The generation of hybrid entangled states between matter qubits and microwave-field qubits is a fascinating area of quantum science and technology. In this work, we propose an efficient method to deterministically prepare hybrid entangled states between multiple superconducting qubits (matter qubits) and microwave-field qubits (flying qubits), by using a system composed of multiple superconducting qutrits and microwave cavities. Here, each superconducting (SC) qubit is encoded with the two lowest levels of a SC qutrit, while each microwave-field (MF) qubit is encoded using discrete-variable (DV) states (e.g., the vacuum and single-photon states) or continuous-variable (CV) states (e.g., coherent states) of a microwave cavity. Due to the nonpopulation of the qutrits' third energy level during the operation, decoherence from this level is significantly reduced. Moreover, the hybrid entangled states can be generated on a large scale. The operation time is independent of the number of SC qubits and MF qubits. Only two steps of the operation are needed for the preparation of the hybrid Greenberger-–Horne–-Zeilinger (GHZ) states as long as the initial states of the system are ready. As an example, our numerical results demonstrate that high-fidelity creation of hybrid DV-DV entangled states or CV-DV entangled states of three SC qubits and three MF qubits is feasible with current circuit QED technology. This method is universal and can be extended to generate hybrid entangled states between other matter qubits (such as atoms, ions, quantum dots, NV centers, and magnons) and microwave- or optical-field qubits.

Variational quantum eigensolvers (VQEs) are a promising approach for finding the classically intractable ground state of a Hamiltonian. The unitary block-optimization scheme (UBOS) is a state-of-the-art VQE method that works by sweeping over gates and finding optimal parameters for each gate in the environment of other gates. UBOS improves the convergence time to the ground state by an order of magnitude over stochastic gradient descent. It nonetheless suffers in both rate of convergence and final converged energies in the face of highly noisy expectation values coming from shot noise. Here we develop two classical postprocessing techniques that improve UBOS especially when measurements have large shot noise. Using Gaussian process regression, we generate artificial augmented data using original data from the quantum computer to reduce the overall error when solving for the improved parameters. Using double robust optimization plus rejection, we prevent outlying data which are atypically noisy from resulting in a particularly erroneous single optimization step, thereby increasing robustness against noisy measurements. Combining these techniques further reduces the final relative error that UBOS reaches by a factor of 3 without adding additional quantum measurement or sampling overhead. This work further demonstrates that developing techniques that use classical resources to postprocess quantum measurement results can significantly improve VQE algorithms.

We may soon see agencies offering public access to quantum communication networks. In such networks it may be a feature that certain resources are available only to priority users or at a higher user fee, as governed by a protective agency overseeing the communication in the network. If the agency wants to restrict the general users to communicate by transmitting states that we categorize as free states of a quantum resource theory (QRT), it may employ resource-destroying channels that do not affect the free states. Such channels, however, only exist for the simplest of QRTs, putting fundamental limitations on how quantum resources can be regulated. In this work, we go beyond the present limitation by devising a nonlinear censorship protocol which makes use of classical information about the transmitted state. We study the requirement disabling malicious users from breaking the censorship. The protocol can establish an unbreakable censorship of imaginarity and entanglement, while no such censorship can be made for quantum discord and Bell nonlocality.

Recent work by Mičuda et al. [Phys. Rev. Lett. 109, 180503 (2012)] suggests that pairing noiseless amplification with noiseless attenuation can conditionally suppress loss terms in the direct transmission of quantum states. Here we extend this work to entangled states: First, we explore bipartite states, specifically the two-mode squeezed vacuum and NOON states, and, second, we examine $M$-partite states, concentrating on W and Greenberger-Horne-Zeilinger (GHZ) states. In analogy with the original proposal, our results demonstrate that in each case under consideration, a correct combination of attenuation and amplification techniques before and after transmission through a pure loss channel can restore the initial quantum state. However, we find that for both W and NOON states, the noiseless attenuation is redundant and not required to achieve loss term suppression. This work clarifies the role of noiseless attenuation when paired with noiseless amplification for entanglement distribution and provides an operational example of how GHZ and W state entanglement differs.

The cost and the error of the adiabatic theorem for preparing the final eigenstate are discussed in terms of path length. Previous studies in terms of the norm of the Hamiltonian and its derivatives with the spectral gap are limited in their ability to describe the cost of adiabatic state preparation for certain physically large systems. We argue that total time is not a good measure for determining the computational difficulty of adiabatic quantum computation by developing a no-go theorem. From the result of time-periodic Hamiltonian cases, we suggest that there are proxies for computational cost which typically grow as path length increases when the error is kept fixed and small and consider possible conjectures on how general the behavior is.

Model Hamiltonians described by fermionic operators are ubiquitous in physics and chemistry, but the quantum simulation of their properties is challenging on near-term quantum computers. Indeed, for any problem with more than two connected neighbors, standard mappings of fermions on qubits lead to many-body operators whose size increases with the size of the problem, quickly making the simulation unfeasible on noisy devices. Here we consider an alternative mapping based on qudits and the auxiliary fermion method, which leads to a significant reduction in the circuit depth and in the number of computational units to be controlled. These advantages increase for highly connected target Hamiltonians, such as lattices with long-range interactions or the molecular systems investigated in quantum chemistry. We numerically test our approach on qudits encoded in molecular spins, by performing the quantum simulation of a fermionic model on a small cluster.

The vibrationally resolved gas-phase electronic photoabsorption spectrum of protonated pentacenequinone was measured at a cryogenic temperature using a combination of a cryogenically cooled ion trap and an ion-storage ring. The spectrum reveals a distinct vibrational structure, with the lowest vibrational band measured at $16912{\mathrm{cm}}^{-1}$ $\left(591.3\mathrm{nm}\right)$, assigned to the $0\to 0$ transition. Excellent agreement is observed between the measured spectrum and the spectroscopic fingerprint predicted by time-dependent density functional theory. Our results show that oxygen-functionalized polycyclic aromatic hydrocarbons of this size can absorb and exhibit a vibrational structure in regions relevant to both extended red emission and diffuse interstellar bands.

Within a joint experimental and theoretical research project, single photoionization of He-like ${\mathrm{B}}^{3+}$ ions was investigated in the energy range from approximately 250 to 1200 eV. With the parent-ion beam in the experiment containing both $1s^2{}^{1}S$ ground-state and $1s2s{}^{3}S$ metastable ${\mathrm{B}}^{3+}$ ions, double-core-hole resonances could be studied. Two series of hollow resonant states were observed, one populated by $K$-shell double excitation $1s^2{}^{1}S\to 2\ell n{\ell }^{\prime }{}^{1}P$ ($\ell =s,p$; ${\ell }^{\prime }=p,s$; $n=2,3,\cdots ,6$) at photon energies up to about 510 eV, the other by $K$-shell single excitation $1s2s{}^{3}S\to 2\ell n{\ell }^{\prime }{}^{3}P$ ($\ell =s,p$; ${\ell }^{\prime }=p,s$; $n=2,3,\cdots ,6$) at energies up to about 310 eV. High resolving powers up to approximately $29000$ were achieved. The relativistic many-body perturbation theory was employed to determine level-to-level cross sections for $K$-shell excitation with subsequent autoionization. The resonance energies were calculated with inclusion of electron correlation and radiative contributions. The energy uncertainties of the most prominent resonances are estimated to be below $\pm 1\mathrm{meV}$. Convergent close-coupling (CCC) calculations provided single-photoionization cross sections ${\sigma }_{34}$ for ${\mathrm{B}}^{3+}$ including the resonant and nonresonant channels. Apart from the resonances, ${\sigma }_{34}$ is dominated by direct ionization in the investigated energy range. The contribution ${\sigma }_{34}^{\mathrm{dir}}$ of the latter process to ${\sigma }_{34}$ was separately determined by using the random-phase approximation with exchange and relativistic Hartree-Fock calculations which agree very well with previous calculations. Direct ionization of one electron accompanied by excitation of the remaining electron was treated by the CCC theory and found to be a minor contribution to ${\sigma }_{34}$.

The oscillating magnetic field produced by unbalanced currents in radio-frequency ion traps induces transition frequency shifts and sideband transitions that can be harmful to precision spectroscopy experiments. Here, we describe a methodology, based on two-photon spectroscopy, for determining both the strength and direction of rf-induced magnetic fields without modifying any dc magnetic bias field or changing any trap rf power. The technique is readily applicable to any trapped-ion experiment featuring narrow linewidth transitions.

A detailed investigation of the radio-frequency-induced oscillating magnetic field in a laboratory ${}^{40}\mathrm{Ca}^{+}$-ion optical clock was conducted using the Autler-Townes (AT) splitting and Zeeman precession methods. It was determined that the corresponding relative second-order Zeeman shifts are below $1\times {10}^{-20}$. By accounting for the quadratic Zeeman shift caused by the oscillating magnetic field, we accurately determined the Landé $g$-factor ratio of $D_{5/2}$ and $S_{1/2}$ states, $g_D/g_S$, to be 0.599 488 79(2). Moreover, we proposed a technique to determine the oscillating magnetic field by evaluating the variation of the measured Landé $g$-factor. This methodology can be easily utilized to determine the oscillating magnetic field in transportable trapped ion optical clocks.

Quantum spin models with a large number of interaction partners per spin are frequently used to describe modern many-body quantum optical systems such as arrays of Rydberg atoms, atom-cavity systems, or trapped ion crystals. For theoretical analysis the mean-field (MF) ansatz is routinely applied. However, besides special cases of all-to-all or strong long-range interactions, the MF ansatz provides only approximate results. Here we present a systematic correction to MF theory based on diagrammatic perturbation theory for quantum spin correlators in thermal equilibrium. Our analytic results are universally applicable for any lattice geometry and spin-length $S$. We provide precomputed and easy-to-use building blocks for Ising, Heisenberg and transverse field Ising models in the symmetry-unbroken regime. We showcase the quality and simplicity of the method by computing magnetic phase boundaries and excitations gaps. We also treat the Dicke-Ising model of ground-state superradiance where we show that corrections to the MF phase boundary vanish.

We investigate phase transitions of the ground state (GS) of spin-1 Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC) and gradient magnetic field. Introducing appropriate raising and lowering operators, we exactly solve the linear system. Analyzing the obtained energy spectrum, we conclude that simultaneous variation of the magnetic-field gradient and SOC strength leads to the transition of excited states into the GS. As a result, any excited state can transition to the GS, at appropriate values of the system's parameters. The nonlinear system is solved numerically, showing that the GS phase transition, similar to the one in the linear system, still exists under the action of the repulsive nonlinearity. In the case of weak attraction, a mixed state appears near the GS transition point, while the GS transitions into an edge state under the action of strong attractive interaction.

The functional determinant approach (FDA) is a simple method to compute exactly certain observables for ideal quantum systems and has been successfully applied to the Fermi polaron problem to obtain the dynamical overlap and spectral function. Unfortunately, its application to bosonic ultracold gases is prohibited by the failure of the grand canonical ensemble for these systems. In this paper we show how to circumvent this problem and develop a bosonic FDA. This yields exact injection and ejection spectra for ideal Bose polarons at arbitrary temperatures. While coherent features visible at absolute zero quickly smear out with rising temperature as expected, the linewidth of the main peak is, counterintuitively, found to decrease near unitarity. Furthermore, we provide explicit formulas for the overlap operator, which allow us to compute the necessary determinants for both Bose and Fermi polarons more efficiently than previously possible.

We investigate the formation of steady states in one-dimensional Bose-Einstein condensates of repulsively interacting ultracold atoms loaded into a quasiperiodic potential created by two incommensurate periodic lattices. We study the transformations between linear and nonlinear modes and describe the general patterns that govern the birth of nonlinear modes emerging in spectral gaps near band edges. We show that nonlinear modes in a symmetric potential undergo both symmetry-breaking pitchfork bifurcations and saddle-node bifurcations, mimicking the prototypical behaviors of symmetric and asymmetric double-well potentials. The properties of the nonlinear modes differ for bifurcations occurring below and above the mobility edge. In the generic case, when the quasiperiodic potential consists of two incommensurate lattices with a nonzero phase shift between them, the formation of localized modes in the spectral gaps occurs through a cascade of saddle-node bifurcations. Because of the analogy between the Gross-Pitaevskii equation and the nonlinear Schrödinger equation, our results can also be applied to optical modes guided by quasiperiodic photonic lattices.

We predict a type of three-dimensional spatiotemporal solitons, or light bullets, in an active metamaterial of randomly dispersed graphene nanoflakes embedded within an optically pumped gain medium (rhodamine 6G). Adopting a generalized nonlinear Schrödinger equation governing optical propagation in such a system, we find that, depending on the external pumping conditions and graphene flake density, these spatiotemporal solitons appear in a wide variety of shapes ranging from inverted toplike objects to vortex tori, supported by the complex nonlinearity of the metamaterial. We uncover their domain of existence by tuning the gain coefficient of rhodamine 6G, finding fundamental and vortex light bullets with distinct topological charges. We further discover that the spatiotemporal profiles and instability gain of the bullets unambiguously correspond to the graphene nanoflakes' volume density and gain coefficient of the active component. Our results provide a route towards the manipulation of three-dimensional spatiotemporal solitons in an easy-to-fabricate metamaterial.

Topological photonics has shown great potential in optical device design, particularly in the development of topological lasers. However, existing research primarily focuses on single topological phases, failing to fully exploit the advantages of multiple topological phases. Conventional cladding-type topological lasers require an interface between topological distinct crystals, with one acting as cladding, which reduces area efficiency. This paper explores single-mode lasing properties of a double-layer hexagonal photonic crystal structure, highlighting both the ideal quantum spin Hall (IQSH) phase and spin higher-order (SHO) phase. In the IQSH phase, the robust waveguide design eliminates the need for a cladding layer, enhancing area efficiency compared to previous models. Additionally, incorporating pendant sites further amplifies lasing intensity by flattening the band structure. In the SHO phase, boundary dispersion splits, forming corner states with antisymmetric or symmetric properties that determine the final lasing mode, providing greater tunability compared to previous higher-order topological lasers. This paper advances the theoretical understanding of nonlinear and non-Hermitian physics in topological phases and optimizes the size and power efficiency of topological lasers, paving the way for multifunctional laser devices and practical photonic applications.

Nonlinear quantum systems behave radically different from their linear counterparts and obstructions, identified as separatrix crossing and bifurcations in the phase space, can prevent their efficient control by standard approaches using adiabatic passage. We provide the exact resonant solution by solving the time-dependent nonlinear Schrödinger equation in terms of a Jacobi elliptic integral, interpreting the dynamics with the motion of a planar pendulum. This is referred to as nonlinear Rabi oscillation, which shows an obstruction to complete population transfer above a certain critical value of the nonlinearity strength, corresponding to an oscillating regime of the pendulum. Below this threshold, the so-called $2K$ pulse induces a complete population transfer, associated with a rotating regime of the pendulum, and representing the nonlinear counterpart of the $\pi$ pulse. We next propose a fast, robust, and high-fidelity control technique by a two-stage optimal inverse engineering strategy. It consists in dynamically compensating (diagonal) third-order nonlinearities, referred to as inverse linearization, combined with robust inverse optimization (RIO) developed for linear systems. We show that a moderate nonlinearity strength dramatically improves robustness.

We study a Kerr-modified cavity magnomechanical system with a focus on its bistable regime. We identify a distinct parametric condition under which bistability appears, featuring two stable branches and one unstable branch in the middle. Interestingly, our study reveals a unique transition where the upper branch loses its stability under a sufficiently strong drive, giving rise to limit cycle oscillation. Consequently, we report a rich phase diagram consisting of both bistable and periodic solutions and study the quantum correlations around them. While in the bistable regime, we find the entanglement reaching a different steady state, and in the unstable regime, entanglement oscillates in time. This study is especially important in understanding quantum entanglement at different stable and unstable points arising in a Kerr-modified cavity magnomechanical system.

Temporal ghost diffraction (TGD) is observed by taking two-photon cross-correlation in the configuration of reciprocal two-slit diffraction where interference fringes develop on the light source side as opposed to the detector side. To this end, a narrow-band chaotic light source and a gated detector are used in the frequency-time domain, which emulate a randomly pointing incoherent light source and a stationary pinhole detector in the momentum-space domain, respectively. Spectral fringes with a signed visibility that closely follows a sinc function of the spectral bandwidth are clear evidence that legitimate TGD fringes due to two-photon interference have developed. This compares with the previous attempt [M. Bellini et al., Phys. Rev. Lett. 90, 043602 (2003)] that is essentially “ghost imaging of spectral fringes” to be distinguished from TGD, which implies that the putative GD reports in the literature might demand a revision in terms of their physical insights.

In this paper, we explore the vibrational behavior of bound-state envelopes on the $Q$-switched mode-locking (QML) spectrum and propose the concept of bound-state-like. We demonstrate an erbium-doped fiber laser using a saturable absorber and nonlinear polarization rotation to generate bound-state-like QML. Numerical simulations based on the coupled Ginzburg-Landau equations solved by the fourth-order Runge-Kutta method support the experimental results. The bound-state-like QML evolution patterns with gain- or polarization-state variations in both experiments and simulations. Our results deepen the understanding of QML pulses in mode-locked fiber lasers and provide a foundation for studying mode-locking nonlinear evolutionary paths and $Q$-switched behavior.