Papers

We introduce quantum tilted walks, a quantum algorithmic framework for solving exact combinatorial optimization problems. The framework applies an average of powers of a tilted Hamiltonian that biases the discriminant matrix of a base Markov chain (mixer) with the objective function. Our starting point is quantum short-path algorithms, which prepare the ground state of such a Hamiltonian and obtain super-quadratic speedups over exhaustive search for certain combinatorial optimization problems. Recently, Le Gall and Tamaki~(arXiv:2604.12131) developed a classical conditioning-and-search algorithm for weighted MAX-E$k$-LIN2 and weighted MAX-$k$-CSP. Under the same assumptions, their algorithm is only sub-quadratically slower than quantum short-path algorithms. Consequently, existing short-path algorithms do not establish a super-quadratic speedup over this stronger classical baseline. For maximization problems, we give conditions under which tilted walks increase the amplitude on the target state with high objective value when initialized from a starting state with lower objective value. This framework captures conditioning-and-search and yields super-quadratic speedups over it for the same problems. While our framework recovers quantum short-path algorithms as a special case, it neither requires ground-state preparation nor initialization in the ground state of the base mixer. We demonstrate these advantages on a synthetic optimization problem for which tilted walks achieve a super-quadratic speedup whereas the short-path algorithms do not.

We investigate the Casimir effect of a massive, self-interacting real scalar field with quartic coupling in a $(3+1)$-dimensional Hořava-Lifshitz-type theory, subject to rough boundaries obeying Dirichlet boundary conditions. Using the effective action and generalized $\zeta$-function approach, we derive the renormalized effective potential, incorporating anisotropic scaling, boundary roughness, and temperature in the low-temperature regime. We determine the topological mass at one-loop order and the Casimir energy up to two loops. In the massless limit, the topological mass and the two-loop Casimir contribution exhibit infrared divergences for odd values $z>1$, associated with the absence of an intrinsic mass scale, while the one-loop Casimir energy remains finite. For $z=1$, the standard relativistic Dirichlet result is recovered in the zero-temperature and vanishing-roughness limits.

We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.

Molecular quantum dynamics simulations that treat both electrons and nuclei quantum mechanically are crucial for predicting chemical reactions. With classical computation, a full wave-function representation of both types of particles requires resources that grow exponentially with their number. Oscillator-qubit processors, including trapped-ion and circuit QED devices, represent electronic states with qubits and nuclear vibrations with oscillators. Their native operations produce linear vibronic interactions, from which programmable anharmonic interactions can be built. Product-formula approaches build the corresponding phase gates by repeating small noncommuting phase steps, and quantum signal processing (QSP) approaches approximate each gate directly with a Fourier series. Simulations apply many such gates in sequence, so accumulated cost and error limit how long the dynamics can be followed. We propose near-optimal quantum primitives for molecular quantum dynamics simulation, covering the representations of both types of particles and their interactions. We synthesize nonlinear and multimode bosonic phase gates using generalized Jacobi-Anger (GJA) expansions within QSP, with a cost that grows near-optimally in both interaction strength and precision. Our interaction model and gate synthesis each have their own accuracy setting. Chosen together, these settings make our multimode benchmark circuits about one-third shorter than those of the previous direct QSP approach. We then simulate energy exchange between the stretching and bending vibrations of a simplified carbon dioxide model. With circuit-QED noise, a short simulation narrowly misses our accuracy criteria at qubit and oscillator lifetimes near 2 ms and 5 ms. These lifetimes mark a concrete checkpoint on the way to simulating anharmonic multimode molecular quantum dynamics on near-term oscillator-qubit processors.

Linear combination of unitaries (LCU) is a fundamental primitive in quantum algorithms, whose cost is typically governed by the most expensive unitary appearing in the combination. We develop a transducer-based LCU framework that reduces this worst-case dependence to a weighted average query complexity, when the constituent unitaries share access to a common set of primitive oracles. Consider $A=\sum_j c_j U_j$, where $c_j>0$ and each unitary $U_j$ can be implemented using $C_j$ primitive queries. Given an upper bound $a\geq \|A\|$, our algorithm implements a block-encoding of $A/\alpha$ with rescaling factor $\alpha=\mathcal{O}(a)$, using $\widetilde{\mathcal{O}} (C_{\max}+\overline{C} {\lambda}/{a} )$ primitive queries, where $\lambda=\sum_j c_j$, $C_{\max}=\max_j C_j$, and $\overline{C}= {\sum_j c_j C_j}/{\lambda}$. By comparison, the standard LCU construction requires $\widetilde{\mathcal{O}} (C_{\max} {\lambda}/{a} )$ primitive queries. The improvement can therefore be substantial when costly unitaries have small weights and $\lambda/a$ is large. As applications, we obtain improved block-encodings of sparse matrices, leading to quantum algorithms for sparse Hamiltonian simulation and quantum linear systems with near-optimal query complexity up to polylogarithmic factors in all relevant parameters. Our main technique is the transducer framework developed by Belovs, Jeffery, and Yolcu [Quantum, 8:1444 (2024)]. Here we develop a complementary operator-level theory tailored to block-encodings. We identify the resolvent norm $K$ as a key complexity measure for transducer implementation besides the existing catalyst complexity. We show that the transducer action can be converted into an $\epsilon$-approximate block-encoding using only $\mathcal{O}\left(K \log(1/\epsilon)\right)$ queries to the transducer, improving the precision dependence from polynomial to logarithmic.

Tauonic flavour-changing neutral-current transitions ($b\to s\tau^+\tau^-$) are sensitive probes of New Physics connected to third-generation quarks and leptons. Motivated by the persistent anomalies in $R(D^{(*)})$ and the indications of enhanced $B^+\to K^{+}\nu\bar\nu$ rates, we revisit and update the predictions for $b\to s\tau^+\tau^-$ processes. Building upon a previous work on a data-driven approach to include the dominant $\psi(2S)$ resonances, we provide predictions for $B\to K^{(*)}\tau^+\tau^-$ ($B_s\to\phi\tau^+\tau^-$) over the full kinematic range. To include possible New Physics contributions within the Weak Effective Theory, we provide semi-analytic expressions for the corresponding branching ratios. We then perform a comprehensive dimension-6 SMEFT analysis of New Physics realised at the TeV scale. We identify regions of parameter space preferred by current data where the branching ratios of $b\to s\tau^+\tau^-$ processes can be enhanced by several orders of magnitude. While current experimental sensitivities remain far above the SM rates, the enhancements suggested by present flavour data imply that forthcoming limits from LHCb, CMS, and Belle~II will probe significant regions of the relevant SMEFT parameter space. Furthermore, we highlight that while different scenarios can lead to the same predictions for $B\to K^{(*)}\nu\bar\nu$ branching ratios, they can be disentangled by measuring $B\to K^{(*)}\tau^+\tau^-$, $B_s\to\tau^+\tau^-$ and $B_s\to\phi\tau^+\tau^-$.

In the present paper, we extend the results in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen from the slowly rotating regime $|a|\ll m$ to the full subextremal range $|a|<m$, thereby completing the proof of the Kerr stability conjecture. The restriction $|a|\ll m$ enters in fact only through the estimates for wave equations and for the Bianchi system established in \cite{GKS22}. To remove this restriction, we crucially rely on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the inhomogeneous scalar wave equation and for inhomogeneous Teukolsky equations on perturbations of Kerr with $|a|<m$. Additionally, some of the results of the present paper are proved in our companion paper \cite{Sze}.

Dark matter N-body simulations that resolve halo substructure (subhalos) with high accuracy can be used for generating reliable catalogs of central and satellite galaxies via galaxy-halo connection models. However, such simulations are computationally expensive, especially when large numbers of realizations are required for statistical analyses such as robust estimations of covariance matrices for (statistical) cosmological quantities. In this work, we present a fast method for populating dark matter halos in a given simulation box with subhalos extracted from a high-resolution simulation box with the same cosmology but arbitrary initial conditions. For each halo in a given test set, the method first predicts whether it hosts at least one subhalo above a given mass threshold using a classifier built on a decision tree regressor. Then, for each predicted host, the method finds another host halo in a given high-resolution box, using a nearest neighbor search in the space of selected halo properties, and appropriately maps subhalos from that halo to the test one. By applying the method to different test sets, we make predictions for abundances, distributions and three-dimensional and projected (two-dimensional) two-point correlation functions of various subhalo populations and sub-populations. In most cases, the percent errors of our predictions are well below 5%. In general, the method can be used to populate halos in low-resolution simulation boxes with subhalos from a high-resolution simulation and also to investigate which halo properties are (more strongly) correlated with subhalo abundance and clustering in a given dark matter simulation.

Quantized Hall transport is traditionally anchored to a bulk spectral gap, which isolates the occupied subspace and exponentially suppresses thermal deviations. Recently discovered critical topological flat bands (CTFBs) challenge this paradigm: an exactly flat band touches a dispersive continuum while retaining a well-defined integer Chern number. However, their finite-temperature transverse transport properties remain entirely unexplored. Here, we develop a low-temperature theory of the intrinsic electrical, thermoelectric, and thermal Hall responses in CTFBs. At fixed particle number, the macroscopic flat-band degeneracy forces a singular Lambert-$W$ drift of the chemical potential, generating an algebraic-logarithmic hierarchy of low-temperature corrections: $T\ln(1/T)$ for electrical Hall, $T[\ln(1/T)]^2$ for thermoelectric Hall, and $T[\ln(1/T)]^3$ for thermal Hall conductivity, replacing the activated thermal protection of a gapped Chern insulator. By contrast, externally pinning the chemical potential to the flat-band energy locks the flat band to half occupation at any nonzero temperature, obstructing the recovery of the fully filled topological ground state as $T\to0^+$. Our results establish that a bulk spectral gap is unnecessary for zero-temperature Hall quantization, but indispensable for its exponential thermal protection.

We establish a no-go theorem for a broad class of quantum algorithms for the dihedral coset problem (DCP). We consider the Fourier-sampling and subset-sum-measurement template proposed by Regev (SIAM Journal on Computing, 2004), which is one of the main approaches to solving DCP. Suppose that, after measuring the lower $n-1$ bits of the subset sum, the algorithm discards any $\omega(\log n)$ bits from each of the Fourier labels. Then we prove that the algorithm cannot succeed in solving DCP. This shows that any algorithm following this template must make extensive use of the Fourier labels, and thus serves as a useful guide for developing algorithms for DCP. As a main application, we show that the recent algorithm by Simon (IACR ePrint:2026/1591, August 11 2026) does not solve DCP. We show that after the subset-sum measurement, this algorithm can be implemented (up to exponentially-small error) using only the most-significant third of the Fourier labels, and is therefore subject to our general no-go theorem. To help with verifiability, we release Lean 4 code for our results.

The bosonic quantum entropy power inequality bounds the entropy of a beam-splitter output in terms of the input entropies. We determine its complete equality class among independent inputs of finite mean photon number: for any number of modes and any transmissivity strictly between zero and one, equality in either the linear or the exponential form holds if and only if the inputs are Gaussian with the same covariance matrix, allowing arbitrary displacements. The main step shows that equality for one output forces the two outputs to be independent: a thermal auxiliary converts equality into preservation of mutual information by a fixed noisy channel, and a two-outcome instrument shows that preservation of mutual information requires a product state with the reference. The quantum Darmois–Skitovich theorem then gives Gaussianity, while a central-limit argument reduces exponential equality to linear equality.

Foundation machine-learning interatomic potentials cover broad configurational and chemical spaces, but their reliability can vary across the atomic environments encountered during a simulation. Here we introduce the calibrated Mahalanobis (CALM) extrapolation grade $\gamma$, a piecewise differentiable per-atom quantity integrated into GRACE foundation models and evaluated alongside energies and forces in a single model pass. We define $\gamma$ from nearest-cluster Mahalanobis distances in latent feature space, setting $\gamma=1$ from the training-distance distribution separately for each element and cluster. Controlled tests show that a normalized random projection of the invariant many-body basis detects structural and chemical extrapolation. On different foundation datasets, OMat24 and SMAX, $\gamma$ correlates with atomic force errors and separates structures with different error distributions. The CALM grade adds percent-level computational cost, and its spatial gradient guides uncertainty-biased data collection toward configurations with larger absolute force errors.

Superconductor and two-dimensional hole gas heterostructures are promising platforms for quantum devices, but their intrinsic properties, e.g., unconventional pairings, are hard to access experimentally. Here, we show that the in-plane-field dependence of the superfluid stiffness and spin susceptibility exhibits nonanalyticities encoding the induced gap structure in the hole gas. Additionally, Fourier harmonics of the stiffness tensor's field-angle dependence, accessible via kinetic-inductance measurements, provide fingerprints of unconventional pairing and cubic Rashba coupling.

Titan, a unique body in the solar system, resembles a life-size Miller-Urey experiment where pockets of liquid water might interact with abundant organic matter. Its young surface (less than a billion years) shows signs of material exchange with the interior, and an isotopic signature is detected in the atmosphere. Cryovolcanism and meteor impacts represent potential high energy mechanism for these exchanges. Although cryolava or impact melt properties are largely unknown, Titan's internal structure makes a significant water content in these fluids highly probable. The temperature of these fluid mixtures at the onset of the flows is above 0~$^\circ$C. The primary objective of this work is to investigate the dynamical and thermal properties of potential Titanian flows, while ensuring their spatial extents remain broadly consistent with the few available observations. We also aim to assess whether their evolution could enable the hydrolysis of encountered organic material. On Earth, in the context of lava flow risk assessment, numerical techniques based on cellular automata have been developed for many years. This approach allows simulating the flow of Bingham fluids over distance scales of several tens of kilometers. In the context of Titan's surface, and within the explored parameter space, flows with a spatial extent of several tens of kilometers can be produced with our model. The resulting flow thickness is about a meter. The flow extent is primarily controlled by the total erupted volume and the terrain topology. As expected, the rheology and thermo-physical properties of the erupted fluid have significant influence on the flow's extent and the cooling rate of the cryolava. We predict hydrolysis reactions between an aqueous cryolava and the organic matter likely ubiquitous on Titan's surface. Our model code is publicly available.

The nature of dark matter sets the shape of galactic halos: collisionless cold dark matter (CDM) predicts triaxial halos, while scattering in self-interacting dark matter (SIDM) rounds them toward sphericity. We show that a large catalog of projected stellar stream tracks can statistically constrain halo shapes, and therefore the particle nature of dark matter, without detailed modeling of any individual stream or gravitational potential. We develop a new geometric diagnostic for stellar streams: if the curvature of any segment along a stream points away from the host galaxy's projected center of mass, then that stream falsifies broad classes of potentials, including spherical ones. We call such a segment convex. The diagnostic needs only a projected stream track and a host-center estimate, requiring no kinematics, distances, progenitor model, or fit to individual host potentials. Halo triaxiality sets the rate at which streams show convex segments, making this rate an observable of the halo-shape distribution and the underlying dark-matter model. We forecast that upcoming survey-scale stream morphology catalogs can discriminate between CDM and SIDM at up to $5\sigma$.

We develop a theory of exact transmission of finite-dimensional $C^*$-algebras through quantum channels. These algebras describe hybrid classical-quantum information, allowing the dimension of the quantum system to depend on the classical message. Allowing arbitrary encodings and decodings yields a transmission set of algebra types, ordered by embedding, that unifies zero-error information theory with operator-algebraic error correction. We ask if this set admits a dominating algebra into which every transmittable algebra embeds. Our central finding is that domination can fail even in small dimensions. In its absence, several incomparable maximal algebras can describe different optimal uses of the same channel, forcing the user to select one depending on the operational task and the type of information to be preserved. We introduce hybrid capacities that reconstruct the only possible dominating algebra type and present a complete finite characterization of domination using minimal forbidden algebra types. We identify dominating algebras for channels whose operator systems are graph-isomorphic to $*$-algebras, including highly divisible channels, and for channels with zero one-shot zero-error quantum capacity. Under tensor products, we prove that joint coding can produce new algebra types, giving an algebraic analogue of superadditivity from Shannon theory. Domination can fail for the joint use of two channels, even when both channels separately admit dominating algebras. Finally, we construct a channel whose $n$-fold tensor powers have doubly exponentially many maximal algebra types, attaining the largest possible growth scaling for finite-dimensional channels. Consequently, new transmittable algebra types appear at arbitrarily large block-lengths for this channel, so its full transmission structure cannot be generated from any finite collection of bounded-block-length codes.

We present an analytical study of impurity-induced density correlations in interacting one-dimensional Luttinger liquids using the Unified Field Bosonization Technique (UFBT). Unlike conventional approaches that treat impurities perturbatively, UFBT incorporates localized impurities exactly at the free-fermion level while treating interactions non-perturbatively. Closed analytical expressions for fermionic Green functions and density-density correlation functions are obtained for strongly inhomogeneous systems, enabling a unified description of the impurity-induced $2k_F$ Friedel oscillations and the $4k_F$ Wigner-crystal like correlations. The corresponding scaling behaviour is derived analytically, revealing a crossover in the dominant long-distance correlations at $g=1/3$: Friedel correlations dominate for $g>1/3$, whereas Wigner-crystal like correlations become dominant for $g<1/3$, corresponding to the regime of sufficiently strong repulsive interactions. A reflection-coupled harmonic analysis is developed to account for the left-right mixing induced by impurity backscattering and to consistently reproduce the resulting density correlations. The spinless limit is also obtained as a direct reduction of the spinful formulation. These results provide an analytically controlled framework for describing impurity-induced and interaction-driven density correlations in strongly inhomogeneous one-dimensional quantum systems.

Production model uncertainties in long-lived particle searches can affect both the inclusive yield and the kinematic distributions sampled by the experimental acceptance. We isolate the latter effect by comparing the modified Weizsäcker–Williams description with the effective quasireal approximation for dark photon production via proton bremsstrahlung after normalizing both spectra on a common physical domain. At fixed production yield within this domain, the resulting acceptance difference directly measures the departure from rate factorization. In the NA62 beam dump geometry, the central calculation gives a fractional acceptance shift $\delta_{\rm NF}>0.3$ at every numerically converged grid point within the displayed NA62 sensitivity overlap. This conclusion persists for effective QRA off-shell scales of 1.0, 1.5, and 2.0~GeV and under the aperture variations considered. Separately, the public NA62 full selection acceptances give a nonconstant dimuon acceptance ratio between the Mixing and Bremsstrahlung production categories, ranging from approximately 0.58 to 4.23, with a median absolute departure from unity of approximately 0.79 over the analyzed HEPData grid. This provides complementary evidence that the published full selection acceptance depends on the production category. More generally, the projection criterion provides a quantitative test of rate factorization. The normalized production shape variation must have negligible projection onto the acceptance response at the required accuracy. When this condition is not satisfied, production model dependence must be propagated through the acceptance calculation or treated as an acceptance uncertainty.

We consider quantum devices restricted to local operations in 2D and subject to local stochastic noise below a constant threshold. We show that such circuits are computationally more powerful than AC0-circuits, i.e., noise-free, geometrically-unconstrained constant-depth classical circuits with unbounded fan-in AND, OR and NOT gates. To this end, we exhibit a computational problem with the following properties: (i) Any instance of the problem is correctly solved with high probability by a certain geometrically 2D-local quantum circuit even if the latter is imperfectly implemented, but (ii) any polynomial-size AC0-circuit fails to solve certain instances of the problem with constant probability. To our knowledge, this isthe first complexity-theoretic separation which applies to planar quantum devices, incorporates noise-resilience and is unconditional, i.e., does not rely on complexity-theoretic assumptions. This brings the experimental demonstration of an unconditional quantum advantage closer to experimental realities.

We review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degenerate case. We use this characterisation to show several novel examples of such structures, providing a complete classification for non-degenerate four-dimensional differential-geometric Poisson brackets under the additional assumption of the Lie algebra to be of quasi-Frobenius type. We also present a complete classification of quasi-Frobenius filiform N-graded Lie algebras, including two families in arbitrary dimensions.

The evolution of wireless communication standards toward higher frequencies and wider bandwidths places increasing demands on acoustic filter technologies. Conventional resonators face scaling limitations above 5 GHz, where lithographic constraints, reduced electromechanical coupling coefficient (k2eff), and spurious mode excitation hinder practical filter implementation. Here, we introduce a bilayer X-cut lithium niobate (LiNbO3) thickness-shear bulk acoustic resonator architecture that leverages symmetry engineering as a new design degree of freedom. By vertically stacking two piezoelectric thin films with a tailored bonding angle, the second-order thickness-shear mode (SH2, slow) is selectively excited. Furthermore, the fast thickness-shear modes inherent to X-cut LiNbO3 are suppressed, yielding a spurious-free in-band response. Devices operating around 6 GHz demonstrate a k2eff of approximately 35%, in close agreement with finite-element simulations and confirming the symmetry-driven mode selection mechanism. Proof-of-concept ladder filters demonstrate a fractional bandwidth of 18.6%, highlighting the wideband capabilities of the proposed architecture. The proposed configuration enables thickness-defined frequency scaling while maintaining high coupling and spectral purity, offering a promising platform for wideband radiofrequency filters in next-generation wireless systems.

Photospheric vector magnetic fields are foundational to modeling, understanding, and forecasting solar activity. These data are usually produced by inverting and disambiguating the full Stokes vector at multiple passbands, which is demanding. Here, we investigate how well we can estimate photospheric vector magnetograms from UV/EUV filtergrams. This problem is challenging and intrinsically ambiguous without polarization information, as the mapping from UV/EUV intensity to the magnetic field is indirect and ill-posed. We introduce MAGiDiff, a machine-learning-based method that uses denoising diffusion models to estimate vector magnetograms from UV/EUV filtergrams. As input, MAGiDiff takes a stack of filtergrams from the Solar Dynamics Observatory (SDO) / Atmospheric Imaging Assembly (AIA); as output, it is trained to estimate the disambiguated vector magnetogram as seen by Hinode / Solar Optical Telescope-Spectro-Polarimeter (SOT-SP). We show that MAGiDiff can accurately mimic the Hinode ground-truth. Additionally, we probe MAGiDiff's understanding of the physical structure and magnetic connectivity. On full-disk, we show that it produces plausible structures for active regions. MAGiDiff generalizes across solar cycles despite hemispheric polarity reversal, and can be fine-tuned to other EUV instruments including STEREO/EUVI and GOES-R/SUVI. While clearly not a substitute for a dedicated instrument, MAGiDiff opens the door to new capabilities.

Finite-bandwidth reservoir engineering can suppress unwanted transitions in a quantum thermal machine, but a physical filter also introduces a finite response time. We study this competition in a continuous three-level heat engine whose hot environment couples parasitically to the cold transition. The corresponding three-state rate network is solved exactly, showing that the parasitic transition produces a hot-to-cold thermodynamic short circuit and yielding a closed threshold for the loss of positive-power operation. We then retain a damped auxiliary mode explicitly as a physical spectral filter. Its Lorentzian response suppresses the detuned parasitic transition, whereas excessive narrowing limits the useful energy throughput. Independent local-GKSL and nonsecular Bloch–Redfield calculations both recover the no-leak Markovian engine in the weak-coupling limit and predict a finite maximum-power bandwidth, although its precise location is model dependent. A frequency-resolved Lorentzian-rate reduction, by contrast, has no interior optimum. The resulting design principle is that spectral selectivity can protect the useful thermodynamic cycle, but a real filter cannot be narrowed without a dynamical throughput cost.

Decoded Quantum Interferometry (DQI) reduces optimization problems with two-variable constraints to decoding cycle codes. For one such problem, namely MaxCut, prior work showed that DQI achieves a nontrivial satisfaction fraction guarantee only on linear-girth graphs, for which MaxCut is classically easy. However, these no-go results rely on minimum distance assumptions that do not represent true decodability thresholds for common noise channels, thus underestimating actual DQI performance. To estimate the true performance, we derive DQI satisfaction guarantees in the presence of imperfect decoding for fixed instances and generalize prior results for random instances. We then study homological cycle codes over arbitrary finite fields, and show that minimum-weight decoding is NP-hard for every field of size $q>2$, in contrast with known results for binary cycle codes. On the Linial–Simkin ensemble of regular graphs with logarithmic girth, we prove maximum-likelihood recovery bounds and a strong converse for a family of non-uniform additive noise channels. Moreover, LP decoders provide polynomial-time recovery of a positive fraction of randomly located errors with arbitrary values. These results allow us to prove upper and lower bounds on the approximate optima achievable by DQI when restricted to classical decoders. These bounds rule out quantum advantage in the regimes we analyze but also identify a family of regular Max-$k$-Cut instances on which DQI efficiently achieves a nontrivial satisfaction fraction guarantee.

The interconversion among different quantum resources has attracted considerable attention, exemplified by the tradeoff between coherence and entanglement. However, the relationship between local and global quantum resources remains largely unexplored. Here, we propose and experimentally demonstrate a local global tradeoff in quantum resources, quantified respectively by the local maximum coherence and the quantum mutual information. Our experiments show that the sum of the local maximum coherence and the quantum mutual information is bounded by a definitive upper limit. These results not only establish a fundamental tradeoff inequality, but also provide direct experimental evidence of the complementarity between local and global quantum resources. Moreover, our findings reveal an important constraint in quantum networks: the local quantum resources available at individual nodes and the global quantum resources of the network are mutually exclusive, implying that enhancing one necessarily limits the other.

Measures of non-stabilizerness (“magic”) of a quantum evolution quantify how hard it is to simulate on a classical computer. A natural question is how to extract information about magic from physical correlators, for example at finite temperature or in the ground state. In this paper we show how to measure magic using out-of-time-order correlators evaluated in an arbitrary state. For every full-rank state, and in particular for every Gibbs state, the resulting quantity vanishes if and only if the evolution is Clifford. We establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove that, even with a single fixed probe operator, it gives a lower bound on the number of $T$ gates needed to implement the dynamics in any circuit architecture.

Continuous measurements simultaneously reveal and modify the dynamics of a quantum system. In this work we consider the tunneling motion of particles between the sites of a one-dimensional lattice. We investigate how weak continuous probing of the occupation of a single lattice site induces entanglement and selects definite values for system properties such as wave function parity and permutation symmetry. Our simulations show how continuous measurement can steer systems of two and three particles, with no prior permutation symmetry, into stable bosonic, fermionic and parastatistical symmetry sectors.

We focus on the Becchi-Rouet-Stora-Tyutin (BRST) quantized version of the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory and (i) discuss its infinitesimal, continuous and off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations, and (ii) derive the corresponding Noether conserved (anti-)BRST and (anti-)co-BRST charges. We demonstrate that these charges are not invariant under the above nilpotent symmetry transformations. We systematically derive the modified versions of the above Noether charges which are found to be invariant under the above symmetry transformations. As a consequence, both types of the above charges anticommute with each-other which proves their linear independence. We also derive the (anti-)BRST and (anti-)co-BRST invariant Curci-Ferrari (CF) type restrictions from the algebraic structures of the Noether conserved charges. In all the above proofs and derivations, we take into account the deep mathematical relationship that exists between the infinitesimal and continuous symmetry transformations and their generators as the Noether conserved charges.

The goal of quantum metrology is to estimate an unknown parameter with better-than-classical precision and, ideally, to attain Heisenberg scaling. In realistic settings, however, noise can substantially reduce this advantage and, in many cases, restore standard-quantum-limit-like performance. Preserving the quantum enhancement therefore requires noise-robust strategies, which can be implemented using quantum error correction. In this work, we develop and analyze a quantum-metrology protocol based on Calderbank-Shor-Steane (CSS) codes. The main result is that, for noise perpendicular to the sensing Hamiltonian, discrete-time error correction preserves Heisenberg-like temporal scaling over a finite interrogation-time window whose duration depends on the correction frequency. It is further shown that recovery applied only after the sensing evolution provides no metrological advantage over the corresponding uncorrected noisy protocol in the setup considered here. An analytical framework is developed for arbitrary CSS codes and applied to the Steane and Shor codes, for which the discrete-time corrected dynamics, the Heisenberg-like-to-SQL-like crossover, and the optimal interrogation time are determined and numerically analysed.

We present a deep large-scale infrared survey of young stellar objects in the Rosette Nebula. Our analysis is based on stacked archival Spitzer/IRAC images. The images have been treated with the software DeNeb to remove nebulous emission. Our catalogue contains ~20000 sources with photometry in all 4 IRAC bands from 3.6 to 8.0 microns, complemented with near-infrared and optical data. From this database, we identify YSOs using multi-filter colour-colour criteria. We select 1528 YSOs, from which 1303 are Class II and 225 are Class I. Using this sample, we compile a list of clusters and groups of YSOs in the Rosette region, including previously known ones, plus three newly identified groups. Using our census of YSOs, in combination with the literature, we derive the Class I ratios and disk fractions for clusters in the nebula. The main clusters in the central cavity, NGC 2244 and NGC 2237 are almost devoid of Class I sources, indicating that star formation has ceased in this area. On the other hand, in an annulus around the centre with radii of 11-16 pc, roughly coinciding with the expanding HII front, about 30% of the YSOs are Class I, a clear sign of ongoing star formation. Other groups further out in the cloud also exhibit a high Class I ratio. Similar patterns are seen in the disk fractions. Our results are consistent with possible triggering by the expanding HII region, combined with star formation beyond the ionisation front.