Two main challenges preventing efficient training of variational quantum algorithms and quantum machine learning models are local minima and barren plateaus. Typically, barren plateaus are associated with deep circuits, while shallow circuits have been shown to suffer from suboptimal local minima. We point out a simple mechanism that creates exponentially many low-quality local minima specifically in the barren plateau regime. These local minima are trivial solutions that optimize only a few terms in the loss function, leaving the rest on their barren plateaus. More precisely, we show the existence of approximate local minima, optimizing a single loss term, and conjecture the existence of exact local minima, optimizing only a logarithmic fraction of all loss function terms. One implication of our findings is that many, if not most, regions with large gradients are vicinities of poor local minima. This highlights additional challenges in finding efficient initialization strategies.

Quantum networks promise an unprecedented leap in semi-device-independent communication and security by capitalizing on quantum steering. However, current methods for assessing quantum network steering are constrained to specific cases. In this work, we introduce the network-Clauser-Horn-Shimony-Holt-like inequality for investigating network steering independent of entanglement source characteristics. We employ this inequality to detect full network steering in both single-node and multinode repeater networks and assess the tolerance of various noise models. Under a specific noise model, our method is used to compute the bound of semi-device-independent communication distance. Through case studies, we also demonstrate that our method, as a semi-device-independent entanglement witness, is more suitable for settings requiring Bell measurements compared to network Bell inequality. These findings open new avenues for broader ways to detect quantum steering independent of entanglement sources.

One of the most important topics in quantum scientific computing is solving differential equations. In this paper, a generalized quantum functional expansion (QFE) framework is proposed. In the QFE framework, a functional expansion of the solution is encoded into a quantum state and the time evolution of the quantum state is solved with variational quantum simulation (VQS). The quantum functional encoding supports different numerical schemes of functional expansions. If the solution space is infinite-order differentiable, the lower bound of the required number of qubits under the quantum function encoding scheme is the double logarithm of the inverse error bound. Furthermore, a parallel Pauli operation strategy is proposed to significantly improve the scalability of VQS. The number of circuits in VQS is exponentially reduced to only the quadratic order of the number of ansatz parameters. Four example differential equations are solved to demonstrate the generic QFE framework.

A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approach to capture the ground state of the nonlinear Schrödinger equation for a range of parameters on real superconducting quantum processors. Specifically, we study the expressivity of real-amplitude, hardware-efficient Ansatz to capture the ground state of this nonlinear system across various interaction regimes and implement different noise scenarios in both simulators and cloud processors. Our investigation reveals that although quantum hardware noise impairs the evaluation of the energy cost function, certain small instances of the problem consistently converge to the ground state. We test and demonstrate a variety of cases on IBM Q superconducting devices and analyze the discrepancies in the energy cost function evaluation due to quantum hardware noise. These discrepancies are absent in the state fidelity estimation because of the shallow state preparation circuit. Our comprehensive analysis offers valuable insights into the practical implementation and advancement of the variational algorithms for nonlinear problems.

We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule based on the number of simultaneously active qubits and prove that an optimal measurement schedule corresponds to a path decomposition of minimal width. Our analysis shows that approximating the spatial cost of a graph is NP-hard, while for graphs with bounded spatial cost, we establish an efficient algorithm for computing an optimal measurement schedule.

Recent advances in generating light in specific quantum states facilitate new sensing applications and enhance or revitalize established measurement and sensing techniques. Stimulated Raman spectroscopy (SRS), a measurement modality based on Raman scattering, could benefit from tuning the quantum properties of the pump and the Stokes lights or the properties of quantum states of the stimulating and excitation fields. Additionally, this modality could also benefit from field enhancement accompanied by plasmon excitation in the surface regions of metal nanoparticles. We present a theoretical investigation of stimulated Raman scattering involving squeezed states of light. The concept of surface- and quantum-enhanced stimulated Raman scattering is introduced. Furthermore, expressions for the respective SRS transition rates are derived, and their dependence on the quantum states of the optical field is discussed, with particular emphasis on the squeezing parameters characterizing these states. For cases involving surface enhancements, we also employ classical computational electrodynamics to guide our exploration of atomically large systems that support plasmon excitation.

The Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory of Casimir forces predicts a repulsion between two material surfaces separated by a third medium with an intermediate dielectric function. This DLP repulsion paradigm constitutes an important example with many applications. We show here that it is broken when the surfaces interact across salted water due to the nonlocal response of the ions in solution. We consider the interaction between silica and gold and show that the zero-frequency contribution, which is the only one affected by the nonlocal response, is dominant for distances in the range near 100 nm and beyond. As a result, the total Casimir force between gold and silica surfaces in salted water is always attractive in spite of the DLP repulsion paradigm.

We report observation of multi-THz quantum beats in the amplitude of superfluorescence in pure argon gas, using a time delayed 780-nm probe beam that interrogates the relevant population densities. The superfluorescence is induced by three-photon absorption of an ultrashort 260.5-nm laser pulse that creates coherent and coupled populations in multiple closely spaced $3d$ and $5s$ Ar levels. Argon pressure and pump laser focusing parameters are seen to modify the frequency of the quantum beats, which is attributed to the absorption of the self-generated, nonresonant third harmonic of the pump from Ar near the zero of the real part of the overlapping linear susceptibilities of the closely spaced $3d$ and $5s$ excited states. The self-absorption of the phase-matched THG photons creates a coherent population of atoms which acts like an atomic excited state ($3\omega$-induced state). We have also observed a new two-step superfluorescent cascade that results from the population redistribution enabled by the 780-nm probe pulse between the $3d^{\prime }{\left[5/2\right]}_3$ and the $3\omega$-induced state and gives rise to a previously unknown transition that emits on 1587 nm.

Tunnel ionization (TI) underlies many important ultrafast processes, such as high-harmonic generation and strong-field ionization. Among the existing theories for TI, many-electron weak-field asymptotic theory (ME-WFAT) is by design capable of accurately treating many-electron effects in TI. An earlier version of ME-WFAT relied on an accurate representation of the asymptotic tail of the orbitals, which hindered its implementation in Gaussian-basis-set-based quantum chemistry programs. In this work, we reformulate ME-WFAT in the integral representation, which makes the quality of the asymptotic tail much less critical, hence greatly facilitating its implementation in standard quantum chemistry packages. The integral reformulation introduced here is therefore much more robust when applied to molecules with arbitrary geometry. We present several case studies, among which is the CO molecule where some earlier theories disagree with experiments. Here we find that ME-WFAT produces the largest ionization probability when the field points from C to O, as experiments suggest. An attractive feature of ME-WFAT is that it can be used with various types of multielectron methods whether of density functional [I. S.Wahyutama et al., Phys. Rev. A 106, 052211 (2022)] or multiconfiguration types, this in turn facilitates tunnel ionization calculation in systems exhibiting a strong multireference character.

Photodissociation cross sections of ${\mathrm{SiH}}^{+}$ have been explored within the uncoupled theoretical framework, notably in the work of Stancil et al. [Astrophys. J. 486, 574 (1997)]. However, in the ${\mathrm{SiH}}^{+}$ system, there are significant nonadiabatic interactions between the $3{}^1\mathrm{\Pi }$ and $4{}^1\mathrm{\Pi }$ states, which substantially affect the photodissociation process, particularly in the region between the Lyman $\alpha$ line and the Lyman limit. These nonadiabatic couplings give rise to numerous Feshbach resonances, significantly altering the final photodissociation cross sections. The present study highlights the critical importance of incorporating nonadiabatic electronic couplings to achieve accurate cross-section calculations. The results substantially enrich the data set on small molecular structures and spectra in interstellar clouds, providing essential theoretical support for future experimental investigations and for the modeling and analysis of stellar spectra. Additionally, this work offers key insights into the underlying physical mechanisms by which Feshbach resonances modulate line shapes in coupled photodissociation scattering cross sections.

We study the dynamics of vortices in a Bose-Einstein condensate within a rotating four-site lattice, which can be effectively described by a multimode model. Such a vortex dynamics develops along the low-density paths that separate the sites, and it is ruled by the phase differences between them. Hence, by appropriately selecting the initial conditions for on-site populations and phase differences, one can access distinct types of evolutions. We show that, by choosing equal populations in alternate sites, one can construct two-mode model Hamiltonians, which allows us to model a large variety of associated vortex orbits. In particular, one can select the type of trajectory of the vortex and predict the creation and annihilation of vortex-antivortex pairs near the trap center. Estimates for the periods of closed vortex orbits and for the times that the vortices spend inside the lattice when dealing with open orbits, are obtained in terms of the two-mode models parameters and the rotation frequency only. We believe that the present study establishes a suitable platform to engineer different vortex dynamics.

In this work we investigate the single-photon transport through two whispering-gallery resonators (WGRs) coupled to a one-dimensional waveguide. Using the Green's-function formalism, we compute the transmission spectra and the photonic density of states for the stationary states. We also obtain the formation of two types of bound states in the continuum (BICs). The first kind is localized in the WGR and is symmetry-protected BICs. In contrast, the second depends on the distance between resonators through the waveguide and is of the Fabry-Pérot kind. These BICs are represented as Dirac $\delta$ functions in the local density of states. Additionally, we show that quasi-BICs manifest as sharp resonances in photonic transmission due to small symmetry-breaking perturbations. Furthermore, we investigate the dynamics of a single-photon wave packet interacting with the WGRs and analyze the mechanism for storing the wave packet in the structure formed by the WGRs and the finite waveguide between them.

Exploring intermixing and interplay between different frequency-mixing processes has always been one of the interesting subjects at the interface of nonlinear optics with quantum optics. Here we investigate coherent competition and control between three-wave mixing (TWM) and four-wave mixing (FWM) in a cyclic $\mathrm{\Delta }$-type three-level superconducting quantum system. In the weak control-field regime, strong competition leads to an alternating oscillation between TWM and FWM signals and this oscillation is a signature of strong energy exchange between these two nonlinear processes. In particular, such oscillation is absent from conventional multiwave mixing in atomic systems. Surprisingly, synchronous TWM and FWM processes are demonstrated in the strong control-field regime and, at the same time, their efficiencies can be as high as 42 and 47%, respectively. Our paper shows that these competitive behaviors between TWM and FWM can be manipulated by tuning the control-field intensity.

In this work, we explore the superradiant behavior of two Dicke models mechanically coupled through a shared vibrating membrane. Using a variational mean-field approach, we analyze the system's critical behavior and derive analytical expressions that reveal a threshold for the mechanical coupling. Below this threshold, the system allows for higher atomic-radiation couplings before resonant damping occurs, thereby extending the superradiant region compared to a single-cavity optomechanical Dicke model. Additionally, we examine the behavior of relevant observables across all regions of the phase diagram. Our findings suggest that these observables provide a more accurate characterization of the system's critical behavior than the traditionally used coupling parameters.

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a framework, nonadiabatic quantum optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered nonintegrable model.

Understanding the relationship between various different forms of nonclassicality and their resource character is of great importance in quantum foundation and quantum information. Here we discuss a quantitative link between quantum entanglement and the anomalous or nonclassical nonreal values of Kirkwood-Dirac (KD) quasiprobability in a bipartite setting. We first construct an entanglement monotone for a pure bipartite state based on the nonreality of the KD quasiprobability defined over a pair of orthonormal bases, in which one of them is a product, and optimizations over these bases. It admits a closed expression as a Schur concave function of the state of the subsystem having a form of nonadditive quantum entropy. We then construct a bipartite entanglement monotone for generic quantum states using the convex roof extension. Its normalized value is upper bounded by the concurrence of formation, and for two-qubit systems, they are equal. We also derive lower and upper bounds in terms of different forms of uncertainty in the subsystem quantified by an extremal trace-norm asymmetry and a nonadditive quantum entropy, respectively. The entanglement monotone can be expressed as the minimum total state disturbance due to a nonselective local binary measurement. Finally, we discuss its estimation using weak value measurement and classical optimization, and its connection with strange weak value and quantum contextuality.

Quantum teleportation is a fundamental ingredient for quantum information science and technology. In particular, the ability to perform quantum teleportation between quantum systems with different natures and encoding types is crucial for building complex systems, such as a distributed quantum internet. Here we propose a scheme to teleport a continuous-variable optical qubit, encoded in an optical qumode by means of a superposed coherent state, onto a discrete-variable solid-state qubit, associated with a single nitrogen-vacancy-center spin in diamond, via hybrid entanglement. By using a newly developed method for Bell-state measurement which relies only on light homodyne detection and spin-polarization measurement, near-deterministic and -perfect quantum teleportation can be achieved for large coherent-state amplitude input. Taking noise effects into account, we find that the average teleportation fidelity can still exceed the classical limit, enabling substantial teleportation distances under realistic experimental conditions.

We study the ground-state phase diagram of a non-Hermitian cluster-$XY$ spin chain in the language of free fermions. By calculating the second derivative of ground-state energy density and various types of order parameters, we establish the global ground-state phase diagram of the model, exhibiting rich quantum phases and corresponding phase transitions. Specifically, the results reveal that the non-Hermitian cluster-$XY$ model contains five different phases and two critical regions, i.e., ferromagnetic (FM), antiferromagnetic (AFM), symmetry-protected topological (SPT), paramagnetic (PM), Luttinger liquid-like phase, as well as critical regions I and II. The order parameters and critical behaviors are investigated and the correctness of the theory is confirmed.

Bound states in the continuum (BICs) have interesting properties and important applications in photonics. A particular class of BICs are found in Fabry-Perot (FP) cavities formed by two parallel periodic dielectric layers separated by a distance $h$. A periodic dielectric layer can totally reflect a plane incident wave with a particular frequency and a particular wave number. Existing FP-BICs are found when $h$ is close to the values deduced from a phase-matching condition related to the reflection coefficient, but they are obtained in FP cavities where the periodic layers have a reflection symmetry in the periodic direction. In this paper, we further clarify the connection between total reflections and FP-BICs. Our numerical results indicate that if the wave number is zero or the periodic layers have a reflection symmetry in the periodic direction, FP-BICs can indeed be found near the parameters of total reflections. However, if the wave number is nonzero and the periodic layer is asymmetric (in the periodic direction), we are unable to find a FP-BIC (with a frequency and a wave number near those of a total reflection) by tuning $h$ or other structural parameters. Consequently, a total reflection does not always lead to a FP-BIC even when the parameters of the FP cavity are tuned.