Papers

Quantum Machine Learning is a novel field of research aimed at devising machine learning approaches exploiting principles of quantum mechanics, such as superposition, entanglement and interference. In this context, we present a scalable hybrid Quantum Diffusion Model, and evaluate its use for medical image analysis. Specifically, our method is based on a Discrete-Time Quantum Walk algorithm, executed on a real quantum device, to model the forward dynamics of the diffusion model. For the backward step of the diffusion model, we devise and evaluate a classical learning model, which is used to reversely denoise the data. In contrast with other existing attempts at applying quantum machine learning for image analysis tasks, severely limited by the size of existing quantum devices, our method allows to process real-world large size medical data. In particular, we present results on grayscale and RGB images, as well as 3D volumes of moderate sizes. We benchmark our results by reproducing an alternative classical counterpart model, based on diffusion models on discrete state spaces. By doing so, we compare the generation capabilities of both models in terms of three distinct state-of-the-art metrics in the field of image generation, showing the competitive, promising results of our approach.

We present microwave characterization measurements of Josephson junction arrays (JJAs) based on epitaxial Al-InAs quantum well heterostructure. The Josephson inductance of the constituent planar junctions can be derived by probing the low-energy plasmon modes of these devices. Applying an out-of-plane magnetic field gives rise to a Fraunhofer-like diffraction pattern, from which the current-phase relation and the effective transparency can be extracted. JJAs can be used to achieve high inductances, suitable for the implementation of quantum circuits. They also provide an excellent test-bed for studying the microscopic excitations of hybrid superconductor-semiconductor devices associated with the presence of Andreev states. Here, we demonstrate their tunability over a broad range of out-of-plane magnetic fields.

We demonstrate optical levitation and feedback cooling of a silica nanoparticle (radius = 78~nm) trapped within a radial vector beam (RVB) in high vacuum. Radial vector beams, when focused by a high-NA lens, produce a smaller focal spot than conventional Gaussian beams, yielding tighter optical potentials and potentially reduced photon-recoil heating rates. A vortex wave plate was used to generate the RVB using an aspheric lens (NA = 0.77) to form the trap. Cold-damping feedback was used to cool the center of mass motion in the radial and axial trap directions to temperatures in the mK range. At higher temperatures and pressures, additional trap frequencies arising from the nonlinear RVB optical potential are observed. This demonstration is a step toward exploiting structured light for levitated quantum optomechanics where these traps can be used to suppress bulk and motional heating.

In atom-cavity systems, mean field theory is widely used, in which the quantum cavity operator is replaced by a classical amplitude. Then the problem is converted into atoms moving in a self-consistent potential. The mean field treatment captures the physics of cavity mediated interactions, and predicts the self-organized superradiant phase. In this work, however, we show that it fails for certain atom-cavity coupling: it predicts zero ground state atomic current where the fully quantum calculation exhibits a finite one. We find that the origin of this failure is the non-zero Berry curvature in the synthetic dimension spanned by the photon Fock ladder and real space. In this synthetic picture, the atomic current can be understood as Hall response of cavity detuning, whereas mean field collapses this dimension and discards the atom–photon correlations required for its Hall response. The same beyond-mean-field geometry predicts Laughlin-like photon generation under adiabatic flux insertion. Our work identifies synthetic Berry curvature as a concrete mechanism for the breakdown of static mean field in atom–cavity physics.

Training quantum neural networks (QNNs) on near-term hardware remains hampered by two compounding difficulties: the exponential vanishing of gradient variance known as the barren plateau, and the $\mathcal{O}(L \cdot 2^n)$ time and memory cost of differentiating through an $n$-qubit, $L$-layer circuit. We propose RLQ-Grad, a reinforcement-learning-based optimizer in which a classical policy $\pi_\phi$ (a spectrally-normalized PPO agent) learns to propose parameter updates directly, conditioned on the QNN's current parameters, loss, accuracy, and previous update. Because the surrogate gradient is emitted by a classical network rather than obtained by differentiating through the unitary $U(\theta)$, its variance is not constrained by the barren plateau concentration bound, and its cost scales with the number of trainable parameters rather than the Hilbert-space dimension. We prove these properties formally and verify them on a hardware-efficient ansatz across four supervised benchmarks with up to $n=20$ qubits. RLQ-Grad preserves a near-flat gradient-variance curve where backpropagation, parameter-shift, and adjoint differentiation decay by 1 to 2 orders of magnitude. Accounting for the full training pipeline (PPO rollouts, actor-critic updates, and optimizer states), RLQ-Grad needs under 2 MB of memory and runs $2490\times$, $7876\times$, and $673\times$ faster per iteration than these three methods at $n=20$. It improves top-1 accuracy by up to $+10\%$ over gradient-based baselines on circuits of up to 12 qubits, and matches dedicated barren plateau mitigation methods on CIFAR-10 at 14 to 20 qubits, where evolutionary and gradient-free optimizers collapse to chance.

In 1975, Polyakov invented a renormalization group algorithm for treating the problem of a classical isotropic planar Heisenberg ferromagnet. Here we define a tool - "parallel transport of frames" - that extends Polyakov's original renormalization group method to local magnetic anisotropies and, most significantly, the non-local dipolar interaction. We apply this tool to the problem of the spin reorientation transition in an ultrathin ferromagnetic slab with finite thickness. We find that integrating out the short wavelength spin wave fluctuations generates two local anisotropies that are absent from the microscopic dipolar energy Hamiltonian. Taking them into account yields the correct topology of the spin reorientation transition line, as observed experimentally and in numerical simulations.

Kagome materials have emerged as a major platform for correlated and topological quantum matter, hosting flat bands, Dirac dispersions and van Hove singularities rooted in frustrated lattice geometry. While their essential physics is epitomized by the canonical single-orbital kagome model, real kagome materials are intrinsically multi-orbital and typically chemically and structurally complex, with additional three-dimensional coupling making kagome geometry and orbital degrees of freedom difficult to disentangle. Here we realize a truly two-dimensional, elemental two-orbital kagome system in monolayer Sb on SiC(0001). Substrate-induced orbital filtering isolates the in-plane Sb p_x/p_y orbitals into a six-band kagome manifold, establishing a chemically simple, minimal platform for multi-orbital kagome physics. We demonstrate two consequences that distinguish this system from the canonical single-orbital model. First, chemically enforced half filling pins the Fermi level to a closed nodal line, whose finite density of states drives a unit-cell-conserving breathing instability and opens a giant insulating gap. Second, we uncover orbital-resolved atomic obstruction: individual orbital-derived manifolds realize obstructed atomic limits, whereas their combined half-filled valence manifold is non-obstructed. Our results establish kagome antimonene as a benchmark system for exploring orbital-driven electronic, structural and topological kagome physics in the genuine two-dimensional limit.

Motile active matter systems, from animal groups to synthetic particles, exhibit spontaneous self-organized transitions between disordered and ordered collective states. These transitions are driven by continuous energy injection, yet how energy consumption and dissipation change during these transitions remains poorly understood due to the challenge of measuring individual energetic fluxes. Here, we introduce a minimal experimental system of synthetic motile spheres that enables the first time-resolved power-budget characterization of collective motion. We show that the transition to an ordered state is accompanied by increased locomotion efficiency and a reorganization of dissipation pathways, shifting dissipation from internal friction to external slip with the environment. Leveraging this energetic reorganization, we construct an active engine powered by collective motion, capable of performing mechanical work against an external load. These findings establish energetic fluxes as quantitative observables for understanding collective state transitions and demonstrate how collective order can be harnessed for work extraction in active matter.

The flat limit of AdS$_4$ spacetime corresponds, at the level of the symmetry algebra, to the Inönü–Wigner contraction $\mathfrak{so}(2,3) \to \mathfrak{iso}(1,3)$. We describe the emergence of the Hilbert space of massive scattering states of arbitrary integer spin $s$ from unitary lowest-weight representations $\mathcal{D}(\Delta,s)$ of the conformal group, using a basis of `pseudo-momentum' states first introduced by Fronsdal. These states nicely reduce to Wigner's momentum eigenstates in the limit of infinite AdS curvature radius $\ell \to \infty$, at fixed $m=\Delta/\ell$. A simple conformal map relates this description to conformal fields in $\mathbb{R}^3$ familiar from radial quantization, with the interior and exterior of the unit ball respectively corresponding to outgoing and ingoing momenta. Under the contraction, and upon appropriate rescaling, the inner product on $\mathcal{D}(\Delta,s)$ converges to the standard Lorentz-invariant inner product of Wigner's massive particles, so that unitarity is preserved throughout. The contraction to massless particles is briefly discussed here, and will be treated in detail in a forthcoming paper.

Periodically time-dependent quantum systems have Floquet solutions. They consist of a phase factor and a Floquet mode which shares the periodicity of the driving. Consequently, any such solution possesses a non adiabatic geometric phase known as the Aharonov-Anandan (AA) phase. It is gauge-invariant and, therefore, is experimentally accessible. We propose a protocol for the measurement of AA phases based on the adiabatic change of the phase of the non-adiabatic driving. We argue that the experimental requirements of the protocol are those of previous measurements of adiabatic phases.

Adaptive optics (AO) is central to high-resolution microscopy, yet conventional implementations often require repeated correction-and-measurement cycles whose number increases with aberration complexity. This measurement burden can become prohibitive when the available temporal window for correction is short or when photon budgets are constrained. Here, we demonstrate an AO strategy that exploits the spatial correlations of entangled photon pairs to retrieve aberrations directly. By using the second-order correlation function as an aberration-sensitive metric, the required correction can be determined with only a few measurements, without relying on image-based feedback or iterative optimization. This correlation-based approach establishes an efficient framework for AO leveraging quantum light, offering a new route toward quantum-enhanced microscopy in regimes where conventional correction strategies become challenging.

Measurements with undetected photons infer properties of a probe beam that is never detected, transferring mid-infrared information onto silicon-friendly wavelengths. Tomography in this paradigm has so far relied on switched settings or scanned phases, referenced across a drift-sensitive campaign; no protocol reads all Jones parameters from one frame. We show that a folded nonlinear interferometer with a diagonally pumped crossed-crystal source performs coherent process tomography of the undetected beam in a single spectrometer frame: it reconstructs all seven parameters of the beam's round-trip Jones matrix, the coherent part of the channel. Birefringent group-delay walk-off, normally a calibration nuisance, acts as a frequency multiplexer: each Jones-matrix element is assigned its own carrier, a spectral fringe period paired with a detector port. Because the multiplexing exploits the down-conversion bandwidth rather than merely tolerating it, a single Fourier transform per detector trace returns all four moduli and all three relative phases across that bandwidth, i.e., the full round-trip Jones spectrum up to a global phase, with no scan or setting change (after a one-time reference frame). Simultaneity makes every relative phase immune to common-mode drift, and a dark carrier, a self-interference term that unitarity forces to vanish, provides a built-in null test. For realistic parameters of a periodically poled KTP source the scheme yields wavelength-resolved mid-infrared polarimetry across 3.5-4.2 microns (~80 spectral points per Jones element) on a silicon camera, extending to depth-resolved Jones matrices, i.e., polarization-sensitive optical coherence tomography with undetected photons. A Fisher-information analysis, the first we are aware of in undetected-photon tomography, sets the precision budget and compares delay multiplexing to sequential protocols at equal photon number.

Routing and search respond in opposite ways to rapid network expansion. Short graph distances make a known destination easy to reach, while the neighborhood accessible within a few hops can be vastly larger than any finite inspection budget. We show that this tension imposes an algorithm-independent constraint on sparse search. If $m_q$ relevant nodes are placed without structural information among $N$ nodes and at most $M$ nodes can be inspected, any target-blind exploration protocol has success probability at most $Mm_q/N$, irrespective of correlations between successive inspections, of revisits, and of any structural preference the exploration rule may have. Geometry determines when this constraint becomes relevant: a target becomes accessible with order-one probability when the graph-distance ball volume satisfies $V(R_c)\sim N/m_q$. At this scale, any inspection mechanism achieving a fixed success probability $\delta>0$ must enrich the probability of inspecting relevant nodes by at least order $N/(Mm_q)$ relative to the neutral target density. For uniformly searched candidate sets, this entails a vanishing visible fraction of the accessible region. Thus rapidly expanding networks can make rare targets geometrically close while target-blind search remains ineffective. Numerical results on Krioukov hyperbolic random graphs and two-dimensional lattices show that this separation can arise within only a few hops in the rapidly expanding case, while the lattice accessibility radius grows algebraically.

Data-driven turbulence models for the Reynolds-averaged Navier-Stokes (RANS) equations offer a promising route to improving predictions of complex flows. Such models, specifically the turbulence constitutive relations, can be learned efficiently from high-fidelity Reynolds-stress data without evaluating the RANS equations during training. However, conventional losses weight all tensor-component and spatial errors equally, although their influence on a quantity of interest (QoI) can differ significantly; reducing the aggregate stress error therefore does not necessarily lead to an improved QoI prediction. Training against flow-level observations accounts for this dependence but requires repeated, potentially expensive RANS solutions. In canonical shear flows, physical reasoning can identify the shear component as the only one relevant for the mean-flow prediction. Motivated by this example, we propose a goal-oriented method to select and weight Reynolds-stress training data for complex flows. For a specified QoI, a single offline adjoint evaluation quantifies its sensitivity to local perturbations of each Reynolds-stress component. These sensitivities are converted into fixed weights in the supervised loss, enabling training without further RANS solutions. We validate the weighting in square-duct and periodic-hill flows, then apply it to a film-cooling jet in crossflow, where it improves velocity and cooling-effectiveness predictions over uniformly weighted training despite using a velocity-only QoI. Beyond turbulence modelling, this work suggests a broader strategy for aligning supervised learning with downstream prediction goals while preserving training efficiency.

Quantum reservoir computers (QRCs) retain information from earlier inputs, whereas reset-window quantum extreme learning machines (QELMs) start afresh and receive only a recent input window. We establish when this window can replace the reservoir's memory. Under our stated assumptions and with exact expectation values, sufficiently expressive QELMs can reproduce reservoir outputs arbitrarily accurately as their windows grow precisely when the influence of the omitted past becomes uniformly negligible. However, longer windows do not always solve the problem. We construct a simple two-qubit reservoir that performs temporal recall exactly, while every fixed-window predictor faces the same positive worst-case error over unbounded delays, regardless of model capacity. Analytical benchmarks and simulations distinguish missing history from limited features and finite measurements. The central conclusion is simple: better representations can improve how available information is used, but cannot recover a past the model never receives.

We investigate Bayesian inference of non-Maxwellian electron distribution functions from collective Thomson scattering (CTS) spectra. We represent distribution functions using multiple candidate models of different complexity and perform inference on synthetic spectra generated from known non-Maxwellian distribution functions. Our analysis demonstrates that a sufficiently flexible model can approximate the overall shape of the ground-truth distribution function. The most plausible model is identified based on model evidence, a statistical measure representing the probability to obtain the observed data given the model. When the candidates include the ground-truth model, the model evidence favors the ground-truth model. Without the ground-truth model as a candidate, the model evidence favors the candidate model with the fewest parameters that adequately approximates the data. The posterior probability density function of the most plausible model reveals the characteristic features and associated uncertainties of the underlying distribution function. The origin of the additional spectral peaks is attributed to a combination of modifications to the dispersion relation and reduced Landau damping. This enables the objective and data-driven identification of distribution functions directly from observed CTS spectra.

The recent realization of two-dimensional (2D) magnets, with CrI$_3$ as a pioneering example, has opened new avenues in the fields of 2D materials and magnetism. This breakthrough has been followed by extensive efforts to manipulate and exploit their magnetic properties. In this work, we investigate the adsorption of alkali-metal atoms as a route to control the magnetic behavior of monolayer CrI$_3$. We show that, upon adsorption, alkali-metal atoms donate an electron to the CrI$_3$ layer, leading to the formation of inequivalent Cr sites, with one Cr atom exhibiting an enhanced magnetic moment of $4~\mu_B$, while the other retains its typical $3~\mu_B$ moment. These modifications significantly alter the magnetic exchange interactions, including the emergence of anisotropic exchange and Dzyaloshinskii–Moriya interactions (DMI). Consequently, the doped systems exhibit non-collinear magnetic ground states, modified temperature-dependent magnetism, and anisotropic spin-wave propagation, with a preferred propagation direction that becomes increasingly pronounced with increasing dopant size. Furthermore, an asymmetry between spin-wave propagation in opposite directions is observed, giving rise to a diode-like effect, particularly for heavier dopants. This behavior is attributed to the enhanced DMI, which breaks the symmetry of the magnon dispersion. These results demonstrate that alkali-metal doping provides an effective route to tune anisotropic and nonreciprocal magnonic properties in two-dimensional magnetic materials.

Anti-altermagnets (AAMs) are a recently identified class of layered magnetic materials where opposite spin-splitting in adjacent layers creates a globally spin-degenerate band structure, rendering conventional spectroscopic detection highly difficult. In this paper, we theoretically demonstrate an all-electrical method to manipulate and probe this hidden magnetic order using a dual-gated transport junction. By applying a perpendicular displacement field, we break the spatial inversion symmetry of the lattice, explicitly lifting the global spin degeneracy. We attach ferromagnetic (FM) leads on either side of the AAM. Using quantum transport calculations, we show that this gate-induced spin-splitting manifests as a strongly asymmetric tunnel magnetoresistance (TMR) as a function of the lead magnetization. We identify specific crystallographic orientations where the TMR retains its symmetry despite the fully split bands, a direct consequence of exact momentum-space compensation. We further reveal that Rashba spin-orbit coupling guarantees robust, highly directional transport asymmetries even in the absence of an explicit chemical potential mismatch between the layers. Our findings establish a clear, electrically tunable framework for exploiting AAMs in next-generation spintronic architectures.

CeRh2As2 is a heavy-fermion superconductor that exhibits distinct low- and high-field superconducting phases, widely interpreted as reflecting a field-induced change in the parity of the order parameter. However, the superconductivity develops in close proximity to magnetic order whose microscopic origin and nature remain unclear. Moreover, the low-lying crystal-electric-field-split doublets of the Ce 4f electrons appear to realize an unusual "quasi-quartet" structure. This has motivated proposals that quadrupolar degrees of freedom play an important role in the low-temperature physics. Here we develop a microscopic heavy-fermion description of CeRh2As2 that incorporates both the quasi-quartet structure and the nonsymmorphic symmetry. Within a multiorbital periodic Anderson model, we include the lowest-lying $\Gamma_7$ and $\Gamma_6$ doublets of the Ce 4f electrons, and allow for nonlocal hybridization with the conduction d electrons. Single occupancy of the 4f states is enforced within the rotationally invariant slave-boson formalism. Adopting a mean-field treatment, we first show that the effective low-energy Hamiltonian is accurately captured by a single-orbital tight-binding model, justifying the minimal descriptions widely employed in the literature. Allowing for a magnetic ground state, we find that our model displays metallic $\mathbf{Q}=(\pi,\pi)$ antiferromagnetic order over a wide parameter regime. Ferromagnetic solutions also occur, but in a smaller region of parameter space and with greater sensitivity to carrier concentration and the form of the f-d hybridization. Quadrupolar moments appear only within magnetically ordered phases and are generally small, becoming substantial only when the $\Gamma_7$ and $\Gamma_6$ doublets are nearly degenerate. Our results provide a microscopic basis for understanding the itinerant heavy-fermion physics and ordered phases of CeRh2As2.

In this paper, we investigate the periodic orbits around a black hole (BH) in Einstein-Maxwell-scalar (EMS) theory and the corresponding gravitational waveforms. First, we study the test particle dynamics around the BH by using the Lagrangian formalism. Using the corresponding conditions, we explore the effect of the spacetime parameters on the marginally bound orbit (MBO) and innermost stable circular orbit (ISCO). The results indicate that MBO and ISCO quantities decrease with the rise of the $\beta$ parameter and BH charge $Q$, and vice versa for the $\gamma$ parameter. Subsequently, we plot the different zoom-whirl orbits around the BH in EMS theory by finding the test particle's corresponding energy and angular momentum. Finally, the gravitational waveforms of the extreme mass ratio inspirals, which contain a supermassive BH in EMS theory and a stellar mass object, are demonstrated. It is shown that the zoom-whirl orbits shrink as the BH charge increases, and, as a result, gravitational waveforms shift towards shorter times.

Considering a cylindrically symmetric spacetime, a novel exact $\kappa$-deformed Schwarzschild-AdS black string solution is derived in General Relativity in the presence of a negative cosmological constant. The geometric properties of the resulting solution are systematically investigated by computing the Ricci and Kretschmann curvature scalars. The analysis reveals the existence of a curvature singularity at the origin, which remains enclosed by an event horizon provided that the $\kappa$-deformation parameter satisfies a specific constraint. Subsequently, the influence of various model parameters on the horizon structure and configuration is examined in detail. The thermodynamic properties of these black strings are thoroughly evaluated; in this regard, the Hawking temperature, entropy, mass, isobaric heat capacity, and Gibbs free energy are self-consistently extracted. The effects of the parameters, particularly the $\kappa$-deformation parameter, on these thermodynamic quantities are comprehensively explored. Furthermore, it is demonstrated that these state variables fundamentally satisfy the extended first law of black hole thermodynamics and yield a modified Smarr relation. Finally, the temporal profile of the Hawking radiation is probed via the dimensionless sparsity parameter, through which the impacts of the underlying parameters on the quantum emission rate are systematically analyzed.

The feedback-based algorithm for quantum optimization (FALQON), which is an extension of the quantum approximate optimization algorithm (QAOA), is a promising approach for finding approximate solutions to combinatorial optimization problems. The FALQON avoids the optimization of variational parameters by using information derived from iterative measurements. To solve a constrained combinatorial optimization problem, it is sometimes more efficient to use an XY mixer rather than the conventional X mixer. We applied the FALQON with the XY mixer to graph coloring and investigated the expectation value of the problem Hamiltonian, success probability of graph coloring, and fair sampling for several small-scale problems. The FALQON with the XY mixer exhibited better performance than that with the X mixer.

The Teukolsky Master Equation (TME) is a powerful technique used to study perturbations of a spacetime with gravitational, electromagnetic, and neutrino components. The well-known Kerr metric is a suitable candidate for this formalism because it is a Petrov type D metric. However, the Kerr metric represents the exterior spacetime of a perfect sphere and only black holes are described using this metric. For another astrophysical object, such as fast-spinning neutron stars, the Kerr metric is not valid due to the rotation induced deformations to the gravitational source. The main goal of the present work is to show a TME for a Kerr-like metric (KL) with a mass quadrupole moment parameter $q$. This new parameter will represent deformations from a perfect sphere; therefore, KL is a better candidate to study perturbations surrounding spinning stars.

Growing biochemical systems are intrinsically noisy, with one important source of stochasticity arising from the discrete reaction events of the underlying biochemical network. Because growing systems do not generally admit stationary abundance distributions, it is unclear how to separate this intrinsic chemical noise from other sources of variability in population and single-cell data. Here we develop a large-deviation theory for exponentially growing stochastic chemical reaction networks by decomposing abundance into volume and composition. In these coordinates, balanced growth corresponds to a stable composition together with exponentially increasing volume. We show that composition fluctuations satisfy a large-deviation principle with speed equal to the volume of the growing system, and the corresponding quasipotential is selected by a solution of the contact Hamilton–Jacobi equation. We also derive a fluctuation theory for accumulated observables and show that their covariances decay with accumulated-volume, rather than with physical time. Applications to a minimal autocatalytic network and a coarse-grained cellular growth model demonstrate how the theory predicts composition quasipotentials, growth-rate fluctuations, and correlations between observables. The framework therefore provides a stochastic null model for single-cell heterogeneity generated by the intrinsic stochasticity of the underlying chemical reaction network.

We find new boundary conditions in four-dimensional Abelian gauge theory with general Chern–Simons boundary couplings. The boundary conditions allow dyonic edge modes and physical boundary symmetries. In particular, one of the new boundary conditions makes both electric and magnetic charges physical. We also study how our boundary conditions and charges transform under the $\mathrm{SL}(2,\mathbb Z)$ duality.

Selective activation of dinitrogen (N$_2$) under mild conditions is difficult: N$\equiv$N is one of the strongest bonds in chemistry, and most heterogeneous catalysts capable of breaking it require high temperature and pressure. Atomically dispersed transition-metal sites offer a computationally tractable route to studying the strongly correlated intermediates involved. We connect periodic DFT calculations with correlated active-space calculations on a finite, non-periodic surface fragment, demonstrating the workflow for the hydrogenation step RuH$_2$(N$_2$)* $\rightarrow$ RuH(NNH)* at an isolated Ru$_1$ site on Ru(0001). A first-shell fragment is extracted from the periodically relaxed structure, an active space is selected with Active Atomic Valence Space (AVAS) around the Ru-N/N-H bond reorganization, and natural-orbital truncation reduces its cost while retaining the relevant correlated degrees of freedom. The reduced Hamiltonian is mapped to qubits with the Jordan-Wigner transformation and solved with the adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver (ADAPT-VQE). Dynamic correlation beyond the active space is examined with strongly contracted NEVPT2 and DSRG-MRPT2. AVAS gives a 22-qubit active space, which natural-orbital truncation compresses to 16 qubits, reproducing the untruncated CASCI state energies to within 0.21 kcal/mol (reaction-energy error 0.2 kcal/mol). Statevector ADAPT-VQE in this reduced space converges for both reaction states under a fixed pool-gradient stopping criterion. NEVPT2 yields anomalously large, state-imbalanced corrections for the finite Ru fragment, while DSRG-MRPT2 retains an endothermic reaction energy at its default flow parameter, although its magnitude depends strongly on that parameter.

Information-theoretic measures for comparing probability distributions are widely used across physics and other fields. When two discrete distributions have non-inclusive supports, however, the Kullback-Leibler (KL) divergence is in general not directly applicable, and various alternative divergences and distances have been introduced. These measures compare the resulting distributions themselves, but do not generally retain information about the representation transformations by which the discrete distributions are generated from underlying continuous ones. Here we introduce a representation-aware transport-information measure for discrete distributions with non-inclusive supports, formulated based on the standard KL divergence. We consider two continuous reference distributions, each transformed into a discrete representation through its own discretization scheme. Rather than comparing only the resulting discrete distributions or their continuous references, we additionally retain local information associated with the representation-change schemes. The resulting measure can therefore distinguish discrete representations that may have identical discrete probability landscapes but originate from different continuous references or discretization schemes. The construction is based on the transport-information cost of continuous-to-discrete representation in the framework of unavoidable canonical nonlinearity (UCN). UCN provides a non-arbitrary correspondence between the transport cost of discretization as an extrinsic geometric operation and the information-theoretic indistinguishability of nearby continuous distributions, thereby allowing a discrete representation to be associated with a local family of underlying continuous distributions on the statistical manifold.

We consider the effect of relativistic principles on the structure of the local evolutions of non-factor quantum systems such as those which naturally arise in quantum spacetimes and causal structures. Generalising a former result that had been given for factor systems, we show that any evolution which can be applied locally on a direct sum of factor systems and without producing superluminal signals must be linear, unitary, and respect the block decomposition of the system.

We investigate the validity of the sub-horizon approximation (SHA) and quasi-static approximation (QSA) for linear matter perturbations in interacting scalar-field dark-energy models. We consider both quintessence and phantom scalar fields and derive their full relativistic perturbation evolution to compare with the corresponding SHA and QSA solutions. We find that, while the SHA reproduces the full evolution with percent-level accuracy for non-interacting and weakly interacting models on sufficiently sub-horizon scales, its accuracy progressively deteriorates with increasing interaction strength and towards larger scales. Moreover, unlike in $\Lambda$CDM and non-interacting scalar-field models, applying the SHA to interacting models does not fully recover the standard Newtonian fluid equations. The QSA generally provides a closer description of the full relativistic evolution than the SHA over the scales considered. By comparing the scalar-field model with $\Lambda$CDM using the full relativistic equations and, separately, using the SHA system, we evaluated whether the SHA is capable of capturing the full extent of the physical differences introduced by the alternative model. We find that the difference between these two comparisons becomes increasingly important for stronger interactions and smaller wavenumbers. Finally, we demonstrate that the resulting differences can reach several percent on scales accessible to large-volume hydrodynamical simulations, implying that the validity of the SHA cannot be assumed solely from the sub-horizon condition. Our results highlight the need to benchmark the approximation over the relevant interaction parameter and wavenumber ranges before employing interacting-dark-energy models in large-volume structure-formation simulations and precision comparisons with large-scale-structure observations.

We consider an interpolation with the parameter $p\in [0,1]$ between the discrete-time quantum ($p=0$) and its intrinsic random ($p=1$) walks on a finite connected graph. Its time evolution is defined by the convex combination of the Kraus (CPTP) maps of the quantum and random walks. The Kraus map of the random walk is represented by taking a kind of projection of that of the quantum walk. The time evolution of the interpolation is interpreted as the combination of the following two dynamics of $2$ walkers on the same graph correlated with each other: $2$ walkers move independently of each other (no-correlation) with probability $1-p$, while $2$ walkers always move into the same position (the maximal correlation) with probability $p$ at each time step. In this paper, we generalize the random walk to a new walk, namely, the correlated walk, which preserves the intrinsic property and relaxes the maximal correlation of the random walk. This correlation is determined by a partition of the arc sets in the underlying graph. We show that the eigenvalues of the interpolating walk between the correlated and quantum walks live in $\{ z\in \mathbb{C}\;|\;1-p\leq |z|\leq 1 \}$ and that the absorption state coincides with that of the correlated walk, which is characterized by the underlying graph structures.