The construction of nonempirical density functional approximations is typically guided by the satisfaction of exact constraints. More recent constructions of semilocal correlation, which tend to satisfy the maximum number of constraints, drop the gradient of the spin polarization ($\nabla \zeta$) as a semilocal ingredient. In this work we prescribe a theoretically sound method for reintroducing explicit $\nabla \zeta$ dependence in the correlation energy of such DFAs. The proposed scheme, when applied to the Strongly Constrained and Appropriately Normed (SCAN) functional, preserves nearly all of its exact constraints. Additionally, one recovers potentially important $\nabla \zeta$-dependent terms in the gradient expansion of the correlation that SCAN drops. The inclusion of $\nabla \zeta$-dependent terms in SCAN correlation is shown to improve the functional description of transition-metal atoms and molecules without significantly affecting SCAN's accurate description of $sp$ systems. For the binding energy curve of the chromium dimer ${\mathrm{Cr}}_2$, the SCAN underbinding is fully corrected at large bond lengths and reduced at short bond lengths.

High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped ions offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that capabilities practically enabled by integrated optics can additionally alleviate laser powers required for both light-shift and Mølmer-Sørensen geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. We present a theoretical analysis of spontaneous photon scattering (SPS) in stimulated Raman processes driven by spatially structured drive fields, which we employ to assess trapped-ion gates utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes. Our calculations indicate that suppressed SPS at intensity nodes allows for gate drives operating at smaller Raman detunings and, as a result, approximately an order-of-magnitude lower power (with significantly larger enhancement in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared with gates using running-wave fields. The SW schemes have the additional benefit of eliminating undesired coherent couplings that can limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for the realization of fast and power-efficient laser-based entangling gates in scalable platforms. Our analysis further suggests potential for structured drive fields to mitigate power and scattering limitations in stimulated Raman processes coupling to atomic motion more broadly in both trapped ions and neutral atoms.

We study a coarse-graining map arising from incomplete and imperfect addressing of particles in a multipartite quantum system. In its simplest form, corresponding to a two-qubit state, the resulting channel produces a convex mixture of the two partial traces. We derive the probability density of obtaining a given coarse-grained state, using geometric arguments for two qubits coarse-grained to one, and random-matrix methods for larger systems. As the number of qubits increases, the probability density sharply concentrates around the maximally mixed state, making nearly pure coarse-grained states increasingly unlikely. For two qubits, we also compute the inverse state needed to characterize the effective dynamics under coarse-graining and find that the average preimage of the maximally mixed state contains a finite singlet component. Finally, we validate the analytical predictions by inferring the underlying probabilities from Monte Carlo-generated coarse-grained statistics.

Quantum error correction codes defined on hyperbolic lattices leverage the unique geometric properties of the hyperbolic space to enhance the performance of quantum error correction. By embedding qubits in hyperbolic lattices, these codes achieve higher encoding rates and lower qubit overhead compared to those defined on conventional Euclidean lattices. Building on recent advances in hyperbolic crystallography, we introduce a unified framework for the systematic construction and scalable benchmarking of CSS quantum error correction codes on hyperbolic lattices. A central component of this framework is the Hyperbolic Cycle Basis algorithm, which employs graph-theoretic methods to efficiently identify all plaquette cycles (parity-check supports) and nontrivial cycles (logical operators). This enables scalable and automated benchmarking of a broad class of CSS codes defined on hyperbolic geometries. We apply this framework to construct and simulate two representative hyperbolic quantum error correction codes (HQECCs), evaluating key performance metrics such as encoding rate, error threshold, and code distance for different sublattices. While HQECCs serve as concrete examples, the framework can be adapted to a wide range of CSS codes, including those with more intricate stabilizer structures such as Floquet codes. This work establishes a foundation for systematic exploration and benchmarking of CSS codes on hyperbolic lattices, paving the way toward practical, high-performance quantum error correction.

Quantum systems are known to offer advantages over their classical counterpart in communication complexity protocols, where the aim is to minimize the amount of information exchange between distant parties to compute global functions of their distributed inputs. In this paper, we establish that any one-way communication protocol implemented using a prime-dimensional quantum system—restricted to stabilizer-state encodings and Clifford-operation decodings—can be exactly simulated by transmitting a classical system of the same dimension, given access to shared randomness between the sender and receiver. In direct analogy with the Gottesman-Knill theorem, which attributes quantum computational speedup to nonstabilizer resources, commonly known as the magic resources, our result identifies the same nonstabilizer resources as the essential ingredient for the quantum advantage in one-way communication complexity. Furthermore, we present explicit tasks where even a “minimal magic resource” suffices to achieve a provable quantum advantage, highlighting its efficient use in communication protocols.

Designing photonic circuits that prepare graph states with high fidelity and success probability is a central challenge in linear optical quantum computing. Existing approaches rely on hand-crafted designs or fusion-based assemblies. In the absence of multiplexing and boosting, both postselected ballistic circuits and sequential fusion exhibit exponentially decreasing single-shot yields—a fundamental limitation that makes optimizing individual resource state generators particularly important, as these serve as building blocks in larger FBQC architectures. We present a general-purpose optimization framework for automated photonic circuit discovery using a polynomial-based simulation approach, enabling efficient strong simulation and gradient-based optimization. Our framework employs a two-pass optimization procedure: The first pass identifies a unitary transformation that prepares the desired state with perfect fidelity and maximal success probability, and the second pass implements a sparsification algorithm that reduces this solution to a compact photonic circuit with minimal beam-splitter count while preserving performance. This sparsification procedure often reveals underlying mathematical structure, producing highly simplified circuits with rational reflection coefficients. We demonstrate our approach by discovering optimized circuits for three-, four-, and five-qubit graph states across multiple equivalence classes. For four-qubit states, our circuits achieve success probabilities of $2.053\times {10}^{-3}$ to $7.813\times {10}^{-3}$, outperforming the fusion baseline by up to $4.7\times$. For five-qubit states, we achieve $5.926\times {10}^{-5}$ to $1.157\times {10}^{-3}$, demonstrating up to $7.5\times$ improvement. These results include the first known state preparation circuits for certain five-qubit graph states.

We propose a universal gate set for quantum computing that operates in the presence of decoherence without the overhead of active error correction. We show that a broad class of anisotropic system-bath couplings can be effectively decoupled by preparing an appropriate system-bath entangled initial state. The initially established entanglement serves as a resource to cancel out the dominant decoherence during evolution, enabling quantum computation to proceed as if the system were effective decoupled from its environment.

In the era of noisy intermediate-scale quantum computing, this paper proposes a hierarchical adaptive quantum approximate optimization algorithm (QAOA) to address quantum resource constraints in graph-coloring problems (GCPs). The algorithm employs a divide-and-conquer strategy by partitioning a large graph into multiple subgraphs, solving subgraph coloring using various QAOA variants, and incorporating a greedy search as a fallback mechanism. During the merging stage, conflicts are resolved through iterative optimization. Experimental results demonstrate that the conflict rate rapidly converges to zero and iterative optimization reduces the number of colors required. Tests on the COLOR benchmark dataset and 50-node $d$-regular graphs show that the adaptive QAOA outperforms the standard QAOA and adaptive noise QAOA in efficiency. For some complex graphs, this algorithm surpasses classical algorithms in terms of the number of colors used. The GCP solution can be applied to subway transportation network instances, achieving effective optimization of scheduling operations. This study presents a hierarchical and precise quantum-classical hybrid computing scheme for NP-hard problems, offering significant value for graph coloring and related practical applications.

We establish necessary and sufficient conditions for the $N$-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the true energy in one-electron reduced density matrix functional theory, regardless of the strength of the interparticle repulsion. Conversely, any functional violating these conditions will necessarily underestimate the true energy for certain systems. These exact constraints impose a stringent restriction on density matrix functional approximations, as many existing functionals—including the Hartree-Fock functional—appear to violate them. This mathematical formalism, therefore, can guide the development of new approximate functionals and numerical algorithms.

In this work, we investigate the applicability of the core-polarization-corrected Dirac-Fock method, formulated within the framework of the local Dirac-Hartree-Fock (LDF) potential, for the accurate determination of static scalar and tensor electric dipole polarizabilities. This work presents theoretical values of blackbody-radiation-induced Stark shifts of atomic energy levels. The Dirac-Fock method augmented by core-polarization corrections is employed not only to evaluate these shifts but also to compute the Bethe logarithm for alkali-metal atoms. The results are critically compared with data available in the contemporary literature, and the strengths and limitations of the present approach are discussed.

Bremsstrahlung emission remains a cornerstone process in the characterization of electron dynamics in diverse high-energy environments. In particular, the accurate description of thin-target electron-ion bremsstrahlung in the presence of high-$Z$ species requires careful treatment of atomic screening effects, especially when atoms are partially ionized. We present a fully analytic screening model based on a multi-Yukawa representation of the atomic potential, enabling the calculation of bremsstrahlung cross sections for arbitrary nuclear charge and ionization state, and electron energies up to a few tens of MeV. This framework extends prior treatments of neutral atoms to include partially ionized high-$Z$ elements in a fully analytic framework.

The triplet state of helium can bind a positron to form a quantum halo state with a nonrelativistic binding energy of only about 0.6 mhartree. Owing to its extremely weakly bound nature, evaluating relativistic corrections to the binding energy is essential for confirming its stability beyond the nonrelativistic limit. In this work we first examine the nonrelativistic structural properties of positronic metastable helium using a highly accurate variational expansion constructed from explicitly correlated Gaussian basis functions. Our results show that the system is remarkably diffuse and meets the established criteria for a quantum halo state. Using the resulting high-accuracy nonrelativistic wave function, we then compute the relativistic corrections within the framework of perturbation theory. The calculations indicate that the system remains bound even after including relativistic effects. Notably, the relativistic corrections to the bound and dissociated states largely cancel, yielding a net change in the binding energy of less than 4%. Finally, we evaluate the annihilation rates and lifetimes of both the quartet and doublet states. We find that the quartet state has a significantly longer lifetime because the positron and all electrons are aligned in a spin-triplet configuration, making three-photon annihilation the dominant decay channel.

The Coulomb focusing effect on different sub-laser-cycle electrons, i.e., prepeak direct and postpeak rescattering electrons, is theoretically investigated using the exact solution of three-dimensional (3D) time-dependent Schrödinger equation (TDSE), as well as semiclassical simulations based on both adiabatic and nonadiabatic models in the orthogonally polarized two-color laser field. By comparing their photoelectron momentum distributions (PMDs) along the light-propagation direction, we find that the nonadiabatic tunneling effect plays a critical role in modulating the relative strength of the Coulomb focusing between the direct and rescattering electrons, showing a pronounced phase dependence. Remarkably, within a specific phase window, this relative strength even reverses, leading to an abnormal behavior where the direct electrons experience stronger Coulomb focusing. Resorting to component-separated nonadiabatic models, we successfully uncover its underling dynamic mechanisms. We further demonstrate that this abnormal behavior can be clearly extracted from the TDSE-calculated PMD, paving the way for its direct experimental detection.

We derive a damping mechanism in the open quantum system description of Bose-Einstein condensates. It stems from previously neglected terms in the derivation of the stochastic projective Gross-Pitaevskii equation (SPGPE), accounting for a nonlinear evaporation of particles from the coherent into the incoherent region. We demonstrate that the mechanism, while so far assumed to be of minor importance, is comparable in strength to the widely employed number damping. We also provide a simplified (pseudo)local and a dimensionally reduced form of this evaporative damping. The process completes the SPGPE description of ultracold Bose gases giving a full first-principles picture of their evolution at finite temperature.

We consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and various mass ratios of the two particles. For low-energy collisions (with dimer kinetic energies much smaller than the binding energy) our results are consistent with those of Lee and Pine [Eur. Phys. J. A 47, 41 (2011)]. For mass ratios much greater than 1 we use the Born-Oppenheimer approximation to show that the scattering length and the effective range of the dimer-wall collision both depend logarithmically on the mass ratio. For collision energies much greater than the binding energy, the dissociation probability is inversely proportional to the square of the incident momentum of the dimer and we find the constant of proportionality analytically, and we use a semiclassical analysis to approximately derive the “angular distribution” of the dissociated pair, where the “angle” $\theta$ depends on the ratio of the velocities of the two outgoing unbound particles.

We present a comprehensive theoretical study of linear wave scattering from magnetic domain walls with varied twist angles $\mathrm{\Theta }$ in spin-$1/2$ Bose-Einstein condensates (BECs). Using a gauge transformation, we show that scattering observables depend solely on the total twist $\mathrm{\Theta }$, independent of chirality. Within the Bogoliubov–de Gennes (BdG) framework, we develop a transfer-matrix method to compute reflection and transmission coefficients for incident phonons and free particles. Our results reveal a scattering threshold at the Zeeman energy $E=\hslash {\mathrm{\Omega }}_0$, separating a pure phonon regime from multichannel scattering involving both collective and single-particle excitations above threshold. Above a critical twist angle ${\mathrm{\Theta }}_c$, the effective spin rotation deviates from the imposed twist angle, leading to comb-like density modulations and Fano-like resonances below the threshold $\hslash {\mathrm{\Omega }}_0$. The transition probability between phonon and particle channels is strongly tunable with $\mathrm{\Theta }<{\mathrm{\Theta }}_c$, enhanced for odd multiples of $\pi$ but suppressed for even multiples. These findings establish twist-engineered domain walls as a versatile platform for controlling quantum transport, with implications for atomtronic devices and quantum simulation.

Optical periodic structures exhibiting a degenerate band edge (DBE) are of significant interest for various applications such as switching, sensing, high-power amplification, and lasing. At the edge of the bandgap in such structures, a fourth-order exceptional point degeneracy arises, leading to an extremely flat dispersion band. We propose and study a silicon-on-insulator-compatible structure composed of two coupled waveguides with asymmetric gratings. The dispersion relations and the field profiles are obtained using three-dimensional finite-difference time-domain simulations, and we provide a set of practical guidelines for the design and optimization of such structures, in order to obtain a DBE. We analyze the transmission and reflection spectra of finite-size devices and investigate their spectral properties near the stationary points. The scaling of the resonance quality factor with the number of unit cells is studied, revealing a performance that surpasses that of conventional periodic structures. Finally, we examine the robustness of the DBE with respect to fabrication tolerances and structural imperfections.

We present a theoretical and experimental study on the propagation and polarization control of hybrid-order Poincaré beams—composed of two vortex beams with different orders—in nonlocal, nonlinear lead glass. The linear stability analysis reveals that stable solitons form only when the power and width of the component vortices satisfy certain conditions. Furthermore, we numerically establish that the polarization rotation of these beams can be controlled linearly by varying the power, and we analytically demonstrate that such a phenomenon arises from different phase shifts between the component beams. The theoretical predictions agree well with the experimental results. This suggests that the controllable polarization evolution of solitons could open an avenue for optical manipulation, imaging, communications, and other photonic applications.