In this paper, we investigate photon-photon scattering in vacuum in the head-on collision of an optical laser and an x-ray free-electron laser (XFEL) of multiple modes. For the XFEL as probe light with focus waist larger than the optical laser, the scattering photons with the same energy of the initial probe XFEL can be separated from the XFEL background due to the different scattering angle at far field. Here, we study the effect of XFEL's transverse profile, due to superposition of modes, in this vacuum diffraction process. Based on the parameters of upcoming facilities with 100-PW optical lasers and intense XFEL, we show that for a given photon number of the probe XFEL, the separable scattering photon number can be greatly enhanced when the XFEL is composed of different Laguerre-Gaussian modes. As an example, with SHINE's setup there will be 185 photons separable from the XFEL background for each shot, which is 2.5 times that of the case with the usual Gaussian profile.

Random quantum states and operations are of fundamental and practical interests. In this paper, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random controlled-Z (CZ) and controlled-controlled-Z (CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law but greatly differ in typicality, namely, the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos.

Quantum computers can provide solutions to certain classically intractable problems. However, current devices have limited computational resources, and an effort is made to develop useful quantum algorithms under this constraint. This work demonstrates experimentally that a single-qubit processor can host a universal classifier based on the re-uploading scheme. The quantum processor used in this work is built with an ion trap, providing highly accurate control on a one-qubit system as required by the re-uploading scheme. A set of nontrivial classification tasks are completed successfully. The training procedure is performed in two steps combining simulation and experiment. Final results are benchmarked against exact simulations of the same method and also classical algorithms, showing a competitive performance of the ion-trap quantum classifier. This work constitutes the experimental implementation of a classification algorithm based on the re-uploading scheme.

We introduce high-order harmonic sideband spectroscopy and show that it can be a robust probe of charge migration (CM) in a halogenated carbon-chain molecule. We simulate both the CM and high-order harmonic generation (HHG) dynamics using ab initio time-dependent density-functional theory. We find that CM dynamics initiated along the molecular backbone induces sidebands in the HHG spectrum driven by a delayed laser pulse that is polarized perpendicular to the molecular axis. Monitoring the spectrum as either the HHG laser frequency or the relative delay is scanned allows for the extraction of detailed information about the time-domain characteristics of the CM process.

High-order above-threshold ionization is studied theoretically beyond the electric dipole approximation. A hydrogen atom is assumed exposed to an ultrashort linearly polarized laser pulse with a central wavelength of 800 nm. The photoelectron momentum distribution from the corresponding nondipole multiphoton ionization process is calculated by means of numerical simulations with the time-dependent Schrödinger equation. In agreement with recent experiments as well as previous theoretical predictions, a forward-backward asymmetry with respect to the light propagation direction is revealed in the resulting momentum spectrum. Investigating separately the role of the linear and quadratic laser-matter interaction terms, i.e., the terms in the system Hamiltonian that are linear and quadratic in the laser's vector potential $\mathit{A}$, respectively, it is found that the linear term introduces a shift of the electron momentum distribution in the laser propagation (forward) direction whereas the quadratic term is responsible for a corresponding backward shift. Nevertheless, only their net effect is observed in the final spectrum, and the quadratic contribution is shown to be responsible for the experimentally observed backward shift of the distribution for small electron momenta. Furthermore, for higher electron momenta it is found that the linear term takes over as the leading source of beyond-dipole ionization, effectively shifting the distribution in the forward direction.

The question of whether the topological insulators can host a stable nontrivial phase in the presence of spatially correlated disorder is a fundamental question of interest. Based on theoretical investigations, we analyze the effect of random-dimer disorder on the quantum phase transitions of the Su-Schrieffer-Heeger model. We explicitly demonstrate that, due to the absence of symmetry, there are no in-gap edge states in certain disordered topological nontrivial gapped phases and the bulk-boundary correspondence breaks down. However, the fractionalized end charges still appear at the ends of the chain. The energy distribution possibility of the in-gap edge states and the possible values of fractionalized end charges are dependent on the concentration of random-dimer disorder. On the other hand, random-dimer disorder and dimer hopping intertwine in an interesting manner. Reentrant localization transition behavior appears, which is evidenced by the fingerprint of the inverse participation ratio, normalized participation ratio, and tunneling conductivity.

Over the past two decades, many studies in the density functional theory context revealed new aspects and properties of strongly correlated superfluid quantum systems in numerous configurations that can be simulated in experiments. This was made possible by the generalization of the local density approximation to superfluid systems by Bulgac [Phys. Rev. C 65, 051305(R) (2002); Phys. Rev. A 76, 040502(R) (2007)]. In the present work, we propose an extension of the superfluid local density approximation, systematically improvable and applicable to a large range of many-body quantum problems getting rid of the fitting procedures of the functional parameters. It turns out that only the knowledge of the density dependence of the quasiparticle properties, namely, the chemical potential, the effective mass, and the pairing gap function, are enough to obtain an explicit and accurate local functional of the densities without any adjustment a posteriori. This opens the way toward an effective field theory formulation of the density functional theory in the sense that we obtain a universal expansion of the functional parameters entering in the theory as a series in pairing gap function. Finally, we discuss possible applications of the developed approach allowing precise analysis of experimental observations. In that context, we focus our applications on the static structure properties of superfluid vortices.

Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance frequencies of these modes cluster in different orders. A nonparaxial vector theory predicts that the frequency degeneracy within these clusters is lifted, such that each order acquires a spectral fine structure, comparable to the fine structure observed in atomic spectra. In this paper, we calculate this fine structure for microcavities and show how it originates from various nonparaxial effects and is codetermined by mirror aberrations. The presented theory, which applies perturbation theory to Maxwell's equations with boundary conditions, proves to be very powerful. It generalizes the effective one-dimensional description of Fabry-Perot cavities to a three-dimensional multi-transverse-mode description. It thereby provides physical insights into several mode-shaping effects and a detailed prediction of the fine structure in Fabry-Perot spectra.

An optical field will undergo coherent diffusion when it is mapped into thermal-motioned atoms, e.g., in a slow or storage light process. As has been demonstrated before, such a diffusion effect is equivalent to a spatial low-pass filter attenuating the high-spatial-frequency (SF) components of the optical field. Here, employing electromagnetically induced transparency (EIT)-based light storage in hot atomic vapor, we demonstrate that the angular deviation between the control and the probe beams could be utilized as a degree of freedom to modulate the SF of the probe beam. The principle is to change the diffusion-induced low-pass filter into a bandpass filter, whose SF response can be tuned by varying the direction and magnitude of the angular deviation. Transverse multimode light fields, such as optical images and Laguerre-Gaussian modes, are utilized to study such SF modulation. Our findings could be broadly applied to the fields of quantum information processing, all-optical image manipulation, and imaging through diffusive media.

We study a model of a quantum collective spin weakly coupled to a spin-polarized Markovian environment and find that the spectrum is divided into two regions that we name normal and exceptional Liouvillian spectral phases. In the thermodynamic limit, the exceptional spectral phase displays the unique property of being made up exclusively of second-order exceptional points. As a consequence, the evolution of any initial density matrix populating this region is slowed down and cannot be described by a linear combination of exponential decays. This phase is separated from the normal one by a critical line in which the density of Liouvillian eigenvalues diverges, a phenomenon analogous to that of excited-state quantum phase transitions observed in some closed quantum systems. In the limit of no bath polarization, this criticality is transferred onto the steady state, implying a dissipative quantum phase transition and the formation of a boundary time crystal.

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, to survive the transition and to remain in the first level, does not depend on whether or not the second level is broadened [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)]. In other words, the seminal Landau-Zener result applies regardless of the broadening of the second level. The same question for the multistate Landau-Zener transition is addressed in the present paper. While for integrable multistate models, where the transition does not involve interference of the virtual paths, it can be argued that the independence of the broadening persists, we focus on nonintegrable models involving interference. For a simplest four-state model, which allows an analytical treatment, we demonstrate that the decay of the excited states affects the survival probability provided that the widths of the final states are different.

We introduce a numerical method to determine the Hamiltonian of mean force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the time evolving matrix product operator (TEMPO) algorithm to imaginary-time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.

The hybrid quantum system in which interactions between superconducting (SC) qubits and atomic qubits are mediated by an auxiliary cavity mode is a promising architecture for quantum information processing. However, compared to the strong coupling $g_1$ between the SC qubits and the cavity, the coupling $g_2$ between the atomic qubits and the cavity is often extremely weak, which limits the operation speed and suffers more from dissipations. Here we propose a built-in fault-tolerant geometric operation to speed up the generation of entanglement between SC qubits and atomic qubits only by linearly driving the qubits. The operation speed is proportional to $\sqrt{g_1{g}_2}$ instead of the weaker coupling $g_2$. Comparing with traditional double-swap method, the speedup can reach around 10 times and the fidelity keeps high under current experimental parameters. This speedup technique can be used in various boson-mediated quantum platforms even if parametric driving or modulation of the boson mode is impossible, enabling exploration of fast quantum information processing.

Discriminating between quantum states is a fundamental task in quantum information theory. Given two quantum states ${\rho }_{+}$ and ${\rho }_{-}$, the Helstrom measurement distinguishes between them with minimal probability of error. However, finding and experimentally implementing the Helstrom measurement can be challenging for quantum states on many qubits. Due to this difficulty, there is great interest in identifying local measurement schemes which are close to optimal. In the first part of this work, we generalize previous work by Acin et al. [Phys. Rev. A 71, 032338 (2005)] and show that a locally greedy scheme using Bayesian updating can optimally distinguish between any two states that can be written as a tensor product of arbitrary pure states. We then show that the same algorithm cannot distinguish tensor products of mixed states with vanishing error probability (even in a large subsystem limit), and introduce a modified locally greedy scheme with strictly better performance. In the second part of this work, we compare these simple local schemes with a general dynamic programming approach which finds both the optimal series of local measurements as well as the optimal order in which subsystems are measured.

We revisit the application of neural networks to quantum state tomography. We confirm that the positivity constraint can be successfully implemented with trained networks that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard neural-network architecture can be adapted with our method. Our results open possibilities to use state-of-the-art deep-learning methods for quantum state reconstruction under various types of noise.

We investigate theoretically the ultimate resolution that can be achieved with passive remote sensing in the microwave regime used, e.g., on board of satellites observing Earth, such as the soil moisture and ocean salinity (SMOS) mission. We give a fully quantum mechanical analysis of the problem, starting from thermal distributions of microscopic currents on the surface to be imaged that lead to a mixture of coherent states of the electromagnetic field which are then measured with an array of antennas. We derive the optimal detection modes and measurement schemes that allow one to saturate the quantum Cramér-Rao bound for the chosen parameters that determine the distribution of the microscopic currents. For parameters comparable to those of SMOS, a quantum enhancement of the spatial resolution by more than a factor of 20 should be possible with a single measurement and a single detector, and a resolution down to the order of 1 m and less than a $\frac{1}{10}$ K for the theoretically possible maximum number of measurements.

We propose a method based on compressed sensing (CS) to measure the evolution processes of the states of a driven cavity quantum electrodynamics system. In precisely reconstructing the coherent cavity-field amplitudes, we have to prepare the same states repetitively and each time perform one measurement with short sampling intervals considering the quantum nature of the measurement and the Nyquist-Shannon sampling theorem. However, with the help of CS, the number of measurements can be exponentially reduced without loss of the recovery accuracy. We use largely detuned atoms and control their interactions with the cavity field to modulate coherent state amplitudes according to the scheme encoded in the sensing matrix. The simulation results show that the CS method efficiently recovers the amplitudes of the coherent cavity field even in the presence of noise.

Besides the intrinsic noise resilience property, nonadiabatic geometric phases are of the fast evolution nature, and thus can naturally be used in constructing quantum gates with excellent performance, i.e., the so-called nonadiabatic geometric quantum computation (NGQC). However, previous single-loop NGQC schemes are sensitive to the operational control error, i.e., the $X$ error, due to the limitations of the implementation. Here, we propose a robust scheme for NGQC combining with the dynamical correction technique, which still uses only simplified pulses, and thus being experimental friendly. We numerically show that our scheme can greatly improve the gate robustness in previous protocols, retaining the intrinsic merit of geometric phases. Furthermore, to fight against the dephasing noise, due to the $Z$ error, we can incorporate the decoherence-free subspace encoding strategy. In this way, our scheme can be robust against both types of errors. Finally, we also propose how to implement the scheme with encoding on superconducting quantum circuits with experimentally demonstrated technology. Therefore, due to the intrinsic robustness, our scheme provides a promising alternation for the future scalable fault-tolerant quantum computation.

An ab initio QED approach to treat a valence-hole excitation in closed-shell systems is developed in the framework of the two-time Green's-function method. The derivation considers a redefinition of the vacuum state and its excitation as a valence-hole pair. The proper two-time Green's function, whose spectral representation confirms the poles at valence-hole excitation energies, is proposed. An contour integral formula which connects the energy corrections and the Green's function is also presented. First-order corrections to the valence-hole excitation energy involving self-energy, vacuum polarization, and one-photon-exchange terms are explicitly derived in the redefined vacuum picture. Reduction to the usual vacuum electron propagators is shown, which agrees in the Breit approximation with the many-body perturbation theory expressions for the valence-hole excitation energy.