We extend the recently introduced Clifford-dressed time-dependent variational principle (TDVP) to efficiently compute many-body wave-function amplitudes in the computational basis. This advancement enhances the study of Loschmidt echoes, which generally require accurate calculations of the overlap between the evolved state and the initial wave function. By incorporating Clifford-disentangling gates during TDVP evolution, our method effectively controls entanglement growth while keeping the computation of these amplitudes accessible. Specifically, it reduces the problem to evaluating the overlap between a matrix product state (MPS) and a stabilizer state, a task that remains computationally feasible within the proposed framework. To demonstrate the effectiveness of this approach, we first benchmark it on the one-dimensional transverse-field Ising model. We then apply it to more challenging scenarios, including a nonintegrable next-to-nearest-neighbor Ising chain and a two-dimensional Ising model. Our results highlight the versatility and efficiency of the Clifford-augmented MPS, showcasing its capability to go beyond the evaluation of simple expectation values. This makes it a powerful tool for exploring various aspects of many-body quantum dynamics.

We examine the impact of long-range Dzyaloshinskii-Moriya (DM) interaction in the extended $XY$ model on the phase diagram as well as the static and dynamical properties of quantum and classical correlation functions. It is known that in the nearest-neighbor $XY$ model with DM interaction, the transition from the gapless chiral phase to a gapped one occurs when the strengths of the DM interaction and anisotropy coincide. We exhibit that the critical line gets modified with the range of interactions which decay according to power law. Specifically, instead of being gapless in the presence of a strong DM interaction, a gapped region emerges which grows with the increase of the moderate fall-off rate (quasi-long-range regime) in the presence of a transverse magnetic field. The gapless chiral phase can also be separated from a gapped one by the decay patterns of quantum mutual information and classical correlation with distant sites of the ground state which are independent of the fall-off rate in the gapless zone. We observe that the corresponding critical lines that depend on the fall-off rate can also be determined from the effective central charge involved in the scaling of entanglement entropy. We illustrate that in a nonequilibrium setting, the relaxation dynamics of classical correlation, the decay rate of total correlation, and the growth rate of entanglement entropy can be employed to uncover whether the evolving Hamiltonian and the Hamiltonian corresponding to the initial state are gapped or gapless.

Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantages on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation indicates that deep circuits are generally untrainable due to the barren plateau phenomenon, which challenges their applications. In this work, we suggest a gate-to-tensor encoding method for parametrized quantum circuits (PQCs), with which two long short-term memory networks are trained to predict both entangling capability and trainability. We call these LG networks. The remarkable capabilities of LG networks afford a statistical way to investigate the entanglement-trainability correlation of PQCs within a data set encompassing millions of generated circuits. This machine-learning-driven method first confirms the negative correlation between entanglement and trainability. Then, we observe that circuits with any values of entangling capability and trainability exist. These circuits with high entanglement and high trainability possess an appropriate high portion of nearest-neighbor nonlocal gates. Furthermore, the trained LG networks can be employed to construct PQCs with specific entanglement and trainability, demonstrating their practical applications in VQAs.

Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well known, provided that the quantum channels are completely characterized. In this work, we have studied the role played by quantum coherence in the estimation of Gaussian channel parameters. For this purpose, we start by considering an initial single-mode vacuum state where coherence is generated through displaced or/and squeezing operations. Then, we consider a probe state with two resources, the average thermal number and the quantum coherence. The results are computed using the quantum Fisher information (QFI) as well as some gain functions defined in the work. We applied the estimation protocol for two paradigmatic bosonic Gaussian channels: the thermal attenuator and the thermal amplifier. Our results show that for the vacuum initial state, coherence can be exploited to obtain a high QFI. Moreover, we can state two important facts: the first being that for a small parameter region of a channel, the QFI depends on the mechanism used to generate the coherence, while the second is that the QFI depends not only on the amount of coherence but also on how it changes as a function of the parameter to be estimated. For the probe state, including also an average thermal number, the two examples show that thermal resources are not always beneficial to the QFI and that this depends on the channel structure. For the attenuator channel, the optimal probe state is only limited by the ability to implement an average thermal number and generate an amount of coherence, while for the amplifier channel, the vacuum probe state with coherence is the optimal state. Finally, we obtain a direct relation between the quantum Fisher information and the relative entropy of coherence, allowing, in principle, an experimental verification based on the measurement of the covariance matrix of the probe system.

We consider bipartite quantum state discrimination and present a quantum data-hiding scheme utilizing an orthogonal separable state ensemble. Using a bound on local minimum-error discrimination, we provide a sufficient condition for the separable state ensemble to be used in constructing a quantum data-hiding scheme. Our results are illustrated with various examples in bipartite quantum systems. As our scheme employs separable states of low-dimensional quantum systems, it becomes more feasible for practical implementation.

We propose a scheme for realizing a deterministic two-photon controlled-$Z$ (cz) gate based on variants of the two-photon quantum Rabi model, which is feasible within the framework of circuit QED. We begin by utilizing the two-photon interaction to implement the nonlinear sign gate and subsequently we construct the cz gate following the Knill-Laflamme-Milburn scheme [Nature (London) 409, 46 (2001)]. We consider three different regimes: the strong-coupling regime, the perturbative ultrastrong-coupling regime, and the large-detuning regime. Our results indicate that the cz gate operates fast with high fidelity. We also show that the photonic state in the waveguide can be input into the circuit QED system through a variable coupler and released after interaction with almost the same waveform except for a $\pi$-phase shift. Our scheme offers a suitable approach for achieving fast and deterministic two-photon quantum gates via light-matter interactions.

We present a single-body adiabatic potential to investigate the role of virtual positronium (Ps) formation in positron scattering with atoms at energies below the Ps formation threshold. Our model is applied to positron scattering by hydrogen and noble-gas atoms. The potential is decomposed into two components: the correlation-polarization (CP) potential, derived from perturbation theory for the positron-hydrogen system and generalized for other atoms, and the virtual positronium (VPs) potential. The VPs potential is modeled as a short-ranged attractive term based on the CP component but shifted toward the atom's vicinity, with its strength controlled by a semiempirical parameter fine tuned to match the scattering length to reference values. Our results show that the inclusion of the VPs term is essential for reproducing experimental measurements and results from other theoretical models for both integrated and differential cross sections.

The discrepancy in the attosecond time delay between theory and experiment near the $3s$ Cooper minimum (CM) of Ar is addressed. It is found that inclusion of the relaxation effects in the time delay difference between Ar $3s$ and $3p$ photoionization near the $3s$ CM dramatically alters the $3s$ time delay and brings the theory into substantial agreement with experiment using the relativistic-random-phase approximation with relaxation. The key point is that $3s$ photoionization is dominated by interchannel coupling in this region and the interchannel coupling matrix elements were found to be considerably altered by the inclusion of relaxation. This implies that relaxation should be important for any atomic or molecular transition that is dominated by interchannel coupling.

It is shown that under optimal conditions the generation of the third, fifth, seventh, and ninth harmonics of the short-wave, ultraviolet or vacuum ultraviolet, laser field by helium atoms is mainly due to transitions between bound states, and the maximum energy of the harmonics is achieved under conditions of their resonant multiphoton excitation. In this case, the optima for the generation of the third, fifth, seventh, and ninth harmonics of the field correspond to three-, four-, five-, and six-photon resonances, and the optimal value of the peak field intensity, depending on the harmonic order, varies from $2.5\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ to $1.2\times {10}^{15}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The total probability of excitation and ionization of an atom at the end of a laser pulse under corresponding conditions exceeds 1/2. With such intensity and not-too-high frequency of the laser field, the Stark effect turns out to be very significant, which allows it to be tuned in resonance with an arbitrary excited state of the atom by changing the intensity of the field without changing its frequency. It is shown that for the laser field parameters maximizing the energy of the $N\mathrm{th}$ harmonic, 3 ≤ $N$ ≤ 9, this harmonic dominates in the dipole acceleration spectrum. At the same time, the amplitudes of the remaining harmonics increase as the harmonic order approaches $N$. In particular, under the conditions maximizing the yield of the ninth harmonic, the harmonic amplitudes increase when moving from the third harmonic to the fifth and then to the seventh and ninth harmonics, and the harmonics form an attosecond pulse train. At the same time, under the conditions maximizing the yield of the third harmonic, its amplitude in the dipole acceleration spectrum exceeds not only the amplitudes of the other harmonics, but also the amplitude of the atomic response at the frequency of the driving field.

We studied the characteristics, regions of existence, and stability of different types of solitons for a distributed model of a mode-locked laser whose dispersion is purely quartic and normal. Among the different types of solitons, we identified three main branches that are named according to their different amplitude: low, medium, and high amplitude solitons. It was found that the first solitons are always unstable while the latter two exist and are stable in relatively large regions of the parameter space. Moreover, the stability regions of medium and high amplitude solitons overlap over a certain range of parameters, manifesting effects of bistability. The energy of high amplitude solitons increases quadratically with their width, whereas the energy of medium amplitude solitons may decrease or increase with the width depending on the parameter region. Furthermore, we have investigated the long term evolution of the continuous-wave solutions under modulational instability, showing that medium amplitude solitons can arise in this scenario. Additionally, we assessed the effects of second- and third-order dispersion on medium and high amplitude solitons and found that both remain stable in the presence of these terms.

We present spectral measurements performed to identify the highly- forbidden electric-octupole $\left(E3\right)$ $4f_{7/2,5/2}\text{−}5s_{1/2}$ transitions in Ag-like highly charged ions and to study the $Z$ dependence of their intensities. Theoretical predictions indicate that these transitions can be observed in a narrow range of elements around tungsten $(Z=74)$, as the strong configuration interaction leads to level crossings and to an increased population of the $5s$ level. Here we probe the atomic structure and population dynamics in Ag-like ions using extreme-ultraviolet spectral measurements in several elements (Yb, Lu, W, Re, Os, Ir, Au) in the range $Z=70$ to 79. The spectra were recorded independently in the compact electron-beam ion trap at the National Institute for Fusion Science and in the electron-beam ion trap at the National Institute of Standards and Technology. The measured wavelengths and the advanced theoretical calculations confirm observations of the $E3$ transitions in Ag-like ions in the predicted narrow element range.

Detailed expressions for satellite intensities have been carefully developed, taking into account Coster-Kronig single and double spectator hole states, and shake-up and shake-off events. The energies corresponding to satellite emissions originating from $M_{4,5}$ vacancies can be classified according to their shift from the $M\alpha$ and $M\beta$ parent peaks; for the specific example of rhenium, this approach enabled to analyze the intensity ratio associated with each energy region. These satellite emission energies and intensity ratios are also obtained experimentally for rhenium, after a parameter optimization routine developed previously, applied to a set of x-ray spectra induced by electron irradiation on a solid target, and acquired by means of a wavelength-dispersive spectrometer. These experimental data are compared to those assessed from the analytical expressions derived.

High-resolution x-ray spectroscopy is an essential tool in high-energy astrophysics, astrochemistry, and x-ray astronomy, enabling detailed studies of celestial objects and their physical and chemical properties. However, comprehensive mapping of high-resolution x-ray spectra for even simple interstellar and circumstellar molecules is still lacking. In this study, we conduct systematic quantum chemical simulations to predict the $\mathrm{C}1s$ x-ray-absorption spectra of ${\mathrm{CN}}^{+}$, CN, and ${\mathrm{CN}}^{-}$. Our findings provide valuable references for both x-ray astronomy and laboratory studies. We assign the first electronic peak of ${\mathrm{CN}}^{+}$ and CN to $\mathrm{C}1s\to {\sigma }^{*}$ transitions, while the peak for ${\mathrm{CN}}^{-}$ corresponds to a $\mathrm{C}1s\to {\pi }^{*}$ transition. We explain that the twofold degeneracy (${\pi }_{xz}^{*}$ and ${\pi }_{yz}^{*}$) of the $\mathrm{C}1s\to {\pi }^{*}$ transitions results in ${\mathrm{CN}}^{-}$ exhibiting a significantly stronger first absorption compared to the other two systems. We further calculate the vibronic fine structures for these transitions using the quantum wave-packet method based on multiconfigurational-level, anharmonic potential-energy curves, revealing distinct energy positions for the 0–0 absorptions at 280.7, 279.6, and 285.8 eV. Each vibronic profile features a prominent 0–0 peak, showing overall similarity but differing intensity ratios of the 0–0 and 0–1 peaks. Notably, introducing a $\mathrm{C}1s$ core hole leads to shortened C-N bond lengths and increased vibrational frequencies across all species. These findings enhance our understanding of the electronic structures and x-ray spectra of carbon-nitrogen species, emphasizing the influence of charge state on x-ray absorptions.

Multielectron polarization (MEP) has been identified as an essential factor that must be considered for understanding nonlinear effects resulting from interactions of intense lasers with highly polarizable targets. While recent studies have mostly focused on intensity modulation induced by MEP in high-order harmonic generation (HHG), this work explores a significant MEP effect on another critical HHG feature: harmonic frequency. In particular, we discover MEP-induced frequency shifts up to 0.8 order (1.24 eV) for harmonics in the cutoff region when a polar molecule CO interacts with a few-cycle laser pulse. These frequency shifts are clarified through their relationship with the MEP-induced phase changes of attosecond bursts and then validated numerically by solving the time-dependent Schrödinger equation. Moreover, we also verify them with available experimental data. Furthermore, we demonstrate the universality of these frequency shifts regardless of varying laser parameters. Importantly, we find a close connection between the MEP-induced harmonic frequency shift discovered in this study and MEP-induced intensity modulation of odd-even HHG reported previously. We claim that they are the two manifestations of the MEP effect on HHG, both stemming from the distortion of the phase difference between the two adjacent attosecond bursts. This comprehensive understanding of the MEP effect on HHG from polar molecules is significant for characterizing intrinsic molecular properties and probing molecular dynamics from HHG.

We present evaporative cooling simulations based on the direct simulation Monte Carlo method. Our system is a 54-cm-long atom guide with reflective barriers at the beginning and the end. The atom guide is continuously loaded with thermal atoms at the beginning. We show that it is critical to control the gravity component in the guiding direction to sustain a high classical phase-space density at the end of the atom guide. Transient oscillations are observed under certain conditions.

This study investigates phase-driven symmetry breaking leading to superradiance phase transitions in cascaded non-Hermitian quantum Rabi cavities. Non-Hermiticity is introduced via the phase coupling $\phi$ between the atom and the optical field. In the thermodynamic limit of the quantum harmonic oscillator, we analytically derive the superradiance phase boundary, validated by observables. An unconventional quantum phase transition without a Hermitian analog arises when $\left|\phi \right|=\frac{\pi }{4}$ or $\frac{3\pi }{4}$, where the phase boundary is uniquely determined by the cavity coupling, at $\mathcal{J}=\frac{1}{2}$ ($\mathcal{J}$ is the ratio of the cavity coupling strength $J$ to the optical field frequency ${\omega }_p$, and $\mathcal{J}=\frac{J}{{\omega }_p}$), independent of the atom-photon coupling strength $g$. For other $\phi$, the phase boundary relies on both $\mathcal{J}$ and $g$, similar to the scenario observed in Hermitian systems. Furthermore, we identify phase-driven first- and second-order superradiance phase transitions, focusing on the quantum criticality of the second-order transition by determining the critical exponents and the universality class. The feasibility of experimental realization is also discussed, aiming to inspire further studies on non-Hermitian superradiance quantum phase transitions.

The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to estimate the unknown transition frequency. In the frequentist approach, we have shown that only reducing the distance between the classical and the quantum Fisher information does not necessarily mean that the estimators as functions of the data deliver an estimate with desirable accuracy, as the classical Fisher information takes small values. We have proposed and investigated a cost function to account for the maximization of the classical Fisher information and the minimization of the aforementioned distance. Due to the nonlinearity of the probability mass function of the data on the transition frequency, the minimum variance unbiased estimator may not exist. The maximum likelihood and the maximum a posteriori estimators often result in ambiguous estimates, which in certain cases can be made unambiguous upon changing the parameters of the external field. It is demonstrated that the minimum mean-square error estimator of the Bayesian statistics provides unambiguous estimates. In the Bayesian approach, we have also investigated the effects of noninformative and informative priors on the Bayesian estimates, including a uniform prior, Jeffrey's prior, and a Gaussian prior.

High-dimensional systems are an important frontier for photonic quantum correlation experiments. These correlation tests commonly prescribe measurements with many possible outcomes but they are often implemented through many individual binary-outcome measurements that use only a single-detector. Here, we discuss how this binarization procedure for multioutcome measurements can open a loophole, unless specific device-characterization assumptions are satisfied. We highlight that correlation tests designed for multioutcome measurements can be trivialized in binarized implementations and we then show how to accurately analyze binarized data to reveal their quantum features. For seminal types of correlation experiments, such as Bell inequality tests, steering tests and prepare-and-measure experiments, we find that binarization may incur a sizable cost in the magnitude of quantum advantages. This emphasizes the importance of both accurate data analysis and implementing genuinely multioutcome measurements in high-dimensional correlation experiments.