Papers

In the study of quantum process tomography, it has remained open how to learn a unitary channel in diamond distance with strictly parallel queries as efficiently as with sequential queries. Sequential queries allow one to exploit adaptivity to refine the estimate and adjust the learning strategy accordingly, whereas such adjustments are impossible for parallel queries. From the perspective of higher-order quantum operations, any parallel learning strategy can be simulated by a sequential one, whereas the converse does not hold in general, suggesting that sequential learning strategies are potentially more powerful. Contrary to this intuition, we present a new protocol for learning an unknown $d$-dimensional unitary channel to within $\varepsilon$ in diamond distance using $\mathcal{O}(d^2/\varepsilon)$ parallel queries, matching the lower bound presented in [Haah, Kothari, O'Donnell, and Tang, FOCS '23]. Our protocol thus closes the gap between parallel and sequential strategies for unitary channel tomography. As applications, it achieves optimal query complexity for boundary-regime quantum channel tomography and improves the query efficiency of the best-known protocol for tomography of fermionic linear optics.

We determine the exact strong converse exponent for secret-key transmission and generation over general finite-dimensional quantum wiretap channels, measuring reliability and secrecy jointly by squared fidelity to an ideal secret key. We introduce a novel Renyi private information whose regularization characterizes this exponent. An exact integral representation in terms of ordinary private information gives a uniform continuity bound, showing that the regularized quantity converges to private capacity as the Renyi order approaches one. This establishes for any wiretap channel an exponential fidelity decay at every rate above private capacity.

We introduce a local and distributed framework for decoding quantum LDPC codes. Built atop belief propagation (BP), the architecture combines strictly local processing of syndrome information, local feedback, autonomous operation, and highly parallelized decoding. We establish the framework at two complementary levels. First, we show that any code exhibiting a threshold under iterative BP decoding can be promoted to an autonomous local measurement-and-feedback dynamics while preserving that threshold. We then turn to codes for which naive BP does not itself exhibit threshold behavior. Our key observation is that BP can nevertheless provide sufficiently accurate local marginal information: active syndrome defects use these local beliefs to move, pair, and annihilate through asynchronous feedback. We demonstrate numerically that this construction exhibits threshold behavior in the point-like sectors of the two- and three-dimensional toric codes, where conventional BP decoding fails. Exploiting the graph-generality of BP, we then study the inference dynamics on the membrane-like sector of the three-dimensional toric code and in a family of bivariate-bicycle quantum LDPC codes.

Can a symmetry be tested optimally without using the quantum resource naturally associated with it? For parallel subgroup-versus-Haar testing, we derive a quantitative representation-theoretic converse for every protocol with zero type-I error: the excess type-II error is bounded below by the sum of two nonnegative penalties, one for weight on suboptimal subgroup types and one for deviations of within-type Schur profiles from their typewise extremal profiles. At optimality, both penalties vanish, yielding support and weight locking for every optimal system marginal. Disjointness of the resulting locked set and the free marginal set rules out resource-free optimality, whereas overlap alone does not establish attainability. For the diagonal torus in dimension $d\geq 2$, optimal testing without coherence is possible only with a single query. We determine both the exact optimal type-II error over all protocols with incoherent system marginals and the minimum system-marginal coherence required to attain the unrestricted optimum. For the orthogonal subgroup in dimension $d\geq 2$, a real protocol attains the optimum at every query number. For the qutrit Clifford group, Wigner-positive optimal protocols exist at three and four queries but not from five through nine; whether they exist beyond nine queries remains open. Together, these results relate the subgroup- and query-dependent resource requirements of optimal symmetry testing to structural constraints on optimal system marginals.

We consider conformal boundaries and defects in Euclidean conformal field theory (CFT) at finite temperature and infinite volume. We distinguish defects that wrap the thermal circle and defects that are localised at a point on it. In both set-ups, and for any dimension and co-dimension, we classify bulk one-point functions of scalar, vector and spin-2 primaries. We relate the low-temperature expansion of bulk scalar one-point functions to zero-temperature defect CFT data and new finite-temperature data of defect primaries. For localised defects, we derive one-point bootstrap sum rules using periodicity and the defect operator expansion. We consider several examples in free bulk CFTs: unitary and non-unitary boundary CFTs, a wrapping monodromy defect, and a localised magnetic line. We determine thermal defect CFT data in all examples. For defects wrapping the thermal circle, we compute thermodynamic observables. For localised defects, we observe a Hurwitz zeta function decomposition of one-point functions suggestive of an underlying dispersion relation.

Reliable multistep quantum lattice-Boltzmann evolution requires controlling computational faults. When ideal collision preserves encoded mass and momentum exactly, changes in those charges can provide syndromes for selected faults at the post-collision checkpoint. A fault that shifts one population then leaves a unique mass-momentum residual labeled by the lattice velocity. A coherent reference register stores the expected charges, so the same test remains valid while the physical fluid charges vary across the lattice. Single bit flips on population number registers occupy disjoint syndrome sectors and satisfy the Knill-Laflamme condition. A state-vector demonstration on eighteen data qubits of the two-dimensional nine-velocity lattice (D2Q9) recovers that single-bit family to double-precision roundoff. Conservation still leaves a fifteen-dimensional kinetic nullspace on the three-dimensional nineteen-velocity lattice (D3Q19). Exact multiple-relaxation-time (MRT) streaming analysis ranks those charge-preserving modes by the order at which they return to density or momentum. A classical D3Q19 decaying-flow simulation at moderate Reynolds number then injects about $1.75\times10^4$ selected single-population shifts per realization. Recovery of that alphabet returns the trajectory to floating-point roundoff. The quantum statements assume an ideal charge-preserving collision and a reliable reference. The result is an inner recovery map for a stated charge-changing alphabet together with a kinetic classification of the unresolved sector.

Time-variable stellar heating may create new climate states, such as permanently hot or cold hemispheres, on asynchronous planets. Planets on eccentric orbits, circumbinary planets and planets on polar orbits around gravity-darkened stars all receive variable irradiation, yet variably irradiated planets (VIPs) have not been studied from a fundamental dynamical perspective. We present the first generalized study of the atmospheric response of variably irradiated tidally locked planets, using a 1.5-layer shallow-water model forced towards a time-dependent radiative equilibrium. We derive linearized analytic expressions for the mean, amplitude and phase lag of the response, which is that of a forced damped harmonic oscillator, and recover the established trends of tidally locked planets in the limit of steady forcing. When the instellation variation and wave timescales match and the damping is weak, a resonance occurs because waves propagate and interfere freely. The resonance produces a global standing wave mode and consequently a temporarily warmer nightside. Linear and nonlinear simulations reproduce these results and show that the hotspot oscillates longitudinally at the forcing frequency and reaches the antistellar point at resonance. The oscillation is eastward or westward of the substellar longitude depending on the rotation rate and the nonlinearity of the system. Synthetic phase curves carry signatures of this variability and invert in shape at resonance because of nightside warming. Among observed systems, we find 11 planets with at least 10% phase curve modulation from variable irradiation. Eccentric, pseudo-synchronous giants are the most promising targets, with HAT-P-2b having the largest predicted modulation.

Multimode optomechanical scattering is ubiquitous in free-space imaging protocols, but its radiation pressure counterpart is challenging to detect with extended objects. Here we demonstrate radiation pressure actuation of a nanomechanical membrane using dynamically structured light from a spatial mode demultiplexer (SPADE). Using single- and two-mode illumination, we directly image the position-dependent intermodal coupling between Hermite-Gauss (HG) modes as mediated by the membrane's motion. As an application, we use multimode radiation pressure feedback to simultaneously cool two nearly degenerate membrane modes. Our results are applicable to diverse mechanical systems and serve as a stepping stone to SPADE-based quantum optomechanics.

Quaternary mixed-metal chalcohalides (MMCHs) are a promising mixed-anion semiconductor family, but their thermodynamic accessibility remains largely unexplored. We combine density functional theory with the Alexandria Materials Database to carry out a rapid and reliable evaluation of the thermodynamic accessibility of 54 M(II)$_2$M(III)Ch$_2$X$_3$ compounds. All evaluated MMCHs are predicted to be thermodynamically unstable, but a considerable fraction of MMCHs lie within computational uncertainty of the convex hull. Their predicted decomposition follows five distinct reaction pathways, most commonly into M(III)$_2$Ch$_3$, M(II)X$_2$, and M(II)Ch. Solution processing of six Sn-based MMCHs supports our analysis. Notably, this includes the first synthesis of the previously unreported Sn$_2$InS$_2$Br$_3$ in a multiphase film. Our approach identifies convex hull proximity and competing phase formation as key constraints on MMCH synthetic accessibility during solution processing, thereby guiding future MMCH exploration.

It is shown that Shannon entropy, Fisher information, and quantum-mechanical kinetic energy may all be viewed as measures of correlation. We begin with a fundamental correlation-destroying map: a joint probability density $\rho(x,y)$ is replaced by $\rho_x(x)\rho_y(y)$, the product of its marginal distributions. In the discrete case, Shannon's entropy is nondecreasing under this map. For continuous distributions, this fundamental map leads to a well-behaved, coordinate-invariant correlation measure, analogous to the discrete Shannon entropy: \[ I[\rho] = h[\rho_x] + h[\rho_y] - h[\rho]. \] In the continuous case, however, another measure appears: Fisher information. The relative Fisher information $J(\rho\|\rho_x\rho_y)$ behaves similarly under the fundamental map. For a normalized real quantum wavefunction, this decrease is exactly proportional to the decrease in mean kinetic energy, \[ \langle T\rangle_\psi - \langle T\rangle_\Phi = \frac{\hbar^2}{8m} J(\rho\|\rho_x\rho_y), \qquad \Phi = \sqrt{\rho_x \rho_y}. \] In Jaynes's language, the result supports a principle of minimum justified correlation: given physical constraints and a set of possible distributions or related amplitudes satisfying those constraints, select from that set those with the least correlation. This is Part I of a two-part paper. Here we develop the entropy, Fisher-information, and kinetic-energy identities above, and state the principle they support. Part II addresses questions which Part I raises but leaves unanswered: multiple solutions, time dependence, the role of spin, a route to the Schrödinger equation itself, and a proposed experimental test. AI has been used.

In 2023, pulsar timing array (PTA) collaborations around the world announced evidence for a nanohertz gravitational-wave background (GWB). Beyond increasing the detection significance, the next major goal is to characterize the GWB and identify its source(s). The typical model-comparison metric used in PTA analyses is the Bayes factor (BF). However, BF computation methods used in the PTA literature, such as product-space sampling and thermodynamic integration, are computationally expensive or inefficient if the models compared are dissimilar or non-nested. In this work, we introduce a PTA model-comparison method using a combination of normalizing flows, nested sampling, and a PTA likelihood that is marginalized over all non-GWB parameters. The flows are trained using a newly-developed Python package coppuccino, which learns the data's copula: the dependence structure after transforming to uniform marginals. We validate the method on both analytic targets and simulated PTA data, recovering the analytic evidence within error bars and achieving an area-under-the-curve (AUC) score of 0.996 when treating the BFs as binary classifiers of the injected models. The result is a method to perform Bayesian model comparison of arbitrary GWB spectral models in minutes on consumer hardware.

In this article, we analyze plane-symmetric solutions to the relativistic Euler equations on spatially flat spacetimes with decelerated expansion. We consider a linear equation of state $p(\rho)=K\rho$ and power law inflation $a(t)=t^{\alpha}$, where $0<K<\frac{1}{3}$ and $0\leq\alpha<1$. Previous results imply nonlinear stability of the homogeneous and isotropic solution above an expansion threshold $\alpha_\text{crit}=\frac{2}{3(1-K)}$. We prove that at and below this critical expansion rate there exist arbitrarily small data that exhibit finite-time singularity formation of the shock type, i.e., gradient blowup while the solution stays bounded. For this type of data, we establish lifespan estimates that are polynomial below and exponential at the critical threshold. In addition, we prove a theorem based on energy estimates that provides lower bounds on the lifespan of plane-symmetric solutions generated from small initial data and generalizes to solutions without symmetry in $3+1$-dimensions.

Gravitational-wave (GW) “dark siren” techniques, namely the statistical association of GW events with a galaxy catalog, have so far been used as a cosmological tool. Yet this association carries distinctive astrophysical information that remains unused—specifically, how compact binaries populate galaxies and the identities of individual hosts. In this work, we turn the dark-siren program into an astrophysical probe by inferring both simultaneously within a single hierarchical framework. The method reduces the many potential hosts to a compact, probabilistically ranked target list, providing a direct follow-up decision tool. Applied blindly to GW170817, it recovers NGC~4993 as the highest-ranked host and constrains the galaxy luminosity weighting, mildly favoring non-uniform host weights. Fixing the galaxy weighting can instead degrade host identification and even favor the wrong host. This framework recasts dark sirens as a potentially unique probe of the astrophysics of electromagnetically dark compact-binary mergers.

Berry curvature and quantum metric of Bloch states govern a wide range of phenomena, yet unified experimental access to both remains limited. Here we show that light spatial-dispersion alters the selection rules of second-order photocurrents and responses forbidden by parity become allowed in centrosymmetric crystals without any external fields, magnetic order, interfaces, strain, or engineered symmetry breaking. The resulting response is intrinsic and its weight is set by the quantum geometry of the Bloch states. Conventional photogalvanic effects are constrained by crystal symmetry and entangle the quantum metric with shift vector contributions. The spatially-dispersive response instead isolates the quantum metric and Berry curvature in distinct polarization channels. Implementing this approach in 1T'-MoTe2 across its temperature-driven transition to Td-Weyl phase, we resolve helicity-even and helicity-odd photocurrents corresponding to quantum metric and Berry curvature contributions, respectively, from the same device. The metric-dominated response persists across both phases and exhibits a robust spectral structure reproduced by first-principles calculations and linked to momentum-resolved quantum metric hotspots. In contrast, the curvature-driven channel emerges only when inversion symmetry is broken and shows strong sensitivity to carrier doping through competing momentum-space contributions. Our results establish photogalvanic effects with spatially varying optical fields as a general route to accessing quantum geometry in materials where photon energy and electronic filling probe different parts of the excitation manifold.

The very high-energy ($E > 100$ GeV) afterglow emission in gamma-ray bursts (GRBs) can be explained by synchrotron self-Compton (SSC). Modeling this emission accurately requires fully numerical codes that solve the time-dependent coupled particle–photon kinetic equations while accounting for Klein–Nishina suppression. However, their substantial computational cost makes them impractical for traditional parameter inference techniques such as Markov Chain Monte Carlo (MCMC) sampling. In this work, we present a highly efficient surrogate model based on artificial neural networks (ANNs) that emulates a one-zone kinetic SSC radiation code. To train our ANN, we use a multi-dimensional model parameter grid that constitutes a sample of 100,800 spectra produced by an infinitely thin spherical blast wave propagating inside a constant density interstellar medium (ISM). The ANN reproduces the numerical spectra well, with the median relative error generally below 2 per cent across the full frequency domain. Using this surrogate framework, we perform Bayesian parameter posterior estimation via MCMC and fit the broadband GRB afterglow observations of GRB 190114C from X-rays to TeV $\gamma$-rays at different epochs. We find an energetic jet with isotropic-equivalent kinetic energy of $E_{\rm k,iso}\simeq7.2\times10^{54}$ erg moving with a coasting bulk Lorentz factor of $\Gamma\gtrsim500$ into an ISM with density $n\simeq0.1\,{\rm cm^{-3}}$. The deviation of our model light curve from observations on long timescales suggests that an ISM environment is inconsistent and a radially stratified external medium, as pointed out by \citet{Aguilar-Ruiz+26}, is preferred instead.

We introduce and numerically demonstrate receiver-informed transmitter (RITX) waveform design for 200 Gb/s PAM-4 C-band direct-detection PON. Using 50 GHz optoelectronics, RITX achieves N1/E1 loss classes with FFE-Free ONU, enabling 40 km reach and 48.1%/66.7% network-wide complexity savings at 1:64/1:128 splits

Dimensional homogeneity is a fundamental constraint on physically meaningful models, requiring invariance under changes of units. We present a data-driven method for constructing surrogate models that satisfy this constraint at the level of the hypothesis class. Starting from a dimension matrix of measured variables, the method derives Buckingham $\Pi$-groups, constructs admissible dimensional prefactors, and approximates the remaining dimensionless dependence using truncated harmonic expansions on normalized invariant domains. Once the prefactor and dictionary are fixed, the coefficients are obtained from a regularized linear regression problem. We test the approach on the simple pendulum, Planck's black-body law, the double-pendulum Lyapunov field, and an experimental COBE/FIRAS black-body spectrum dataset. The results show that dimensional constraints improve conditioning, robustness to noise, and sample efficiency relative to unconstrained baselines, while the choice of dictionary becomes important in non-periodic or multi-invariant settings. The learned expressions are explicit and inexpensive to evaluate, which makes them useful as surrogate models for structured physical problems.

Suppose a Hamiltonian $H$ has a unique ground state $|\psi_0\rangle$ with an eigenvalue $E_0$, and we have an estimate $\tilde{E}_0$ such that $|\tilde{E}_0-E_0|\leq\delta$, and there is a gap of at least $3\delta$ between $E_0$ and all other eigenvalues. Suppose we have a unitary $A$ available that can produce a "guiding state'" $A|0\rangle$ that has overlap at least $\gamma$ with $|\psi_0\rangle$. We show how to obtain an $\eta$-approximation of $|\psi_0\rangle$ with probability at least $1-\varepsilon$ using $O(\log(1/\varepsilon)/\gamma\delta + \log(1/\eta)/\delta)$ applications of $U=e^{iH}$ its inverse, and $O(\log(1/\varepsilon)/\gamma)$ applications of $A$ and its inverse. We give two different algorithms, one based on interleaving amplitude amplification and error-reduction in the style of [HMdW03], and one using the composition of transducers. This paper is the state-preparation follow-up to our two recent ground-state-energy estimation papers [JW26,SdW26]. Combined with the optimal energy-estimation of [JW26], our results show the claimed upper bound for ground-state preparation. The bound is optimal up to a constant factor in terms of the number of applications of $U$ and $U^\dagger$ if $\varepsilon=\eta$, as follows from [SdW26]. In one of our approaches to ground state preparation, we construct transducers for amplitude amplification and LCU that might be of independent interest.

Ship structural vibrations contribute to noise, fatigue, and equipment damage, while dynamic-compliance topology optimization can produce pathological designs near resonance. This study extends neural-reparameterized topology optimization using a convolutional Kolmogorov-Arnold network (KATO) to forced-vibration design with active input power (AIP) as the objective. Applications include a 100 Hz engine-supporting deck panel and an 18 Hz thruster foundation frame. Helmholtz PDE filtering and Heaviside projection control feature sizes and manufacturing tolerance. Across both deck families, all eight optimized layouts reduce AIP relative to size-optimized references and, after finite-depth extrusion, also achieve lower static compliance. For unrestricted, manufacturing-aware, and stress-aware frame variants, KATO matches GCMMA in AIP within 0.5 dB while yielding 22-36x lower static compliance after matched-volume binary re-analysis. In a near-resonant 300 Hz case, both methods reduce initial AIP by more than 32 dB; KATO maintains a connected design, achieves 59x lower binary static compliance, and reduces maximum AIP over 1-500 Hz by 2.7 dB. KATO runs 6.4-10.4x faster than GCMMA for the implemented stress-aware formulations. The results demonstrate neural AIP-driven topology optimization as an efficient approach for designing connected, feature-size-controlled ship structures with improved forced-vibration performance.

An emergent gauge field can control boundary critical behavior without changing the bulk quantum spin liquid. We investigate the boundary criticality in $(2+1)$-dimensional $U(1)$ Dirac spin liquid, whose low-energy physics is described by massless quantum electrodynamics. Using a perturbative renormalization-group analysis in a half-space, we show that Neumann and Dirichlet boundary conditions for the emergent gauge field lead to distinct boundary universality classes. We determine the boundary scaling dimensions of the fundamental fields and gauge-invariant operators that provide observable signatures. We further propose a fermion-gauge lattice model with tunable boundary interactions as a microscopic setting for realizing and probing these boundary universality classes.

Quantum algorithms are powerful tools for finding symmetries of classical objects, most famously through Shor's algorithm and the Hidden Subgroup Problem (HSP). In this work, we study quantum algorithms for learning symmetries of quantum objects. Existing work in this area centres on the recently introduced State Hidden Subgroup Problem (StateHSP), a quantum generalisation of HSP in which the task is to learn the symmetry subgroup of a quantum state. We develop efficient quantum algorithms for non-abelian StateHSP when the hidden subgroup is normal and the ambient group belongs to a broad class of non-abelian groups, extending the previous general theory beyond the abelian setting. StateHSP learns Bose symmetries, under which a state must be invariant exactly under the action of the symmetry group. In quantum mechanics, however, physically equivalent pure states are defined only up to global phase. Motivated by this, we introduce a natural notion of Anyonic state symmetry learning, based on invariance up to global phase. We give an efficient quantum algorithm by reducing the problem to StateHSP, where the reduction rests on a new correspondence between linearisations of projective representations and linear error-correcting codes. As an application, we obtain an improved algorithm for learning stabiliser groups of mixed qudit states of arbitrary local dimension. Finally, we introduce symmetry learning problems for other quantum objects, including unitaries, Hamiltonians, and finite collections of states, and give efficient algorithms for them by reduction to state symmetry learning. Together, these results broaden the scope of state symmetry learning as a common algorithmic primitive for learning quantum symmetries.

We show that the optimal commuting operator correlation for a variant of Coladangelo's two-player generalized nonlocal game, based on the embezzlement of entanglement, is a commuting operator self-test. Our result gives the first correlation self-test for an exact entanglement embezzlement protocol in the commuting operator framework. Because the unique optimal correlation necessitates the exact embezzlement of entanglement, the correlation is unrealizable using quantum tensor-product models, even if the local spaces are allowed to be infinite dimensional. As such, our result provides an example of a commuting operator self-test where the Hilbert space shared by the two parties cannot be factored into a tensor-product of local spaces that is compatible with the local measurement operators. Our main proof technique relies on Harris' unique abstract state characterization of exact embezzlement of entanglement involving Cuntz algebras.

The escape of ionizing photons from galaxies during the Epoch of Reionization is often inferred indirectly because the intervening neutral hydrogen in the intergalactic medium (IGM) is expected to absorb all flux blueward of Lyman-$\alpha$ at these redshifts. However, in this work, we report the significant detection ($\approx7\sigma$) of flux blueward of Ly$\alpha$ in a massive ($M_{\ast}\approx10^{9.1}\ M_{\odot}$) star-forming galaxy at $z\approx7.57$, JADES-GS-z7-LAF, using JWST/NIRSpec PRISM spectroscopy. We independently confirm this detection of the Ly$\alpha$ forest (LAF) using JWST/NIRCam F090W imaging ($\approx10\sigma$). The blueward flux in F090W is spatially coincident with the galaxy and emerges $\approx0.4$ pkpc from its UV centroid at $\lambda_{\mathrm{rest}}\approx1500\ \mathrm{\mathring{A}}$. We find no evidence for a foreground interloper producing the observed flux, although we cannot formally reject this interpretation with the existing data. The transmitted flux implies an extraordinarily transparent sightline ($x_{\mathrm{HI}}\ll0.1\%$) through the IGM at $z \approx 5.5-7.5$, a sightline that is spatially and kinematically coincident with numerous high-redshift galaxy overdensities, which possibly explains the emergence of this flux. We observe a smooth and gradual turnover around the Ly$\alpha$ break that is either consistent with an extreme damping-wing ($N_{\mathrm{HI}}\approx10^{23.3}\ \mathrm{cm}^{-2}$) or a strong nebular continuum (contributing $\approx60-70\%$ of the flux at $\lambda_{\mathrm{rest}}=1500\ \mathrm{\mathring{A}}$). JADES-GS-z7-LAF is far more luminous ($M_{\mathrm{UV}}\approx-21.5$, similar to GN-z11) than the faint sources usually invoked as the drivers of cosmic reionization. If such systems are common in the early Universe, massive galaxies may contribute more to the ionizing photon budget than suggested by other indirect constraints.

For every odd prime power $q$ and $D=q+1$, we construct an infinite family of Ramanujan quantum expanders of degree $D$. The construction transfers Morgenstern's Ramanujan Cayley graphs on $\operatorname{PSL}_2(\mathbb{F}_{p})$ for $p$ which is an even power of $q$, through the odd irreducible subrepresentation of the Weil representation of $\operatorname{SL}_2(\mathbb{F}_{p})$. For a quantum expander of dimension $N$, our implementation uses $O(\log^2 N)$ elementary gates, and $O(\log N)$ ancilla qudits, using a fixed finite gate set depending on $q$. An advantage compared to the previous work of Iyer, Jain, Jordan, and Somma (FOCS 2026) is that assuming the quantum circuit is implemented exactly, we satisfy the $2\sqrt{D-1}/D$ singular value bound exactly without any additive error.

We review mathematical results about the spectrum of spin-$s$ chains with a nearest neighbor interaction given by the projection onto the singlet state of two spin-$s$ degrees of freedom. Up to normalization, these interaction terms generate a Temperley-Lieb algebra at loop parameter $d=2s+1$. We also present several new results. First, we prove a ferromagnetic ordering of energy levels across symmetry sectors of the model, thus generalizing a previous result of Nachtergaele, Spitzer and Starr (2004) for the spin-$\tfrac12$ $XXZ$ chain. This enables us to determine a uniform lower bound on the finite volume spectral gap for these spin chains. By combining a variational estimate with Knabe's finite size criterion, we show that the exact spectral gap of the GNS Hamiltonian of the fully polarized state is $1-2/d$. Furthermore, this value serves as a lower bound for the gap of the maximally mixed ground state. Finally, we show that the ground state projectors on open chains satisfy the Jones-Wenzl recursion, thereby recovering a known result that the degeneracies are the quantum integers $[L+1]_q$ for $q+q^{-1}=d$. We discuss how the high degeneracy of the ground states allows the model to break a continuous symmetry while remaining gapped, and renders that gap unstable.

We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonical quantum speedups in this model are witnessed by Grover search and Bernstein-Vazirani, leading to the longstanding conjecture $$ \mathsf{R}(\mathcal C)=O(\mathsf{Q}(\mathcal C)^2+\mathsf{Q}(\mathcal C)\log N). $$ We first refute this conjecture by constructing concept classes $\mathcal C$ and $\mathcal C'$ satisfying \[ \mathsf{R}(\mathcal C)=\Omega\!\left(\frac{\mathsf{Q}(\mathcal C)^3\log N}{\log \mathsf{Q}(\mathcal C)}\right) \qquad\text{and}\qquad \mathsf{D}(\mathcal C')=\Omega(\mathsf{Q}(\mathcal C')^3\log N). \] The first bound matches the upper bound of Arunachalam et al.~[Quantum'21] up to constant factors, while the second matches the upper bound of Servedio and Gortler~[SICOMP'04]. In particular, this shows that the saving in the randomized upper bound of Arunachalam et al. fundamentally relies on randomness. Apart from characterizing the optimal relationship between classical and quantum query complexity, our results are the first to show that quantum speedups for learning can go beyond the Grover and Bernstein-Vazirani paradigms.

The kagome metal CsV$_3$Sb$_5$ exhibits charge density wave (CDW) and superconducting transitions, both of which are substantially affected by pressure. Recent x-ray diffraction experiments identify a new charge-ordered phase at a pressure coinciding with the dip of the superconducting dome. This CDW phase displays a distinctive wavevector $\mathbf{Q} = (3/8, 0, 1/2)$ and monoclinic symmetry, in contrast to the $2\times2\times 2$ and $2\times2\times 4$ orders reported at ambient pressure. In this letter, we show that density functional perturbation theory (DFPT) calculations on a fine reciprocal-space grid predict the leading lattice instability of CsV$_3$Sb$_5$ to be at this wavevector. Finite-displacement calculations reveal that while anharmonic effects stabilize the conventional $L_2^-$ CDW at ambient pressure, the competing $3/8$ instability becomes energetically favorable above $\sim$1 GPa, consistent with experimental observations. Interestingly, the nesting function displays a peak at the same wavevector. A Landau free energy analysis explains the emergence of the monoclinic distortion observed in x-ray diffraction, in addition to several bond-ordering patterns that may be relevant to the observed trends in the superconducting $T_c$.

Scientific foundation models are commonly evaluated after heterogeneous physical problems have already been translated into a compatible gridded, tokenized or symbolic representation. This leaves the scientific interface outside both the pretrained model and the audit of what is actually reused. We study the complementary setting in which boundary histories, sparse monitor records and loading histories retain their native inference classes and their outputs remain on Cartesian, latitude-longitude and unstructured domains. GEODE couples task-specific scientific interfaces to a shared routed library of wavelet operators. A single jointly pretrained model represents cavity flow, radiation dose and elastoplastic stress, then acquires a heat exchanger and a reactor subchannel by training a private interface containing 2.1% of its parameters. Earlier predictions remain unchanged by parameter isolation, whereas unrestricted fine-tuning degrades them by factors of 14-29. Crucially, preservation alone does not establish reuse: norm-matched randomized-library controls show that the contribution of pretrained computation is conditional on the task and data regime. A separate decomposition shows that full-field relative L2 error can substantially understate error relative to spatial variation when field level dominates the norm. Task-specific operators remain more accurate on three of the five problems. These results distinguish multi-task coverage, preservation and pretrained reuse as separate properties that must be tested independently when scientific foundation models span heterogeneous interfaces.

We study the effective potentials for various probe D-branes surrounding AdS$_5$ black holes in consistent truncations of type IIB supergravity on Sasaki-Einstein 5-manifolds $Y^{p,q}$, focusing in particular on the conifold base $T^{1,1}$. The probes are either dual Giant Gravitons having support on AdS spacetime dimensions or D3 probe branes wrapped on non-contractible cycles of the internal manifold, which then appear "point-like" in the AdS spacetime. The non-contractible cycles of $T^{1,1}$ and $Y^{p,q}$ topologically stabilize the branes at a finite size, and we find stable supersymmetric wrapped D3 branes on Gutowski-Reall black holes, effectively providing a stable BPS composite system in AdS$_5$ made by a black hole surrounded by a baryonic condensate. We show that the onset of superradiance in the black hole backgrounds matches the emergence of stable minima in the probe effective potentials, extending the constructions of Dual Dressed Black Holes and the Grey Galaxies. We comment on the relevance of this result for recent studies concerning the classical cohomology problem and the associated fortuitous states in the dual Klebanov-Witten theory.

A simple model gives good agreement between observed emissions of CO2 into the atmosphere from the combustion of fossil fuels and observed increases of the atmospheric concentrations C of CO2 and decreases of the isotope delta value delta13C. If fossil fuel emissions were to cease the model predicts that: (1) the difference between the CO2 concentration C and the preindustrial value, Co = 280 ppm, would decay exponentially with time constant of 60 y; (2) the difference between the concentration-delta-value product C x delta13C and the preindustrial value Co x delta13Co = (280 ppm) x (-6.5%%), would decay exponentially with a time constant of 8 y. The decay times are different because of isotopic exchange, largely driven by photosynthesis and respiration on the land.