We present highly accurate variational calculations of triplet excited states of the beryllium atom using all-electron explicitly correlated Gaussian basis sets. The employed approach that treats the electrons and the nucleus on the same footing enables precise determination of the energy spectrum, wave functions, and transition properties of low-lying ${}^3{S}^e$ and ${}^3{P}^o$ states of the naturally occurring ${}^9\mathrm{Be}$ isotope and the model ${}^{\infty }\mathrm{Be}$ system. Benchmark-quality total and transition energies, as well as oscillator strengths determined in both the length and velocity gauges, are reported. The results are compared with available theoretical and experimental data. The comparison shows excellent agreement of the present results with the experiment. They also provide refinement for the values where discrepancies had existed before.

A Bose-Einstein condensate in a modulated, one-dimensional, anharmonic potential can exhibit dynamical tunneling between islands of regular motion in phase space. With increasingly repulsive atomic interactions, dynamical tunneling is predicted to cease due to self-trapping [S. Wüster et al. Phys. Rev. Lett. 109, 080401 (2012)]. This suppression of tunneling oscillations is related to the same phenomenon that occurs in the two-mode dynamics of a repulsively interacting Bose-Einstein condensate in a double-well potential. Here we present a two-mode model for dynamical tunneling based on nonlinear Floquet states and examine the range of validity of the approximation. We characterize nonlinear dynamical tunneling for different trap strengths, modulation amplitudes, and effective Planck constants. Using the linear Floquet states we derive an expression for the critical nonlinearity beyond which tunneling ceases. Finally we demonstrate the dynamical instability of selected nonlinear Floquet states and show how to initialize some Floquet states in experiments. Our detailed survey will enable experiments to target accessible parameter regimes for the study of nonlinear dynamical tunneling.

In recent years, optical systems have emerged as a platform for solving hard computational problems, demonstrating their ability to simulate and accelerate the search for the ground state of a given Ising Hamiltonian. Yet, their implementations, exploiting both free-space propagation and scattering media, lack tunability. In this study, we demonstrate enhanced control over the interaction length between spins in an Ising system by tailoring the optical properties of the scattering medium. Finally, we leverage our control to observe correlations between local clusters of spins across replicas.

We develop the theory of dispersive shock waves in optical fibers for the case of long-distance propagation of optical pulses, when the small Raman effect stabilizes the profile of the shock. The Whitham modulation equations are derived as the basis for the Gurevich-Pitaevskii approach to the analytical theory of such shocks. We show that the wave variables at both sides of the shock are related by the analog of the Rankine-Hugoniot condition that follows from the conservation laws of the Whitham equations. Solutions of the Whitham equations yield the profiles of the wave variables that agree very well with the exact numerical solution of the generalized nonlinear Schrödinger equation for propagation of optical pulses.

We study algorithmic error mitigation via Richardson-style extrapolation for quantum simulations of open quantum systems modelled by the Lindblad equation. Focusing on two specific first-order quantum algorithms, we perform a backward-error analysis to obtain a step-size expansion of the density operator with explicit coefficient bounds. These bounds supply the necessary smoothness for analyzing Richardson extrapolation, allowing us to bound both the deterministic bias and the shot-noise variance that arise in postprocessing. For a Lindblad evolution with generator bounded by $\ell$, our main theorem shows that an $n=\mathrm{\Omega }\left({log}_{10}(1/\varepsilon )\right)$-point extrapolator reduces the maximum circuit depth needed for accuracy $\varepsilon$ from polynomial $O({\left(\ell T\right)}^2/\varepsilon )$ to polylogarithmic $O\left({\left(\ell T\right)}^2\left({log}_{10}\left(\ell T\right)\right){log}^2(1/\varepsilon )\right)$ scaling, an exponential improvement in $1/\varepsilon$, while keeping sampling complexity to the standard $1/{\varepsilon }^2$ level, thus extending such results for Hamiltonian simulations to Lindblad simulations. Several numerical experiments illustrate the practical viability of the method.

Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states—called Wigner entropy for brevity—emerges as a fundamental information-theoretic measure in phase space and is subject to a conjectured lower bound, reflecting the uncertainty principle. In this work, we prove that this Wigner entropy conjecture holds true for a broad class of Wigner-positive states known as beam-splitter states, which are obtained by evolving a separable state through a balanced beam splitter and then discarding one mode. Our proof relies on known bounds on the $p$-norms of cross Wigner functions and on the interference formula, which relates the convolution of Wigner functions to the squared modulus of a cross Wigner function. Originally discussed in the context of signal analysis, the interference formula is not commonly used in quantum optics although it unveils a strong symmetry under convolution exhibited by Wigner functions of pure states. We provide here a simple proof of the formula and highlight some of its implications. Finally, we prove an extended conjecture on the Wigner-Rényi entropy of beam-splitter states, albeit in a restricted range for the Rényi parameter $\alpha \ge 1/2$.

In the typical implementation of a quantum error-correcting code, each stabilizer is measured by entangling one or more ancilla qubits with the data qubits and measuring the ancilla qubits to deduce the value of the stabilizer. Recently, the dynamic circuit approach has been introduced, in which stabilizers are measured without ancilla qubits. Here, we demonstrate that dynamic circuits are particularly useful for the Floquet code. Our dynamic circuit increases the timelike distance of the code, automatically removes leakage, and both significantly increases the threshold and lowers the logical error rate compared to the standard ancilla-based circuit. At a physical error rate of ${10}^{-3}$, we estimate a nearly $3\times$ reduction in the number of qubits required to reach a ${10}^{-12}$ logical error rate.

Recently, Sasmal et al. [Phys. Rev. Lett. 133, 170201 (2024)] introduced probabilistic projective measurements (PPMs) for sequential sharing of nonlocality. Here we develop a general framework for sequentially witnessing quantum correlations, including bipartite and genuine multipartite entanglement, via PPMs. We show that a class of positive-operator-valued measures admits a unified PPM realization and present an explicit formula linking the initial state, intermediate channels, and witness operators, providing both computational efficiency and structural insight. Using this framework, we demonstrate unbounded sequential entanglement sharing for pure and certain mixed states, as well as detection of genuine multipartite entanglement in Greenberger-Horne-Zeilinger-type states. Our results highlight the nontrivial role of PPMs in sequential entanglement witnessing and address generalized multipartite sharing, as discussed in a recent review article [Phys. Rep. 1098, 1 (2025)].

We report on modulation transfer spectroscopy (MTS) of the ${}^{1}S_0\to {}^{3}P_1$ transition of ytterbium in a vapor cell. We stabilized our laser on the MTS error signal and measured the offset frequencies relative to modes of an ultralow expansion cavity. The isotope shifts were extracted through these measurements. The Zeeman splitting of ${}^{171}\mathrm{Yb}$ and ${}^{173}\mathrm{Yb}$, two fermionic isotopes with hyperfine structure, were also studied. Our results show significant deviations from linear Zeeman-effect calculations at intermediate magnetic fields of less than 60 G. Quadratic corrections to the Zeeman effect derived through second-order perturbation theory explain the observed nonlinearities. Such quadratic corrections are essential when using Zeeman-structure measurements to obtain the fermionic isotope shifts.

Neutral atom manipulation along with the modern laser cooling and trapping techniques have revolutionized the field of atomic physics, enabling innovation among atomic clocks as well as in the study of parity violation and the search for electron electric-dipole moment and nuclear anapole moment. The realization of highly precise and accurate atomic clocks evidently requires high signal-to-noise ratio, which is inversely proportional to Allan deviation. Keeping this in mind, we have calculated magic wavelengths $\left({\lambda }_{\mathrm{magic}}\right)$ for optical clock transitions in ${}^{85}\mathrm{Rb}$, ${}^{133}\mathrm{Cs}$, and ${}^{223}\mathrm{Fr}$ atoms, viz, $5S_{1/2}\text{−}6P_{1/2,3/2}$, $6S_{1/2}\text{−}7P_{1/2,3/2}$, and $7S_{1/2}\text{−}8P_{1/2,3/2}$, respectively, particularly in the visible-near-infrared spectrum, owing to the fact that Allan deviation rapidly decreases with higher wavelengths of the electromagnetic spectrum, making them more acceptable for newer navigation systems, quantum computation devices as well as tools for high-precision experiments. In this study, we also recommend investigating near-resonant ${\lambda }_{\mathrm{magic}}$ for ${}^{85}\mathrm{Rb}$ [420.81(2), $418.21\left(4\right),421.390\left(4\right)$, and 417.67 nm] and ${}^{133}\mathrm{Cs}$ [458.84(4) nm], utilizing dual-purpose lasers of $\approx 420$ nm and $\approx 459$ nm for cooling and pumping of atoms for four-level active optical clock system based on Rb and Cs frequency standards, respectively. We believe that these findings will aid in overcoming trapping challenges for atomic clocks as well as support studies for physics beyond the standard model.

The quantum gravity mediated entanglement protocol offers a method to probe the quantumness of gravitational interactions at nonrelativistic scales. This protocol leverages the Stern-Gerlach effect to create $O\left(\mu \mathrm{m}\right)$ spatial superpositions of two nanodiamonds (mass $\sim {10}^{-15}$ kg) with nitrogen-vacancy spins, which are then allowed to interact and become entangled solely through the gravitational interaction. Since electromagnetic interactions such as Casimir-Polder and dipole-dipole interactions dominate at this scale, screening them to ensure the masses interact exclusively via gravity is crucial. In this paper, we propose using magnetic traps based on microfabricated wires, which provide strong gradients with relatively modest magnetic fields to trap nanoparticles for interferometric entanglement experiments. The design consists of a small trap to cool the center-of-mass motion of the nanodiamonds and a long trap with a weak direction suitable for creating macroscopic superpositions. In contrast to permanent-magnet-based long traps, the microfabricated wire-based approach allows fast switching of the magnetic trapping and state manipulation potentials and permits integrated superconducting shielding, which can screen both electrostatic and magnetic interactions between nanodiamonds in a gravitational entanglement experiment. The setup also provides a possible platform for other tests of quantum coherence in macroscopic systems and searches for novel short-range forces.

We propose an experimental scheme for sorting vector vortex beams using a system of three optical cavities. The method targets the separation of the four-vector vortex modes of a given order $m$ by exploiting their symmetry properties with respect to radial axes. The first cavity separates the modes into two pairs—one symmetric and one antisymmetric under horizontal flip—by transmitting one pair and reflecting the other. Each output is then directed into a second cavity, which further resolves the pairs into individual modes based on their parity. A key element between the cavities is a system introduced in this work, the profile rotator, which rigidly rotates the beam profile (including its polarization structure) using an appropriately calibrated K-mirror and a Faraday rotator. The theoretical framework is based on the analysis of mode symmetries and their interaction with cavity boundary conditions. This work lays the groundwork for experimental implementations of efficient mode sorting, with potential applications in high-dimensional quantum information processing, optical communications, and structured light manipulation.

We investigated a one-dimensional non-Hermitian trimer Su-Schrieffer-Heeger (SSH) model with nonreciprocal intercell couplings. By constructing the non-Bloch Hamiltonian and analyzing the non-Hermitian skin effect, we demonstrated that the boundary states exhibit qualitative similarities to those in the Hermitian case, albeit emerging at distinct locations. We established the bulk-boundary correspondence through numerical calculations of the non-Hermitian sublattice Zak phase. Furthermore, we extended the concept of the sublattice winding number to define the non-Hermitian sublattice winding number and derived its exact analytical expression. The role of the non-Hermitian sublattice winding number in characterizing topological properties is analogous to that of the non-Hermitian sublattice Zak phase. The non-Hermitian sublattice winding number provides a different approach to characterizing the bulk-boundary correspondence in non-Hermitian systems lacking chiral symmetry. Finally, by applying the criterion for the infernal points (IPs) in non-Hermitian systems, the IPs in the non-Hermitian trimer SSH model are identified.

A distinctive feature of non-Hermitian systems is the skin effect, which has recently attracted widespread attention. Quantum walks provide a powerful platform for investigating the underlying mechanisms of the non-Hermitian skin effect. Additionally, hybrid entanglement generation in quantum walks is recognized as another crucial property. However, experimentally investigating the influence of skin effect on the evolution of entanglement dynamics in the non-Hermitian systems remains a challenge. In this paper, we present a flexible implementation of 20-step discrete-time quantum walks using an optimized time-multiplexed loop configuration. By optimizing the coin parameter, we achieve maximal coin-position entanglement after 20-step quantum walks. Moreover, we experimentally measure the polarization-averaged growth rates and the evolution of coin-position entanglement under specific coin and loss parameters. We observe the asymmetric Lyapunov exponent profiles and the entanglement suppression induced by the non-Hermitian skin effect. Interestingly, this entanglement suppression weakens with increasing coin parameters and enhances with increasing loss parameters and evolution steps. Our results demonstrate the potential of quantum walks as a powerful platform for investigating hybrid entanglement properties and skin effects in non-Hermitian systems.

We present an efficient algorithm for the MultiReference Unitary Coupled-Cluster (MR-UCC) approach that integrates quantum computing techniques with particle number conserved (PNC) gates. This algorithm makes it possible to use sophisticated MR wave functions with minimal use of computer resources to calculate the ground-state energies of LiH, ${\mathrm{BeH}}_2$, and ${\mathrm{H}}_6$. The higher-order correlations in the subsequent UCC calculations can be included requiring only Single and Double excitations of the wave operator. This algorithm achieves a higher accuracy compared with other available sophisticated quantum computational models, using a single quantum circuit across the entire bond length including the dissociation length region.

Entanglement witnesses (EWs) are fundamental tools for detecting entanglement. However, traditional linear witnesses often fail to identify most of the entangled states. In this work, we construct a family of nonlinear entanglement witnesses by taking the envelope of linear witnesses defined over continuous families of pure bipartite states with fixed Schmidt bases. This procedure effectively “bends” the hyperplanes associated with linear witnesses into curved hypersurfaces, thereby extending the region of detectable entangled states. The resulting conditions can be expressed in terms of the positive semidefiniteness of a family of matrices, whose principal minors define a hierarchy of increasingly sensitive detection criteria. We show that this construction is not limited to the transposition map and generalizes naturally to arbitrary positive but not completely positive maps, leading to nonlinear analogs of general entanglement witnesses. We emphasize that the required measurements remain experimentally accessible, as the nonlinear criteria are still formulated in terms of expectation values over local operator bases. Through both analytical and numerical examples, we demonstrate that the proposed nonlinear witnesses outperform their linear counterparts in detecting entangled states which may evade individual linear EWs in the construction. This approach offers a practical and conceptually elegant enhancement to entanglement detection in finite-dimensional systems.

Traditional methods for handling (inequality) constraints in the quantum approximate optimization algorithm (QAOA) typically rely on penalty terms and slack variables, which increase problem complexity and expand the search space. More sophisticated mixer-based QAOA variants restrict the search within the feasible assignments but often suffer from prohibitive circuit complexity. This paper presents a penalty-free formalism for incorporating inequality constraints into the cost function of QAOA using an oracle-based subroutine that evaluates constraint satisfaction in an additional register, subsequently called indicator function QAOA (IF-QAOA). Applied to the knapsack problem, we demonstrate in numerical simulations the superior performance of IF-QAOA over conventional penalty-based approaches. Using advanced QAOA simulation techniques, we find that IF-QAOA achieves significantly higher solution quality and a faster time to solution in 82% of our benchmark cases, even though circuit depth is approximately three times larger. Analysis of the scaling behavior shows favorable scaling of IF-QAOA compared to penalty-based methods. Also, benchmarks against the recently developed quantum tree generator QAOA for knapsack problems (P. Christiansen et al., arXiv:2411.00518) demonstrated higher solution quality for circuits of similar depth. Additionally, this paper introduces a method for approximating the indicator function when the number of ancillary qubits is limited or the constraint function is noninteger. With a specialized simulation algorithm based on projective measurements, we empirically demonstrate that this formalism can encode general inequality constraints using a fixed number of ancillary qubits.