CT-bMPS), a scalable approximate contraction method for general closed tensor networks. CT-bMPS represents the boundary tensor and its complementary environment at each edge of a contraction tree as matrix product states. This representation allows local compression based on a reduced transition matrix to incorporate environment information along arbitrary contraction trees, while keeping the time and memory costs polynomial in the network size and bond dimension. We benchmark the method on a variety of models and applications, including Ising partition functions, random tensor networks, kicked Ising dynamics, and quantum error correction decoding. These benchmarks demonstrate improved accuracy and computational efficiency over existing general-purpose approximate contraction methods, together with the ability to handle larger and more complex networks. Optimized contraction trees and environment updates substantially improve accuracy without increasing the bond dimension. These results establish CT-bMPS as a general and scalable approximation framework with flexible contraction orders and environment-based compression for a wide range of applications.

Magnetic Ap stars that have a strong enough field and a sufficiently low v sin i show spectral lines resolved into their magnetically split components. This allows their mean magnetic field modulus <B> to be determined. We complement the existing knowledge of the rotational magnetic variability and of the binarity of a sample of 34 Ap stars with resolved magnetically split lines by analysing observations obtained between 1999 and 2004 that had not been exploited before and, when available, observatory archive data. We determine the values of <B> and of the radial velocity by measuring the magnetic splitting and the wavelength shift of the Fe lambda 6149.2 Å line in high-resolution spectra recorded in natural light. Combining our measurements with published ones, we characterise the variability of both quantities. We derived for the first time the accurate, unambiguous values of the rotation periods of HD 29578 and HD 165474. We set lower limits of years to decades to the rotation periods of six stars and identified four more that have not shown any significant <B> variations over timescales of 13 to 33 years. We established that HD 47103 is the first Ap star with a rotation period of years known to have a magnetic field significantly exceeding 7.5 kG. We achieved the first determination of the orbital elements of HD 116114, HD 142070, and HD 144897, and we refined the orbital elements of six other binaries.

The magnetic properties of Sm-based intermetallics are governed by a delicate interplay between localized $4f$ states, exchange interactions, and valence fluctuations, yet the role of dynamical $4f$ correlations remains poorly understood. Here we investigate the electronic structure and magnetic anisotropy of SmCo$_5$ and SmCu$_5$ using self-consistent DFT+$U$(ED), which explicitly treats dynamical fluctuations of the Sm $4f$ shell. We find that SmCo$_5$ exhibits pronounced Sm$^{2+}$–Sm$^{3+}$ valence fluctuations, with the $4f$ ground state dominated by $f^5$ and $f^6$ configurations. The resulting dynamical $4f$ correlations yield near compensation of the Sm spin and orbital moments and provide a quantitative description of the electronic structure, magnetic moments, and large uniaxial magnetic anisotropy of SmCo$_5$. Upon replacing Co with Cu, the balance shifts toward the $f^6$ configuration, with substantial changes in the Sm spin and orbital moments. In SmCu$_5$, this evolution of the $4f$ configuration is accompanied by a pronounced reduction of both the total magnetic moment and magnetic anisotropy. These results demonstrate that dynamical $4f$ valence fluctuations are essential for understanding the contrasting magnetic properties of SmCo$_5$ and SmCu$_5$ and provide a microscopic framework for describing magnetic anisotropy upon Co to Cu substitution in Sm(Co,Cu)$_5$.

Full-field Fourier-domain optical coherence tomography (FF-FD-OCT) enables rapid volumetric imaging but lacks the confocal gating inherent to point-scanning OCT. By acquiring volumes under multiple oblique illuminations, a digital confocal volume can be synthesized in post-processing, a technique originally developed within the framework of reflection matrix imaging (RMI). Existing implementations, however, are often time-domain, off-axis, or use a Michelson interferometer, which reduces sensitivity, speed and the usable space-bandwidth product (SBP). Here, we present an oblique-illumination FF-FD-OCT system in a Mach-Zehnder configuration. This setup enables optimal use of SBP, providing up to a fourfold increase in effective acquisition throughput. In addition, we pose the scattering and aberrations as an overdetermined system, allowing a closed-form solution of an alternating least squares problem. The resulting iterative optimization is equivalent to the state-of-the-art closed-loop accumulation of single scattering (CLASS) algorithm. We demonstrate the setup and reconstruction method in lens tissue, a PSF phantom, a USAF target, and a model eye. The resulting digital confocal volumes provide locally optimized focusing and detection quality, and show improved resolution and signal-to-noise ratio (SNR) compared to conventional FF-FD-OCT. The technique combines the advantages of FF-FD-OCT and confocal OCT while mitigating the limitations of both approaches.

We examine, in the Landau background gauge, the effective action of a quantum theory of gravitational and matter fields. We analyse the BRST invariance of this theory and study the Ward identities which implement the symmetry of the background effective action. The off-shell and on-shell counterterm Lagrangians are explicitly calculated in this gauge at one-loop order. We argue that the matter self-energy in the Landau background gauge, which is finite to this order, may be finite also at higher loops.

Mid-circuit measurements with feedforward reduce the optimal worst-case quantum depth for exact $n$-qubit unitary synthesis from $\Theta(n)$ to $O(1)$, using arbitrary one- and two-qubit gates and unrestricted ancillary space. Measurements and resets without feedforward remain subject to the circuit causal-cone bound. Our deterministic construction uses single-qubit measurements, $O(1)$ rounds of parity feedforward, and $O(n4^n\log(n+2))$ total qubits, with all ancillas starting and ending in $|0\rangle$. Classical processing is not counted in quantum depth. We teleport only the matrix error of an approximation by Nehoran and Yuen. An exactly prepared ancillary state encodes this error, whose action is added back by coherent interference. At operator-norm error $2^{-n}$, one step of amplitude amplification suffices. Coherent fanout circuits achieve the same constant-depth bound, while circuits using only one- and two-qubit gates attain depth $\Theta(n)$ with $O(4^n\log^2(n+2))$ gates. Generic targets require $\Omega(4^n/(h+1))$ qubits at depth $h$, even under unrestricted classical control. Our depth-width trade-offs meet this bound within a factor $O(n^2)$ for $1\le h\le2^n$.

As the nearest radio galaxy, Centaurus A (Cen A) has been observed across multiple wavelengths and over a broad range of angular scales, providing valuable insights into the functioning of radio galaxies. However, despite being a known source of gamma rays, the physical mechanisms responsible for these high energy emissions remain unclear. In this study, we explore the capabilities of the Cherenkov Telescope Array Observatory (CTAO) to provide insights into the origin of the gamma-ray emission from Cen A. Using simulated observations based on the CTAO Instrument Response Functions (IRF) for the Alpha Configuration of telescopes, we investigate both the spectral and morphological domains to assess the observatory's potential to constrain competing models of particle acceleration in the kiloparsec-scale jet and the Southern Giant Lobe. For the jet, we explore CTAO observations with t=50 and 200h for different leptonic and hadronic origin scenarios for the very-high-energy gamma-ray emission. We show that longer observation campaigns (t=200h) would probe the presence of hard spectral components extending to tens of TeV. Morphological simulations demonstrate that CTAO can resolve the extended gamma-ray emission along the jet, discriminating between point-like and Gaussian spatial models within t=50h, assuming a known background model and an optimistic zenith angle $\vartheta=$20{\deg}. Under similar hypotheses, we studied the Giant Lobes evaluating both diffuse and filamentary emission templates for the S1 region detected by Fermi-LAT. We found that CTAO-South can be sensitive to hadronic scenarios with proton energies extending beyond 10 TeV, for the Alpha Configuration and $\vartheta=$20{\deg}. Overall, our results indicate that CTAO observations of Cen A can provide a decisive step toward unveiling the mechanisms driving the high-energy emission and particle acceleration in radio galaxies

I present a short approach to discretizing continuous unitary evolution. It gives a correspondence in both directions between continuous unitary evolutions and products of unitaries in finite dimensions, and I use it to reduce discrete adiabatic theorems to continuous ones. At fine steps, holding truncated samples of a regulated Hamiltonian on a suitable finite partition gives an approximating product. Conversely, rounding the clock identifies a product of $T$ unit-step samples with a continuous evolution, up to two half-step phases. I bound its operator-norm distance from the original evolution by $O(1/T)$ through cancellation within each time step. This assumes bounded first and second derivatives, bounded spectral width, and eigenvalue differences bounded away from nonzero multiples of $2\pi$, uniformly in $T$. For a unitary walk with these derivative bounds, a fixed common free spectral arc supplies a Hermitian logarithm path satisfying the comparison hypotheses. Continuous simulation guarantees then transfer to the phase-corrected product, and continuous adiabatic bounds to the product itself, with an explicit additive $O(1/T)$ error and each adiabatic theorem's hypotheses retained. For positive definite quantum linear systems of condition number $\kappa$, this comparison and continuous adiabatic theory give a rescaled qubitized walk with $O(\kappa/\delta)$ steps for leakage $\delta$, matching the scaling previously obtained through a discrete adiabatic theorem. These products need no discrete adiabatic theorem.

Magic-state distillation is a major resource cost in fault-tolerant quantum computing. The cost of a magic-state factory depends strongly on its failure rate, which grows with the number of input magic states. Although symmetry-restricted methods have recently made distance two searches tractable, distance three and above have remained elusive at moderate input counts. We develop symmetry- and AI-assisted methods to search this regime. We present a unified binary-matrix formulation encompassing both triorthogonal-code and direct circuit searches. We show that distance at least three is equivalent to nonzero, pairwise distinct syndromes, separating the choice of syndromes from the search for compatible output gates. We restrict the syndrome search using group symmetry and language-model agents, followed by deterministic solving and independent verification. Our searches yield 699 factory classes, including 564 new ones. These include factories for pure-T states and factories with entangled outputs comprising combinations of T, CS, and CCZ magic states. The pure-T factories [[63, 11, 3]] and [[850, 128, 6]] achieve the lowest overhead exponents we know among protocols with at most 100 and 1000 inputs, respectively, with $\gamma = 1.589$ and $\gamma = 1.057$. Our [[1715, 287, 6]] factory, with $\gamma = 0.998$, is the smallest known pure-T factory with $\gamma < 1$. We also provide a context directory of search briefs and campaign notes with which readers can train their own agents and tailor the search to their requirements. With these results, we begin constructing an active, open-source repository of magic-state distillation protocols for the quantum community, supplemented by our methods and data, for the practical fault-tolerant quantum computing regime.

We present a generalization of the Mermin-Peres magic square game to $N$ players, in which the square is replaced by an $N$-dimensional hypercube. We show that the winning probability of the optimal classical strategy remains $8/9$ for all $N$, while for $N \ge 3$, a generalization of the quantum strategy for $N = 2$ achieves a winning probability between $1/3$ and $3/4$. This loss of quantum advantage for $N \ge 3$ is a consequence of monogamy.