Understanding equilibration times in closed quantum systems is essential for characterising their approach to equilibrium. Chaotic many-body systems are paradigmatic in this context: they are expected to thermalise according to the eigenstate thermalisation hypothesis and exhibit spectral properties well described by random matrix theory (RMT). While RMT successfully captures spectral correlations, its ability to provide quantitative predictions for equilibration timescales has remained largely unexplored. Here, we study equilibration within RMT using the framework of equilibration as dephasing, focusing on closed systems whose Hamiltonians are drawn from the Gaussian unitary ensemble (GUE). We derive an analytical expression that approximates the average equilibration time of the GUE and show that it is independent of both the initial state and the choice of observable, a consequence of the rotational invariance of the GUE. Numerical simulations confirm our analytical expression and demonstrate that our approximation is in close agreement with the true average equilibration time of the GUE. We find that the equilibration time decreases with system size and vanishes in the thermodynamic limit. This unphysical result indicates that the true equilibration timescale of realistic chaotic many-body systems must be dominated by physical features not captured by random matrix ensembles -- the GUE in particular.

Polarization provides additional diagnostic opportunities for probing the structured environments of massive stars as well as the illumination of those environments by stars that are not spherical. After a brief overview of polarization considerations relevant to hot massive stars, selected applications are presented. Examples related to dense Wolf-Rayet winds are chosen: clumpy wind flow, co-rotating interaction regions, and colliding wind interactions. Brief remarks are given about the prospects for opening a new window on massive star studies using UV spectropolarimetry with the {\em Polstar} mission concept.

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a broad family of channel divergences collapse to a closed-form, single-letter expression, regularization is unnecessary, and all error exponents (Stein/Chernoff/strong-converse) are explicitly computable with no adaptive advantage. Crucially, this yields the strong converse property for this channel family, which is an important open problem for general channels. When the inclusion fails, asymmetric exponents become infinite, implying perfect asymptotic discrimination. We apply the results to GNS-symmetric channels, showing discrimination rates for large number of self iterations converge exponentially fast to those of the corresponding idempotent peripheral projections. If the two channels do not share a common invariant state, we provide a single-letter converse bound on the regularized sandwiched Rényi cb-divergence, which suffices to establish a strong converse upper bound on the Stein exponents.

We present 72 additional galaxy-galaxy strong lenses that complement the sample discovered in the Euclid Quick Release 1 data (63.1 deg^2) of the Strong Lens Discovery Engine (SLDE) papers A-E. It is shown that previous pre-selection of potential lenses, which excluded objects from the Gaia catalogue, led to missing several bright and low-redshift strong lenses, adding more than 10% new strong lens candidates compared to the previous search. In total, the catalogue includes 38 "grade A" (confident) and 34 "grade B" (probable) candidates. These lenses are identified through a combination of two independent searches for bright nearby objects: one based on machine-learning models followed by expert visual inspection, and the other based solely on expert visual inspection, targeting objects not included in the initial machine-learning selection (a limitation identified only after extensive visual inspection). With these additional strong lens candidates, we augment the expected number of high-confidence candidates in the Euclid Wide Survey from previous forecasts to 120000. Detailed semi-automated lens modelling confirms at least 41 systems out of 72, a fraction consistent with that found in SLDE A (315 out of 488). These include: multiple edge-on disc lenses; sources with arcs near the lens centre; "red sources"; and an edge-on disk galaxy lensing a galaxy merger, producing two sets of lensed features, an Einstein ring and a doubly imaged component. The median redshift of these systems is $Δ$ z ~ 0.3 lower than that of the SLDE A sample.

In this work we investigate a class of random walks that interacts with its environment called Tree Builder Random Walk (TBRW). In our settings, at each step, the walker adds a random number of vertices to its position sampled according to a distribution $Q$. Previous works showed that the walker is ballistic with a well-defined speed, and that the TBRW admits a renewal structure, meaning that the process can be split into i.i.d epochs. We show that the first renewal time has exponential tail. Moreover, we show two consequences of the light tail of the first renewal time: an exponential upper bound for the empirical speed of the walker, and, for the case in which the walker adds only one vertex with probability $p$, we show that the limiting speed is an analytic function of the parameter $p$. In some of our proofs, we apply techniques from bond percolation, which consist of extending probabilities to the complex numbers and using the Weierstrass $M$-test.

In this paper, we extend the theory of parabolic implosion in complex dimension 2 to the case of holomorphic maps tangent to the identity at order 2. We investigate the bifurcation phenomena that occur when a fully parabolic fixed point is perturbed. Under the assumption of a non-degenerate characteristic direction with a formal invariant curve and director $α$ satisfying $\reα> 2$, we establish the existence of Lavaurs maps as limits of iterates $f_{ε_n}^n$ for specific sequences of the perturbation parameter $ε_n$. Finally, we apply these results to prove the discontinuity of the Julia sets $J_1$ and $J_2$ for holomorphic endomorphisms of $\mathbb{P}^2$, generalizing classical one-dimensional results to this higher-dimensional setting.

This paper provides the first systematic economic analysis of token pricing in the large language model (LLM) inference market. Assembling a novel dataset integrating OpenRouter API data (318 models), Epoch AI records (3,237 models), and 62 cross-validated milestone observations spanning 2020-2026, we document an approximately 600-fold decline in token prices and propose the "Tiered Super-Moore" hypothesis. Economy-tier models exhibit a price half-life of 1.10 years and mid-tier models 1.55 years -- both significantly faster than Moore's Law's two-year benchmark -- while flagship models display near-zero exponential fit (R^2 = 0.031) due to a reasoning premium averaging 31.5 times non-reasoning prices. A Chow structural break test identifies May 2024 as the critical market inflection point (F = 5.74, p = 0.005), marking a transition from technology-driven to competition-driven price acceleration. Cost decomposition reveals that total factor productivity residuals account for approximately 103.7% of cost reduction, with GPU hardware contributing only -0.9%, confirming that software and architectural innovation -- not hardware advances -- drive the decline. Data Envelopment Analysis shows a Malmquist Productivity Index peaking at 4.11 during 2024Q1-Q4, with technological frontier shift (TC = 4.13) as the dominant driver. Training cost-inference pricing elasticity is 0.432, and the 63-fold training cost gap between U.S. and Chinese firms is statistically attributable to architectural innovation ($/FLOP difference insignificant, p = 0.228) rather than factor price differentials. Market concentration declined sharply, with HHI falling from 4,558 to 2,086 over three years. These findings establish token economics as a distinct subfield of digital goods pricing and carry implications for competition policy, AI accessibility, and international technology governance.

Kemeny Consensus is a well-known rank aggregation method in social choice theory. In this method, given a set of rankings, the goal is to find a ranking $Π$ that minimizes the total Kendall tau distance to the input rankings. Computing a Kemeny consensus is NP-hard, and even verifying whether a given ranking is a Kemeny consensus is coNP-complete. Fitzsimmons and Hemaspaandra [IJCAI 2021] established the computational intractability of achieving a desired consensus through manipulative actions. Kemeny Consensus is an optimisation problem related to Kemeny's rule. In this paper, we consider a decision problem related to Kemeny's rule, known as Kemeny Score, in which the goal is to decide whether there exists a ranking $Π$ whose total Kendall tau distance from the given rankings is at most $k$. Computation of Kemeny score is known to be NP-complete. In this paper, we investigate the impact of several manipulation actions on the Kemeny Score problem, in which given a set of rankings, an integer $k$, and a ranking $X$, the question is to decide whether it is possible to manipulate the given rankings so that the total Kendall tau distance of $X$ from the manipulated rankings is at most $k$. We show that this problem can be solved in polynomial time for various manipulation actions. Interestingly, these same manipulation actions are known to be computationally hard for Kemeny consensus.

In this paper, we extend the enumerative study of planar hypermaps with an alternating boundary introduced in an earlier work of Bouttier and the second author. In that article, an explicit rational parametrization was obtained for the associated generating function in the case of m-constellations, using a variant of the kernel method. We develop here a new strategy to obtain an algebraic equation in the general case, which includes maps decorated by the Ising model, through a classical many-to-one correspondence. One of the main steps of our strategy is the simultaneous elimination of two catalytic variables. We then apply this strategy to the case of Ising quadrangulations, where we obtain an explicit rational parametrization. As a consequence, we show that some notable properties of the constellations case are no longer satisfied in general.

The spectral evolution characteristics of the prompt emission in gamma-ray bursts (GRBs) have been extensively studied, but detailed investigations of spectral evolution in a GRB flare remain lacking. In this work, we present the first analysis of spectral parameter evolution in a GRB flare through high time-resolved spectral fitting of the Brightest Flare in GRB 221009A. We find that the $α$-Flux, $E_p$-Flux, and $E_p$-$α$ relationships during both the overall phase and the rise phase of flare can be well described by simple power-law model, showing positive correlations. Therefore, we conclude that Brightest Flare exhibits "Double-tracking" behavior. Since values of $α$ do not exceed the synchrotron "death line" (-2/3), we explain this phenomenon using a magnetic dissipation synchrotron radiation model. In the decay phase of flare, the $E_p$-Flux and $E_p$-$α$ correlations become notably flatter, with their power-law indices decreasing significantly compared to those in the rise phase. This may be due to the fact that the next flare begins to erupt before the Brightest Flare has completely ended, resulting in the combined effects of both two flares. Our study of spectral parameter relations of the Brightest Flare provides new insights into the radiation mechanisms of both GRB prompt emission and flares.

We study the evolution of symmetry-resolved entanglement entropy in bulk-driven Floquet conformal field theories (CFTs). Focusing on the two-dimensional free compact boson CFT, we analyze how symmetry-resolved Rényi entropies approach or depart from equipartition among charge sectors. We show that the existence of an $\mathfrak{sl}^{(k)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra introduces a free parameter, the label $k$, which allows us to control the breakdown of equipartition. We argue that this effect originates from an explicit coupling between low- and high-frequency modes. Based on a general oscillator representation of the Virasoro algebra, we expect this mechanism to persist beyond the free boson CFT. Finally, we discuss how the real-time dynamics of fine-grained symmetry-resolved entropies of a boundary state are modified under non-unitary evolution, which can be associated with post-selected weak measurements.

Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field approximations that neglect temporal changes in group composition. Here, we show that group dynamics is not a secondary effect but a central aspect that determines the macroscopic transition class of higher-order contagion processes. We develop an analytically tractable approximate master equation model that effectively interpolates between quenched and mean-field limits through a group composition turnover rate. Our results reveal the rich impact of time-varying structures: it can induce discontinuous phase transition, broaden the bistable region, and at the same time promote or suppress contagion near criticality. Moreover, when real-world turnover rates and group-size heterogeneity are taken into account, the system exhibits a qualitatively richer phase diagram with four distinct dynamical phases, combining continuous or discontinuous transitions with localized or delocalized activity. In localized regimes, we uncover multistable active phases with multiple coexisting active states, which are observed in neither the annealed nor the quenched limits, and extend classical absorbing-active bistability. Finally, we demonstrate that the emergence of discontinuous transitions in real-world systems requires stronger nonlinear reinforcement than previously thought, indicating that simulations in static structures can yield qualitatively misleading predictions.

We prove the asymptotic mixed normality of the least absolute deviation (LAD) estimator for a locally $α$-stable stochastic differential equation (SDE) observed at high frequency, where $α\in(0,2)$. We investigate both ergodic and non-ergodic cases, where the terminal sampling time diverges or is fixed, respectively, under different sets of assumptions. The objective function for the LAD estimator is expressed in a fully explicit form without necessitating numerical integration, offering a significant computational advantage over the existing non-Gaussian stable quasi-likelihood approach.

We study the multichannel quickest change detection problem with bandit feedback and controlled sensing, in which an agent sequentially selects one of the data streams to observe at each time-step and aims to detect an unknown change as quickly as possible while controlling false alarms. Assuming known pre- and post-change distributions and allowing an arbitrary subset of streams to be affected by the change, we propose two novel and computationally efficient detection procedures inspired by the Upper Confidence Bound (UCB) multi-armed bandit algorithm. Our methods adaptively concentrate sensing on the most informative streams while preserving false-alarm guarantees. We show that both procedures achieve first-order asymptotic optimality in detection delay under standard false-alarm constraints. We also extend the UCB-driven controlled sensing approach to the setting where the pre- and post-change distributions are unknown, except for a mean-shift in at least one of the channels at the change-point. This setting is particularly relevant to the problem of learning in piecewise stationary environments. Finally, extensive simulations on synthetic benchmarks show that our methods consistently outperform existing state-of-the-art approaches while offering substantial computational savings.

Distributed energy systems with prosumers require new methods for coordinating energy exchange among agents. Coalitional control provides a framework in which agents form groups to cooperatively reduce costs; however, existing bottom-up coalition-formation methods typically require full information sharing, raising privacy concerns and imposing significant computational overhead. In this work, we propose a limited information coalition-formation algorithm that requires only limited aggregate information exchange among agents. By constructing an upper bound on the value of candidate coalitions, we eliminate the need to solve optimisation problems for each potential merge, significantly reducing computational complexity while limiting information exchange. We prove that the proposed method guarantees cost no greater than that of decentralised operation. Coalition strategies are optimised using a distributed approach based on the Alternating Direction Method of Multipliers (ADMM), further limiting information sharing within coalitions. We embed the framework within a model predictive control scheme and evaluate it on real-world data, demonstrating improved economic performance over decentralised control with substantially lower computational cost than full-information approaches.

This paper investigates energy efficiency (EE) optimization for an uplink multiuser system assisted by a movable-element reconfigurable intelligent surface (ME-RIS) and a base station equipped with movable antennas (MA-BS). We jointly optimize the uplink postcoder vectors, user transmit powers, RIS phase shift, and the positions of both the BS antennas and RIS elements to maximize the system EE. The resulting non-convex fractional problem is solved using an alternating optimization (AO) framework, where subproblems are handled via Dinkelbach's method combined with successive convex approximation (SCA). Simulation results show that the proposed scheme achieves significant EE gains over fixed-antenna BS and fixed-element RIS benchmarks.

Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian nonparametric framework for spatio-temporal Hawkes processes using additive Gaussian processes for the prior distributions on the background rate and the triggering kernel. This additive structure enhances interpretability by decoupling temporal and spatial effects while maintaining high modelling flexibility across the entire spatio-temporal domain. To address scalability, we develop a sparse variational inference scheme based on the Gaussian variational family. Synthetic experiments demonstrate that the proposed method accurately recovers background and triggering structures, achieving superior performance compared to existing alternatives. When applied to real-world datasets, it achieves higher held-out log-likelihoods and reveals interpretable spatio-temporal structures of the self-excitation mechanism. Overall, the framework provides a flexible, scalable, interpretable, and uncertainty-aware approach for modelling complex excitation patterns in spatio-temporal event data.

We present a theory of polarized photoluminescence of triplet excitons in semiconductor nanocrystal ensembles with the random fine structure contributed by the electron-hole exchange and carrier-nuclear hyperfine interactions. The interaction parameters are assumed to be normally and isotropically distributed. In particular, the exchange interaction is described by the Gaussian orthogonal ensemble of random matrices. The intensity of luminescence as well as the optical orientation and alignment are calculated as functions of the fine structure splitting parameters and the exciton lifetime. We have also analyzed the suppression of optical alignment and enhancement of optical orientation in an external longitudinal magnetic field.

We present the development of a digital twin-based reconstruction framework for dielectric laser acceleration (DLA) based on machine-learning-assisted inversion of single-shot electron energy spectra. DLA as a promising candidate for compact electron accelerator designs using optical nearfields in dielectric nanostructures lacks on direct diagnostics on the laser-electron interaction. Thus, the outgoing electron energy distribution is one of the few experimentally accessible observables. To exploit this information, DLA interaction and mapping on the downstream spectrometer are treated as nonlinear measurement device whose response is described by the symplectic sixdimensional tracking code DLAtrack6D. This forward simulation model serves as a digital twin mapping laser-electron interaction parameters onto resulting energy spectra. For diagnostics, we are interested in the inverse mapping represented by a neural network trained by synthetic datasets generated with the forward simulation model. The reconstruction performance and parameter identifiability of the inverse model are evaluated for parameter ranges relevant to planned experiments at the ARES linac in the SINBAD facility at DESY. Simulation studies demonstrate that the method can recover pulse front tilt angles with an accuracy of about 1 deg and phase offsets with an RMSE of about 0.36 rad corresponding to a difference of 0.4 fs in arrival time. Training with noisy spectra further improves robustness against spectrometer noise. The trained surrogate model evaluates in the millisecond range, enabling shot-to-shot parameter estimation compatible with the 50 Hz repetition rate of ARES. The approach effectively transforms the DLA interaction region into a virtual in situ diagnostics for otherwise inaccessible laser parameters during experiment and provides a foundation for real-time monitoring and control of future DLA experiments.

An algebraic soliton of the massive Thirring model (MTM) is expressed by the simplest rational solution of the MTM with the spatial decay of $\mathcal{O}(x^{-1})$. The corresponding potential is related to a simple embedded eigenvalue in the Kaup--Newell spectral problem. This work focuses on the hierarchy of rational solutions of the MTM, in which the $N$-th member of the hierarchy describes a nonlinear superposition of $N$ algebraic solitons with identical masses and corresponds to an embedded eigenvalue of algebraic multiplicity $N$. We show that the hierarchy of rational solutions can be constructed by using the double-Wronskian determinants. The novelty of this work is a rigorous proof that each solution is defined by a polynomial of degree $N^2$ with $2N$ arbitrary parameters, which admits $\frac{N (N-1)}{2}$ poles in the upper half-plane and $\frac{N(N+1)}{2}$ poles in the lower half-plane. Assuming that the leading-order polynomials have exactly $N$ real roots, we show that the $N$-th member of the hierarchy describes the slow scattering of $N$ algebraic solitons on the time scale $\mathcal{O}(\sqrt{t})$.

Positive geometry provides a geometric framework where physical observables are encoded as canonical forms associated to regions of kinematic space. In this paper we consider a generalisation to an infinite union of line segments, which allows us to capture canonical forms beyond rational functions. In the continuum limit of positive geometries, we show that we can generalise even further and describe positive geometries whose canonical forms contain branch cuts. We will constrain which functions can be obtained as the canonical form of one-dimensional positive geometries. We introduce the notion of the pseudogenus to classify meromorphic functions, and show that canonical forms can be written as the $\mathrm d\log$ of a function with pseudogenus zero. Furthermore, we argue that the spectrum encoded by a union of line segments is consistent with the presence of a stringy tower of states or a Kaluza-Klein tower with three or more compact directions only if nearly all such states do not contribute to the scattering amplitude. In addition, we show how the d log of both open and closed string amplitudes admits a positive geometry. This allows us to give a fully geometric interpretation for the KLT double copy at four points.

Medical device regulators in the United States(FDA), China (NMPA), and Europe (EU MDR) all use the language of risk, but classify devices through structurally different mechanisms. Whether these apparently shared concepts carry transferable classificatory signal across jurisdictions remains unclear. We test this by reframing explainable AI as an empirical probe of cross-jurisdictional regulatory overlap. Using 141,942 device records, we derive seven EU MDR risk factors, including implantability, invasiveness, and duration of use, and evaluate their contribution across a three-by-three transfer matrix. Under a symmetric extraction pipeline designed to remove jurisdiction-specific advantages, factor contribution is negligible in all jurisdictions, indicating that clean cross-jurisdictional signal is at most marginal. Under jurisdiction specific pipelines, a modest gain appears only in the EU MDR-to-NMPA direction, but sensitivity analyses show that this effect is weak, context-dependent, and partly confounded by extraction and representation choices. Reverse direction probes show strong asymmetry: FDA-derived factors do not transfer meaningfully in any direction, and NMPA-derived factors do not carry signal back to EU MDR. Zero-shot transfer further fails on EU MDR Class I, consistent with a mismatch between residual and positional class definitions. Overall, cross-jurisdictional transfer is sparse, asymmetric, and weak. Shared regulatory vocabulary does not, under this operationalisation, translate into strong portable classification logic. The findings challenge a common assumption in cross-jurisdictional regulatory AI and show how explainable AI can be used to measure, rather than assume, regulatory overlap.

This paper investigates the shadowing properties in semi-hyperbolic systems. We introduce three classes of shadowing properties defined on families of manifolds, and prove that a semi-hyperbolic family possesses the $L^p$ bi-shadowing property, the limit bi-shadowing property, and the asymptotic bi-shadowing property under certain conditions. The proof strategy is to transform the shadowing problem into a fixed-point problem, and then apply the Brouwer fixed-point theorem to complete the verification.

Between 1933 and 1937, the treatment of relativistic spin-1/2 particles, initially rooted in Hole theory, evolved into the modern framework of quantum field theory. This paper reconstructs the crucial stages of that transition by examining the formal and physical progress of the numerous authors who shaped the field's modern formalism. This historical study traces the development of fermionic field theory in full, beginning with the foundational work of the 1920s, focussing on the results of the 1930s, and concluding with the influential synthesis of Wolfgang Pauli in 1941, the content of which has shaped the subsequent tradition. Within this framework, particular emphasis is given to Ettore Majorana's 1937 quantisation procedure and argument for anti-commuting fermionic quantum fields. This study demonstrates that Majorana's work was not merely a technical variant, but the definitive rejection of the concept of negative energy solutions, whose conceptual clarity and educational value remain vital today.

In an article published in 1993, P. Colmez formulated a remarkable conjecture, which asserts that the Faltings height of a CM abelian variety can be computed as a linear combination of logarithmic derivatives of Artin $L$-functions. Noting that the Faltings height is an average of transcendental quantities summed over the embeddings of a number field of definition of the abelian variety, we propose a refinement of this conjecture, which identifies each of these transcendental quantities. We also show how our conjecture would imply the existence of fine reciprocity laws for Siegel modular forms with rational coefficients evaluated at CM points, and we prove our conjecture for elliptic curves, using old results of Siegel and Hasse on elliptic units.

We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $Γ$ is an irreducible uniform lattice in a non-compact connected semisimple Lie group of real rank at least $2$, then for any finite-dimensional representation $π:Γ\to \operatorname{O}_N$, every $π$-quasimorphism (that is, a map with bounded defect with respect to $π$) is bounded.

We consider families of solitary waves in the Korteweg--de Vries (KdV) equation coupled with the linear Schrödinger (LS) equation. This model has been used to describe interactions between long and short waves. To characterize families of solitary waves, we consider a sequence of local (pitchfork) bifurcations of the uncoupled KdV solitons. The first member of the sequence is the KdV soliton coupled with the ground state of the LS equation, which is proven to be the constrained minimizer of energy for fixed mass and momentum. The other members of the sequence are the KdV solitons coupled with the excited states of the LS equation. We connect the first two bifurcations with the exact solutions of the KdV--LS system frequently used in the literature.

Hybrid superconductor-semiconductor systems with large spin-orbit coupling are important platforms for realizing topological or triplet superconductivity. Planar Josephson junctions made using these materials are predicted to enter the topological state by tuning the phase difference between the two superconductors from 0 to $π$. The 0-$π$ transition can be driven by magnetic field through Zeeman splitting of subbands in the semiconductor. It is expected to manifest as a node, or a re-entrance, in the critical current. Here we present re-entrant switching currents from several InAs/Al planar Josephson junctions in high in-plane magnetic fields. We find that re-entrances in some devices conform with expected signatures for topological or 0-$π$ transitions. However, we show that the data can also be explained in terms of mode interference in the junction in the presence of disorder. We also present simulations of supercurrent interference under in-plane fields that can reproduce re-entrances due to corrugated weak link without invoking the Zeeman effect or topology.

6G In-body Subnetworks (IBSs) represent a key enabler for supporting standalone eXtended Reality (XR) applications. IBSs are expected to operate as an underlay to existing cellular networks, giving rise to coexistence challenges when sharing radio resources with other cellular users, such as enhanced Mobile Broadband (eMBB) users. Such resource allocation problem is highly dynamic and inherently non-convex due to heterogeneous service demands and fluctuating channel conditions. In this paper, we propose an intelligent radio resource slicing strategy based on the Soft Actor-Critic (SAC) deep reinforcement learning algorithm. The proposed SAC-based slicing method addresses the coexistence challenge between IBSs and eMBB users by optimizing a refined reward function that explicitly incorporates XR cross-modal delay alignment to ensure immersive experience while preserving eMBB service guarantees. Extensive system-level simulations are performed under realistic network conditions and the results demonstrate that the proposed method can enhance user experience by 12-85% under different network densities compared to baseline methods while maintaining the target data rate for eMBB users.

We introduce Exchange Quantum Polynomial Time (XQP) circuits, which comprise quantum computation using only computational basis SPAM and the isotropic Heisenberg exchange interaction. Structurally, this sub-universal model captures decoherence-free subspace computation without access to singlet states. We show that XQP occupies an intermediate position between BPP and BQP, as its efficient multiplicative-error simulation would collapse the polynomial hierarchy to its third level. We further provide evidence that additive-error simulation of XQP would enable efficient additive-error simulation of arbitrary BQP computations. Remarkably, the restricted family of XQP circuits consisting solely of $\sqrt{\mathrm{SWAP}}$ gates remains hard to simulate to multiplicative error. We additionally prove that circuits generated by $\sqrt{\mathrm{SWAP}}$ gates are semi-universal, generate $t$-designs for the uniform distribution over $SU(2)$-invariant unitaries, and maximise the entangling power within XQP. Finally, we derive structural results linking computational basis states in XQP to the Gelfand-Tsetlin basis of the symmetric group, and expressing XQP output probabilities as partition functions of the six-vertex and Potts models. Our findings indicate that XQP circuits are naturally suited to near-term hardware and provide a promising platform for experimental demonstrations of quantum computational advantage.