We find the dispersion relations of two elusive families of core-bound excitations of the Gross-Pitaevskii (GP) vortex, varicose (axisymmetric) and fluting (quadrupole) waves. For wavelengths of order the healing length, these two families -- and the well-known Kelvin wave -- possess an infinite sequence of core-bound, vortex-specific branches whose energies lie below the Bogoliubov dispersion relation. In the short-wavelength limit, these excitations can be interpreted as particles radially bound to the vortex, which acts as a waveguide. In the long-wavelength limit, the fluting waves unbind from the core, the varicose waves reduce to phonons propagating along the vortex, and the fundamental Kelvin wave is the only core-bound vortex-specific excitation. Finally, we propose a realistic spectroscopic protocol for creating and detecting the varicose wave, which we test by direct numerical simulations of the GP equation.

We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be leveraged to perform non-Clifford gates in $\mathbb{Z}_2$ surface codes, thus enabling universal computation with well-established means of performing logical Clifford gates. Moreover, for suitably chosen groups, we demonstrate that arbitrary reversible classical gates can be implemented transversally in the group surface code. We present the logical operations in terms of a set of elementary logical operations, which include transversal logical gates, a means of transferring encoded information into and out of group surface codes, and preparation and readout. By composing these elementary operations, we implement a wide variety of logical gates and provide a unified perspective on recent constructions in the literature for sliding group surface codes and preparing magic states. We furthermore use tensor networks inspired by ZX-calculus to construct spacetime implementations of the elementary operations. This spacetime perspective also allows us to establish explicit correspondences with topological gauge theories. Our work extends recent efforts in performing universal quantum computation in topological orders without the braiding of anyons, and shows how certain group surface codes allow us to bypass the restrictions set by the Bravyi-K{ö}nig theorem, which limits the computational power of topological Pauli stabilizer models.

The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's fault tolerance and overhead, the decoder's quality, and the device's constraints, such as physical qubit count and connectivity. This work makes two contributions towards error-corrected quantum devices. First, we introduce mirror codes, a simple yet flexible construction of LDPC stabilizer codes parameterized by a group $G$ and two subsets of $G$ whose total size bounds the check weight. These codes contain all abelian two-block group algebra codes, such as bivariate bicycle (BB) codes. At the same time, they are manifestly not CSS in general, thus deviating substantially from most prior constructions. Fixing a check weight of 6, we find $[[ 60, 4, 10 ]], [[ 36, 6, 6 ]], [[ 48, 8, 6 ]]$, and $[[ 85, 8, 9 ]]$ codes, all of which are not CSS; we also find several weight-7 codes with $kd > n$. Next, we construct syndrome extraction circuits that trade overhead for provable fault tolerance. These circuits use 1-2, 3, and 6 ancillae per check, and respectively are partially fault-tolerant (FT), provably FT on weight-6 CSS codes, and provably FT on \emph{all} weight-6 stabilizer codes. Using our constructions, we perform end-to-end quantum memory experiments on several representative mirror codes under circuit-level noise. We achieve an error pseudothreshold on the order of $0.2\%$, approximately matching that of the $[[ 144, 12, 12 ]]$ BB code under the same model. These findings position mirror codes as a versatile candidate for fault-tolerant quantum memory, especially on smaller-scale devices in the near term.

Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present the first sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure or locality. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. The final sample complexity depends on linear-system conditioning, which we find empirically to be moderate for a broad class of physically motivated models. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.

We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by decoding the generalized checks using a maximum a posteriori (MAP) decoder as part of the check node processing of each decoding iteration. We mainly study the finite-length setting and show that the proposed enhanced generalized BP decoder for quantum Tanner codes significantly outperforms the standard quaternary BP decoder with memory effects, as well as the recently proposed Relay-BP decoder, even outperforming generalized bicycle (GB) codes with comparable parameters in some cases. For other classes of quantum low-density parity-check (qLDPC) codes, we propose a greedy algorithm to combine checks for generalized BP decoding. However, for GB codes, bivariate bicycle codes, hypergraph product codes, and lifted-product codes, there seems to be limited gain by combining simple checks into more powerful ones. To back up our findings, we also provide a theoretical cycle analysis for the considered qLDPC codes.

We present a fast and effective framework for analysing and designing syndrome-extraction circuits (SECs). Our approach is based on left-right circuits, a general design for SECs which maintain low depth by staggering $X$ and $Z$ checks without interleaving gates. Initially proposed for specific classes of codes, we generalise this construction to arbitrary CSS codes and optimise the circuit structure to achieve low qubit idling time, large effective distance, and reduced minimum-weight failure mechanisms. A key component of our framework is the formal notion of residual errors and their associated distance metrics, which form lightweight tools for capturing error propagation and quantifying the potential harm of circuit-level errors. Applying our automated framework to diverse classes of codes, we observe consistent improvements in logical performance of up to an order of magnitude compared to existing single-ancilla SEC designs. We also use these tools to prove that no non-interleaving SEC can achieve circuit distance $12$ for the gross code, and identify an explicit circuit that we conjecture achieves distance $11$, exceeding previously known constructions.

We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge the gap between theory and implementation by developing and comparing three concrete realizations of the algorithm. First, we implement a sparse initial state preparation combined with product-formula (Suzuki-Trotter) Hamiltonian simulation. Second, we implement a fully quantum, oracle-based framework in which classical data are accessed via oracles, the Hamiltonian is block-encoded, and time evolution is performed using QSVT-based Hamiltonian simulation. Third, we propose an efficient alternative that combines the sparse state-preparation routine of the first approach with the oracle and block-encoding-based simulation pipeline of the second. We provide these implementations on Classiq, a high-level quantum design platform and provide appropriate resource benchmarks. Our simulation results show that the complex initial state preparation proposed by Babbush et al. can be circumvented at least in the linear-chain case. Finally, we illustrate two physical applications-extracting normal modes and simulating coarse-grained energy propagation-demonstrating how the algorithm connects to measurable observables. Our results clarify the resource requirements of the algorithm and provide concrete pathways toward practical quantum advantage.

We conducted a HI 21cm absorption study of a sample of 147 nearby (z < 0.1) low-power radio sources with $10\,\mathrm{mJy} < S_{1.4\,\mathrm{GHz}} < 30\,\mathrm{mJy}$ and $\log(P_{1.4\,\mathrm{GHz}}/\mathrm{W\,Hz^{-1}}) = 20.5-23.7$, using the Five-hundred-meter Aperture Spherical radio Telescope. By investigating the origin and kinematics of HI absorbing gas, we aim to study the interplay between the active galactic nucleus (AGN) and its surrounding interstellar medium. Our observations detect 12 new absorbers, combining results from the pilot survey (three absorbers out of 26 sources), yielding a detection rate of $\sim10.2^{+3.1}_{-2.0}\%$. The detection rate in our sample is lower than in higher-power samples, which is likely due to emission dilution and the dominance of extended sources, indicating a gas-rich and star-forming-dominated population in low-power sources. Among new detections, most line profiles are narrow and show velocities close to systemic ones, consistent with rotating disks, while four show disturbed kinematics indicative of inflows or outflows. The fraction of outflow candidates rises with radio power, while the fraction of inflow ones remains constant, suggesting the effect of radio emission on driving HI outflows. In our sample, compact sources show a higher HI detection rate than extended sources. Contrary to expectations from higher-power samples, MIR-bright sources at low-power radio do not exhibit a higher HI detection rate or more disturbed kinematics. In low-power radio sources, blueshifted absorption occurs only in Seyferts and low-ionization nuclear emitting regions, indicating the connection between atomic outflows and the ionization state of AGN.

Warped compactifications of massive type IIA supergravity on a 3-sphere with spacetime-filling O6/D6 sources are known to admit a half-maximal gauged supergravity description in 7D. We study the effect of introducing open string degrees of freedom (scalars and fluxes) in such dimensional reductions, associated with the spacetime-filling sources. From the 7D supergravity point of view, this can be realized by coupling the gravity multiplet with extra vector multiplets and adding new components to the embedding tensor describing the gauging. The scalar potential of the underlying theory exhibits novel AdS7 vacuum solutions, with and without supersymmetry. Finally, we explore the net of domain wall solutions interpolating between the different pairs of vacua, and present analytical as well as numerical solutions.

Acoustic scattering by vehicle surfaces can have significant effects on overall noise levels. In this paper, we present a space-time Galerkin time-domain boundary element method (TDBEM) that offers several distinct advantages over contemporary scattering methods for prediction of acoustic scattering and shielding of complex aeroacoustic sources such as propellers and rotors. The time-domain approach allows efficient simulation of transient, rotating, and broadband noise sources, while the Galerkin formulation is robust and unconditionally stable without any tuned numerical parameters. The main challenge of the Galerkin approach, namely the numerically difficult double space-time integration, is resolved through an efficient decomposition-based quadrature procedure. We present three cases with analytical solutions to validate the method and study its numerical properties, demonstrating excellent agreement for scattering and shielding by a variety of different geometries. We then apply the TDBEM to a trailing edge-mounted propeller case, comparing the numerical predictions with experimental measurements. The results demonstrate good agreement between predicted and measured scattering and shielding in a practical application case.

In this article, convex optimization is introduced as a promising tool to study Eshelby based inverse micromechanics problems. The focus is on inverse micromechanics using the Eshelby-Mori-Tanaka model given the dielectric constants of the composite material and of all of its components. The model is exactly the same for the conductivity properties as well. This choice of model is made since the model is fairly simple and has a closed form analytical solution for the case of spheroidal inclusions as well. The forward or direct micromechanics problem deals with the determination of effective properties of a composite material given the properties of its components and microstructural information. The focus is on isotropic composites and the distribution of inclusions is assumed to be such that this holds. The inverse micromechanics problem considered in this paper deals with the determination of microstructural information given the properties of the composite material and all of its components. Since in this paper, isotropy of the composite and only spherical inclusions are considered, the goal is to determine just volume fractions of the components of the composite material. The inverse problem is formulated as a Linear Programming problem and is solved. Before this, the inverse problem and certain important variants of it are examined through the lens of convex optimization. Lastly, promising results regarding the relationship between dispersive materials, noise in measurements, and quality of obtained volumetric splits are showcased. The scope of the use of convex optimization in inverse micromechanics is discussed.

We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe symmetries and we derive constants of motions. After showing linear stability for rotating circles, we prove the existence of rotating waves by combining a bifurcation-theoretical approach together with critical point theory. Finally, by exploiting the Hamiltonian structure, we show that whenever volume and barycenter are fixed to be the same as those of rotating circle, this solution is also conditionally energetically stable. This holds in the irrotational case as well, in agreement with the stability analysis of rotating cylinder jets in Rayleigh [25].

Indirect searches for dark matter using dwarf spheroidal galaxies are limited by systematic uncertainties in modeling diffuse gamma-ray backgrounds. We present a likelihood-based comparison of locally constructed empirical background models and theoretically-motivated models that incorporate the Fermi-LAT diffuse background. The empirical models we study include both an independent-binning approach and a covariance-based approach that captures cross-energy correlations. Using ensembles of blank-sky regions and information criteria which account for model complexity, we find that empirical background descriptions provide a statistically competitive fit to gamma-ray data on degree scales in high-latitude regions.

Optical control of magnetization is often symmetry-forbidden because electric fields and magnetization transform differently under inversion and time-reversal. However, through even-order nonlinear response, optical excitation can generate a nonequilibrium magnetic density (the nonlinear Edelstein effect) that acts as an internal Edelstein-Zeeman field coupling to slower magnetic degrees of freedom. Here we demonstrate non-thermal, ultrafast optical control of ferromagnetism in the centrosymmetric van der Waals semiconductor Cr$_2$Ge$_2$Te$_6$ via a resonant nonlinear Edelstein effect. Using time-domain THz emission spectroscopy under near-infrared excitation, we directly observe magnetic dipole radiation arising from optically driven magnetization dynamics. The polarization, fluence, and temperature dependences of the THz emission are quantitatively captured by a mean-field description of a weakly anisotropic Heisenberg ferromagnet subject to an Edelstein-Zeeman field. Our results establish a general nonequilibrium route to optical control of magnetism in centrosymmetric materials.

Accurate prediction of muon hyperfine constants is useful for interpreting muon spin spectroscopy data, yet standard methods such as density functional theory (DFT) compute muon-electron pair density functions, and thus hyperfine constants, by treating the muon as a fixed classical particle. This work uses the variational quantum Monte Carlo method with neural-network trial wavefunctions, a highly accurate and flexible approach recently applied to other quantum chemical problems. The muon can be treated classically or included in the many-particle electron-muon wavefunction, in which case the fully quantum mechanical pair density is obtained directly. We calculate muon hyperfine constants in muoniated methyl and ethyl radicals for both quantum mechanical and fixed classical muons. The hyperfine constants obtained from our fixed-muon calculations in the methyl and ethyl radicals differ from the corresponding DFT results significantly, highlighting the limitations of DFT even when the muon is treated classically. The results with quantum muons are closer to experiment after accounting for environmental effects. These findings suggest that explicitly calculating the quantum mechanical muon-electron pair density improves the accuracy of muon hyperfine constant predictions.

Quantum memory is a scarce and costly resource, yet little is known about which learning tasks remain feasible under severe memory constraints. We study the problem of computing global properties of quantum sequences when quantum systems must be measured individually, without storing or jointly processing them. In our setting, a bit string $x \in \{0,1\}^n$ is encoded into an $n$-qubit product state $|ψ_{x_1}\rangle \otimes \cdots \otimes |ψ_{x_n}\rangle$, and the goal is to infer $f(x) \in \{0,1\}$ from measurements of this quantum encoding. We consider a simple local strategy, which we call the greedy strategy, that applies the same optimal single-system measurement independently to each subsystem and then infers $f(x)$ from the outcomes. Our main result gives a complete characterization of when the greedy strategy is optimal: it achieves the same maximum success probability as an unrestricted global measurement if and only if the target Boolean function is affine (in all but finitely many cases). We establish a universal performance guarantee for general Boolean functions, showing that the success probability of the greedy strategy is always at least the square of the optimal global success probability, in direct analogy with the Barnum-Knill bound for the pretty good measurement. These results demonstrate that even under extreme memory constraints, simple local measurement strategies can remain provably competitive for learning global properties of quantum sequences.

Bubble-shaped Bose-Einstein condensates (BECs) constitute a unique class of quantum fluids with a hollow, thin-shell geometry that supports a wide variety of phenomena that are distinct from those of compact condensates. Numerical simulation of such systems is particularly challenging due to their inherently three-dimensional structure and extreme aspect ratios. We present an efficient finite-difference simulation framework designed for solving partial differential equations in such nontrivial topologies with a focus on the static and dynamical modeling of bubble-shaped BECs. By employing selective spatial sampling on a semi-structured grid, our method substantially reduces memory usage and achieves more than an order-of-magnitude improvement in computational performance compared to conventional split-step Fourier solvers. The algorithm is naturally extendable for highly parallel execution on GPUs, enabling large-scale, time-dependent simulations of thin-shell condensates. We apply this framework to simulate the formation of bubble BECs through a controlled hollowing-out protocol using ab initio trapping potentials relevant to the Cold Atom Laboratory aboard the International Space Station. From these simulations, we identify characteristic timescales and parameter ramps required to achieve adiabatic evolution, thereby assessing the feasibility of experimentally realizing bubble-shaped condensates in microgravity environments.

We describe our method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for a contour deformation, which is one of the main computational bottlenecks in numerical integration. We demonstrate clearly how the method works on two examples, and benchmark the performance against contour deformation as implemented in pySecDec, where we observe performance gains of up to several orders of magnitude. We describe an improvement in the resolution procedure using the Generic Cylindrical Algebraic Decomposition algorithm, which generalises our method to any Feynman integral, including those with massive propagators.

Machine-learned interatomic potentials (MLIPs) promise to provide near density-functional theory accuracy at a fraction of the computational cost, offering a transformative route toward genuinely predictive chemistry. Yet their predictive validity beyond the training regime remains largely untested experimentally. Here we use pressure-dependent broadband inelastic neutron spectroscopy (INS) as a direct experimental probe of MLIP transferability. Employing a newly developed high-pressure superalloy clamp cell, we measure INS spectra of crystalline 2,5-diiodothiophene at 10~K under ambient conditions and at 1.5~GPa. A MACE-based MLIP, fine-tuned on targeted DFT data, reproduces the experimental spectra across 0--1200~cm$^{-1}$ at both pressures and remains thermodynamically stable under rigorous molecular dynamics validation at 300~K. The model captures systematic pressure-induced blue shifts arising from steric stiffening and reproduces an anomalous red shift at 453~cm$^{-1}$ driven by pressure-modified intermolecular interactions, providing direct validation of its many-body character. This constitutes the first experimental demonstration of MLIP transferability across distinct thermodynamic states using neutron spectroscopy, and establishes high-pressure INS as a stringent benchmark for predictive machine-learned potentials.

In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin $1/2$ system with long range exchange interactions($K$), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction $K_c$ and in the valance bond solid phase above $K_c$. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy,correlation length, and order parameters of leading post-measurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the post measurement states across the phase boundary under weak measurements. Especially, the trajectory $\left(\downarrow \downarrow\right)$ describing a uniform measurement outcome given the all ancilla spins initiated in the same $\left(\downarrow \right)$ state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when $K<K_c$ whereas it weakly decreases when $K>K_c$. We argue with numerical evidences that observed asymmetry in entanglement would lead to a weak first order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement induced effects linked to the strength of weak measurement and probability of post-measurement states.

The electron temperature is a crucial parameter for the determination of the gas-phase metallicity of galaxies. Low electron temperature is expected for metal-rich galaxies, theoretically. We report the discovery that temperature, as measured through auroral-to-strong line ratios of O$^+$, trends in reverse directions at 12+log(O/H) $\geq$ 8.7. This trend remains consistent regardless of the emission line fitting method employed and is not attributable to contamination or dust attenuation correction. Notably, this phenomenon is not observed in other low-ionization ions, such as S$^+$ and N$^+$, which also probe electron temperature. The results are verified in two independent datasets. We analyze the potential cause for the high [OII] auroral-to-strong line ratios at high metallicities, finding that no specific reason could account for that. This finding challenges the fundamental principles of the direct $T_e$ method for metallicity measurement, warranting further investigation into its physical interpretation.

We investigate the scattering of hydrogen isotopes at the W(110) surface using both classical and quantum dynamics approaches to elucidate the role of quantum effects in this system. To characterize the scattering process we focus on key observables, including the absorption probability and diffraction channels that we evaluate at the quasi-classical and quantum levels. The quantum dynamics reveal pronounced resonance structures in the absorption curve that we rationalize in terms of diffraction-mediated selective adsorption and focused sticking mechanisms. Diffraction probabilities for reflected trajectories exhibit strong quantum effects at low incident energies, where classical dynamics underestimate the back scattering probability. These effects become less pronounced with increasing isotope mass, from hydrogen to tritium, however discrepancies between the classical and quantum description persist at low incident energies.

Cross-entropy benchmarking (XEB) with single-qubit reference sequences is widely used to characterize multi-qubit gates in large-scale quantum processors, despite the lack of a rigorous theoretical justification. Here we show that the commonly employed additive single-qubit errors approximation underlying this approach breaks down and leads to a systematic overestimation of gate fidelities. We derive an analytical expression for the joint decay of simultaneous single-qubit reference sequences and introduce a refined expression for the interleaved gate fidelity estimation. Experiments on a superconducting quantum processor validate the theory and demonstrate that fidelities obtained using XEB with single-qubit references agree with those extracted from standard interleaved randomized benchmarking (IRB), while achieving higher precision due to reduced reference-sequence errors. Our results establish theoretical foundation for the single-qubit-based XEB and show that, with appropriate post-processing, it enables a reliable and robust approach for entangling gates benchmarking without the need for multi-qubit Clifford reference sequences.

Manganese sulfide (MnS) is a p-type magnetic semiconductor whose physicochemical properties are sensitive to nanocrystal (NC) morphology, yet the thermodynamic driving forces governing morphology across MnS polymorphs remain poorly understood. Here, we use density functional theory (DFT) to predict the equilibrium morphologies of rock salt (RS), zinc blende (ZB), and wurtzite (WZ) MnS NCs as a function of the relative chemical potential of sulfur, $Δμ_{S}$. Benchmarking against Heyd$\unicode{x2013}$Scuseria$\unicode{x2013}$Ernzerhof (HSE06) hybrid functional calculations reveals that the r$^2$SCAN meta-generalized gradient approximation reproduces experimental lattice constants and thermochemical reaction energies but underestimates S-terminated polar surface energies by up to a factor of five; applying a Hubbard $U$ correction (r$^2$SCAN+$U$, $U = 2.7$ eV) to the Mn 3d states brings the results into close agreement with HSE06. Using the validated r$^2$SCAN+$U$ framework with the Gibbs$\unicode{x2013}$Wulff theorem, we predict that RS-MnS NCs favor nanocubes across nearly the entire stability window, ZB-MnS NCs transform from rhombic dodecahedra (Mn-rich) to polyhedra with 16 triangular faces (S-rich), and WZ-MnS NCs adopt rod-like morphologies with $Δμ_{S}$-sensitive base truncation. Synthesized RS-MnS NCs confirm the predicted cubic morphology, and high-temperature oxidative solution calorimetry yields an apparent surface energy of 1.15 $\pm$ 0.38 J$\cdot$m$^{-2}$, higher than the theoretical equilibrium value (0.42$\unicode{x2013}$0.43 J$\cdot$m$^{-2}$) due to high-index facet exposure, surface area uncertainty, and non-ideal surface configurations in real samples. This work establishes a framework for predicting the equilibrium morphologies of metal chalcogenide NCs.

Quantum tracking control encodes the desired dynamics into a tailored driving field; here, we let the system find its own way there. We propose a real-time feedback control framework in which a proportional controller continuously corrects a simple transform-limited field based on the instantaneous mismatch between two systems' responses - producing the required control on the fly, without prior waveform design. The framework is demonstrated on two distinct examples: a single-active-electron atom, where hydrogen is driven to mimic argon's strong-field optical emission, and a Fermi-Hubbard chain, where a weakly interacting lattice reproduces the transport dynamics of a Mott-insulating reference. By shifting the control paradigm from predesigned inputs to adaptive response tracking, this approach establishes closed-loop feedback as a broadly applicable route to programmable quantum dynamics.

The sub-parsec circumnuclear density profiles of galaxies represent a key element in our understanding of the accretion history and fuel availability of supermassive black holes (SMBHs). Observations that directly resolve sub-parsec scales in galaxies require extremely high resolution and generally hot (bright) environments, making this impossible in all but the nearest active galaxies. Transient accretion events onto previously quiescent SMBHs, such as a tidal disruption event (TDE), offer a new avenue to understand SMBHs and their environments. Radio-bright outflows from TDEs directly probe the ambient density at $10^{-3}-1$ pc scales, allowing direct constraints on the circumnuclear density of TDE host galaxies (i.e., quiescent galaxies). Here we present, using radio observations of a sample of 11 TDE hosts, a new methodology for fitting observed TDE radio emission to constrain their sub-parsec circumnuclear density profiles. Our findings reveal that TDE host galaxies exhibit circumnuclear density profiles remarkably consistent with the expectations of a simple Bondi accretion flow ($n_e\propto R^{-3/2}$). Under the assumption of a Bondi profile, we present a new method to jointly fit the outflow mass and ambient densities, in order to constrain the Bondi accretion rate and temperature. For the TDE host galaxies in our sample, we constrain a sample average Bondi accretion rate Eddington fraction of $\log_{10}f_{\rm{Edd}} = -3.96^{+0.30}_{-0.38}$ (as well as individual fits to each host). This work provides a methodology by which radio observations of TDEs can provide powerful constraints on the sub-parsec density distribution of quiescent SMBHs -- well inside the Bondi sphere. This opens up a new observational avenue to constrain sub-parsec gas distributions in a broad range of galaxies.

We investigate the formation and interaction of solitons in the non-integrable Ostrovsky equation characterized by anomalous (positive) dispersion. This equation is relevant for describing wave phenomena in various media, including plasma, solids, and optical fibers. Our findings indicate that certain Ostrovsky solitons, which possess zero total ''mass'' and exhibit non-monotonic asymptotic behavior, can arise from initial perturbations of a pulse-like nature. These solitons may organize into regular trains, where they are arranged according to their amplitude, or they may form irregular, nonstationary configurations of bound interacting solitons, or even multi-soliton structures. Furthermore, we demonstrate that the interactions between solitons in the Ostrovsky equation are inelastic, resulting in the emergence of a dominant soliton, or ''soliton-champion,'' within closed systems, such as those with periodic boundary conditions. In such systems, the soliton with the highest amplitude acts as a ''terminator,'' annihilating smaller amplitude solitons and absorbing a portion of their energy. We also analyze the recurrence phenomenon and determine that, although it resembles that of the Korteweg-de Vries equation, it exhibits distinct features.

I reduce the cost to prepare magic states with lattice surgery operations on the surface code by using a recursive implementation of 15-to-1 magic state distillation. On a rotated surface code with distance $d$, $|T\rangle$ preparation requires a $d$-by-$3 d$ grid of data qubits for up to $15 d$ error correction cycles, and $|CCZ\rangle$ preparation requires a $3 d$-by-$2 d$ grid for up to $10.5 d$ cycles. However, a significantly lower physical error threshold than that of the underlying surface code is required to match the error probability of the output magic state with the logical error rate of the output surface code at large code distances.

We study the Fourier approximation $\mathcal{F}_N$ of the sign function by the Krawtchouk polynomials. We give numerical evidence that the Gibbs phenomenon of the approximation differs from the classical Gibbs constant; this is in contrast to other families of orthogonal polynomials. We also show that the steepness $\mathcal{F}_N'(0)$ of the approximation is bounded by explicitly proving $\lim_{N \to \infty} \mathcal{F}_N'(0) = \log 4$. This is also in contrast to approximations by classical orthogonal polynomials, where the steepness has been shown to be unbounded as the degree increases.

We analyze a linear parabolic equation with homogeneous Dirichlet boundary conditions posed in domains whose evolution may involve topological transitions. The domains are described as sublevel sets of a smooth space-time level set function, allowing for transitions such as domain splitting and merging and the creation or vanishing of islands and holes. We introduce anisotropic space-time function spaces that extend the classical Bochner spaces used in cylindrical domains and establish key functional-analytic properties of these spaces, including the density of compactly supported smooth functions. This framework enables the application of the Babuška-Banach theorem, yielding existence, uniqueness, and a priori estimates for weak solutions. The analysis applies to domain evolutions generated by level set functions with isolated nondegenerate critical points, which correspond to the generic topology changes classified by Morse theory in two and three spatial dimensions.