Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited, especially compared to the study of classical algorithms. We propose and study an alternative class of hybrid approaches to quantum optimization, termed iterative quantum algorithms, which in particular generalizes the recursive quantum approximate optimization algorithm (QAOA). This paradigm can incorporate hard problem constraints, which we demonstrate by considering the maximum independent set (MIS) problem. We show that, for QAOA with $p=1$ circuit layers, this algorithm performs exactly the same operations and selections as the classical greedy algorithm for MIS. We then turn to deeper $p>1$ circuits and other ways to modify the quantum algorithm that can no longer be easily mimicked by classical algorithms, and empirically confirm improved performance. Our work demonstrates the practical importance of incorporating proven classical techniques into more effective hybrid quantum-classical algorithms.

We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-not (cnot) gate up to single-qubit operations. These gates belong to the local equivalence class [cnot]. Additionally, we explore which local equivalence classes of two-qubit operations can be naturally generated by braiding Fibonacci anyons. We discovered that most of the generated classes are located near the edges of the Weyl chamber representation of two-qubit gates, specifically between the local equivalence classes of the identity $\left[\mathbb{1}\right]$ and [cnot], swap and between those of the double-controlled-not [dcnot] and [swap]. Furthermore, we found a numerically exact implementation of a local equivalent of the swap gate using a sequence of only nine elements from the Fibonacci braiding gate set.

We measured the spontaneous and photoinduced decays of anionic gold clusters, ${\mathrm{Au}}_N^{-}$, with sizes ranging from $N=2$ to 13 and 15. After production in a sputter ion source, the size-selected clusters were stored in the cryogenic electrostatic ion-beam storage ring DESIREE, and their neutralization decays were measured for storage times between 0.1 and 100 s. The dimer was observed to decay by electron emission in parallel to neutral atom emission at long times, implying a breakdown of the Born-Oppenheimer approximation, analogous to the behavior of copper and silver dimers. Radiative cooling is observed for all other cluster sizes. The decays of clusters $N=3,6,8–13,15$ show only a single radiative cooling time. For $N=6–13$ the cooling times have a strong odd-even oscillation with an amplitude that decrease with cluster size and with the even $N$ having the faster cooling. We compare our results with previous measurements of radiative cooling rates of the corresponding cationic gold clusters, ${\mathrm{Au}}_N^{+}$, which also show an odd-even effect with a similar oscillation amplitude but at orders of magnitude shorter timescales and out of phase with the anions. The tetramer and pentamer both show two cooling times, which we tentatively ascribe to different structural forms at different ranges of high angular momenta of the ions in the ${\mathrm{Au}}_4^{-}$ and ${\mathrm{Au}}_5^{-}$ beams. For ${\mathrm{Au}}_7^{-}$, the shape of the decay curve suggests that the cluster cools by emission of low-energy photons. The calculated limit on photon energies strongly suggests that cooling is by vibrational transitions in this case. For ${\mathrm{Au}}_5^{-}$, time-resolved studies of photoinduced decays were performed to track the evolution of the internal energy distribution. We conclude that the radiative cooling is dominated by sequences of vibrational transitions in the IR. The laser-enhanced neutralization rate of ${\mathrm{Au}}_5^{-}$ was exponential, in contrast to its spontaneous decay rate, indicating that the cluster had already been cooled to a very narrow internal energy distribution at 120 ms as the total (integrated) laser-enhanced intensity was independent of the laser firing time at later times. The unimolecular rate constants decreased from 500 ${\mathrm{s}}^{-1}$ when laser excited at 0.12 s to 40 ${\mathrm{s}}^{-1}$ when laser excited at 0.62 s.

This paper investigates the capability of the two-step (TS) approaches in calculating the cross section of the electron-impact double ionization (DI) of ions. The TS approach proposed by Gryziński [M. Gryziński, Phys. Rev. 138, A336 (1965)] considers electron-impact direct DI as two sequential electron-impact single ionizations. Furthermore, we introduce the energetic differential cross sections of primary single ionization as the energy distribution for intermediate electrons that participate in the subsequent single ionization process. Such differential cross sections can be calculated using the analytic Mott formula [Y.-K. Kim and M. E. Rudd, Phys. Rev. A 50, 3954 (1994)]. The electron-impact indirect DI is considered as TS, in which a primary electron-impact single ionization of an inner-shell electron is followed by a single autoionization. The cross sections of the direct and indirect DI are calculated independently to result in the total DI cross section. Comparing with the available experimental data shows that the present TS approach can reproduce well the DI cross sections for ions with electron number $N\le 10$ such as ${\mathrm{Li}}^{+}$, ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{+}$, ${\mathrm{N}}^{2+}$, ${\mathrm{O}}^{+}$, ${\mathrm{O}}^{2+}$, ${\mathrm{Ne}}^{q+}$ ($q=1,2,3$, and 5), and ${\mathrm{Ar}}^{q+}$ ($q=8,9,10$, and 11) ions. The contributions of the direct and indirect DI can be identified based on our calculations.

We investigate the ultrafast electron dynamics of a model of a wide-band-gap material with inner, valence, and conduction bands excited by an intense few-femtosecond pump and monitored by a delayed attosecond extreme-ultraviolet probe pulse. Complementary computational methods are utilized and compared, based on the semiconductor Bloch equations (SBEs) and time-dependent density functional theory (TDDFT). TDDFT is employed to study a finite-size system, while the SBEs are utilized to investigate the corresponding solid with periodic boundary conditions imposed, with the crystal-momentum-dependent energy bands and interband couplings calculated in the parallel-transport structure gauge. The resulting strong-field electron dynamics are used to predict experimentally accessible attosecond transient absorption spectroscopy (ATAS) signals as a function of the probe-pulse frequency and pump-probe interpulse delay. Both simulation protocols similarly capture the time-delay-dependent spectral features in the ATAS signals. The very good agreement between our ab initio TDDFT simulations and SBE-based results allows us to validate our SBE-based model and identify the key contributing interband couplings. An interpretation model building on these validated SBE-based results allows us to quantify the amplitude of the ATAS spectral features in terms of the intraband dynamics of the electron-hole pairs generated by the attosecond probe pulse.

We experimentally utilize two linearly polarized femtosecond laser pulses, termed the alignment pulse and the control pulse, with specific polarization angles and time delays, to distinguish and control the ultrafast rotation of CO molecules in even and odd rotational states. The spatiotemporal evolution of the rotating CO molecules is tracked by measuring the time-dependent momentum distributions of ionic fragments resulting from Coulomb explosion, induced by a circularly polarized femtosecond laser pulse. Our results demonstrate that CO molecules in even and odd rotational states can be distinguished at rotational revivals, exhibiting opposite rotational directions. These rotational directions can be controlled by adjusting the polarization of the control pulse. The experimental results are supported by quantum numerical simulations.

The study of collective excitations is a crucial tool for understanding many-body quantum systems. For instance, collective excitations play a central role in the exploration of superfluidity and other quantum macroscopic phenomena in Bose and Fermi systems. In this work we present a variational and a numerical study of a parametrically driven Bose-Einstein condensate confined in a cylindrical harmonic trap in which the aspect ratio can be varied from a prolate (cigar-shaped) to an oblate (pancake-shaped) system. The excitation can be applied by periodically modulating the harmonic frequencies of the trap or alternatively the interatomic interaction strength at a frequency that matches that of the system's breathing mode. As a result, we observe the formation of dynamical density patterns that depend on the geometry of the trap: a fringe pattern in a prolate system and a ring pattern in an oblate one. By decomposing the total energy into its kinetic, potential, and interaction terms, we show that the onset of these patterns coincides with the redistribution of kinetic energy in the weakly trapped directions of the sample, indicating the three-dimensional nature of the studied phenomena. Finally, our analysis shows that the difference between the two excitation mechanisms lies in the system stability. Modulating the trap destabilizes the system quicker than modulating the interactions, leading to earlier formation of the patterns.

Degenerate four-wave mixing in diamond generates a quantum state ${\rho }_{\mathrm{SaS}}$ composed of Stokes (S) and anti-Stokes (aS) time-correlated photon pairs (SaS). Here, polarization state tomography of ${\rho }_{\mathrm{SaS}}$ is performed in four pertinent scattering configurations: Raman shift in resonance and out of resonance with the phonon energy, and incident light polarized in the direction parallel to or $\pi /4$ rotated from a diamond crystallographic axis. We reconstruct the density matrix, calculate concurrence and purity for the four configurations, and directly measure and analyze the diagonal terms of ${\rho }_{\mathrm{SaS}}$ in different bases. We establish ${\rho }_{\mathrm{SaS}}$ as an entangled linear combination of electronic four-wave mixing and SaS Raman process, mixed with uncorrelated S and aS photons, with the weight constants depending on the scattering conditions, which can be engineered for future applications.

We study two squeezed-state-dependent schemes of the quantum optical tap for information encoded in quantum-correlated fields from a two-mode entangled source. We find that, by using two independent squeezed beam splitters, the quantum information encoded in entangled dual beams can be divided into four parts without noise increase. We calculate the corresponding transfer coefficients to confirm that quantum optical tapping is achieved. As a variation to the original tapping schemes, we consider parametric amplifiers to replace beam splitters as tapping devices and find that they work equally well and have the advantage of tolerance to external losses. We also analyze the scalability of the schemes by cascading two outputs into the next stage and find that the output signals of the first stage can be further split noiselessly by the second stage. This shows that the scheme is cascadable and scalable for efficient quantum information distribution in an optical network.

Non-Hermitian systems have Riemann surface structures of complex eigenvalues that admit singularities known as exceptional points. Combining with geometric phases of eigenstates gives rise to unique properties of non-Hermitian systems, and their classifications have been studied recently. However, the physical realizations of classes of the classifications have been relatively limited because a small number of modes and exceptional points are involved. In this paper, we show in microcavities that all five classes [J.-W. Ryu et al., Commun. Phys. 7, 109 (2024)] of three modes can emerge with three exceptional points. In demonstrations, we identify various combinations of exceptional points within a two-dimensional parameter space of a single microcavity and define five distinct encircling loops based on three selected exceptional points. According to the classification, these loops facilitate different mode exchanges and the acquisition of additional geometric phases during the adiabatic encircling of exceptional points. Our results provide a broad description of the geometric phases-associated topology induced by multiple exceptional points in realistic physical systems.

High-dimensional quantum entanglement and the advancements in their experimental realization provide a playground for fundamental research and eventually lead to quantum technological developments. The Horodecki criterion determines whether a state violates the Clauser-Horne-Shimony-Holt (CHSH) inequality for a two-qubit entangled state, solely from the state parameters. However, it remains a challenging task to formulate similar necessary and sufficient criteria for a high-dimensional entangled state for the violation of a suitable Bell inequality. Here we develop a Horodecki-like criterion based on the state parameters of arbitrary two-qudit states to violate a two-outcome Bell inequality involving $2^{n-1}$ and $n$ measurement settings for Alice and Bob, respectively. This inequality reduces to the well-known CHSH and Gisin elegant Bell inequalities for $n=2$ and 3, respectively. While the proposed criterion is sufficient to violate the Bell inequality, it becomes necessary as well for the following cases: (i) $m$ copies of Bell-diagonal states for arbitrary $n$, (ii) nondecomposable states whose correlation matrix is diagonalized by local unitaries, and (iii) for any arbitrary two-qubit state when $n=3$, where the maximal value of the Bell functional is achieved with Bob's measurements being pairwise anticommuting. For any states, we derive the constraints on Alice's measurements in achieving the maximum quantum violation for this inequality.

Recent advances in high-precision spectroscopy of highly charged ions necessitate an understanding of energy shifts of ionic levels caused by external electric and magnetic fields. Beyond the well-known Stark and linear Zeeman shifts, trapped ions may also exhibit quadratic Zeeman and electric quadrupole shifts. In this contribution, we present a systematic approach for the theoretical analysis of these shifts for arbitrary many-electron ions. Based on the derived expressions and making use of the multiconfigurational Dirac-Fock approach, we performed calculations of quadratic Zeeman shift coefficients and quadrupole moments for various ionic states in ${\mathrm{Ca}}^{14+}$, ${\mathrm{Ni}}^{12+}$, and ${\mathrm{Xe}}^{q+}$ ions. These ions attract particular interest for ongoing and future experiments in optical clocks and tests of fundamental physics.

Self-focusing of intense optical beams in transparent media is one of the most fundamental phenomena in nonlinear optics. Usually, for near-infrared and visible laser pulses, Kerr nonlinearity dominates the self-focusing, while the laser-induced plasma leads to the defocusing of laser pulses. Recent tremendous strides made in intense terahertz radiation sources have enabled the extremely nonlinear physics in the terahertz frequency range. Here, we investigate via numerical simulations the propagation dynamics of high-power terahertz radiation in a weakly ionized gas and demonstrate the self-focusing of terahertz pulses at a peak power much lower than the critical power for Kerr self-focusing. This seemingly anomalous non-Kerr-driven self-action phenomenon is attributed to the donut-shaped plasma profile produced by the terahertz field-induced electron-impact ionization of gases. The spatiotemporal evolution of plasma generation results in exotic focusing dynamics of terahertz pulses such as axiconlike line focusing and superluminal focal spot propagation. The self-focusing behavior as a function of various terahertz radiation and gas properties is parametrically studied. Our results shed light on the distinct propagation dynamics of intense terahertz pulses in media compared with the well-known near-infrared cases, which could have important implications for nonlinear terahertz wave-matter interactions and applications like remote terahertz spectroscopy.

We formulate a perturbative approach for studying a class of multilevel time-dependent quantum systems with constant off-diagonal couplings and diabatic energies being odd functions of time. Applying this approach to a general multistate Landau-Zener (MLZ) model with all diabatic levels crossing at one point (named the one-crossing MLZ model), we derive analytical formulas of all its transition probabilities up to fourth order in the couplings. For one-crossing MLZ models it is difficult to obtain such analytical results by other kinds of approximation methods; thus, these perturbative results can serve as reliable benchmarks for future studies of any one-crossing MLZ models that have not been exactly solved.

Environment-induced steady-state quantum coherence (SSQC) is a captivating phenomenon that challenges conventional understandings of decoherence. In this article, we delve into the foundational aspects of environment-induced SSQC, shedding light on its emergence within the framework of system-bath interactions. Starting from a microscopic system-bath-coupled model, we investigate the dependence of SSQC on environmental memory effects, the bath temperature, the system-bath coupling strength, and squeezing parameters. Our findings reveal that the environment not only acts as a generator but also as a disruptor of SSQC. A peak will exist for a non-Markovian bath, which is a result of competition between these two mechanisms. Interestingly, the peak disappears in the Markovian case. Additionally, we observe that the generated SSQC can be further amplified through environment squeezing.

Quantum information theory explores numerous properties that surpass classical paradigms, offering novel applications and benefits. Among these properties, negative conditional von Neumann entropy (CVNE) is particularly significant in entangled quantum systems, serving as an indicator of potential advantages in various information-theoretic tasks, despite its indirect observability. In this paper, we investigate the relationship between CVNE and the violation of Bell inequalities. Our goal is to establish upper bounds on CVNE through semidefinite programming applied to entangled qubits and qutrits, utilizing selected Bell operators. Our findings reveal that a semi-device-independent certification of negative CVNE is achievable and could be practically beneficial. We further explore two types of robustness: robustness against detection efficiency loopholes, measured by relative violation, and robustness against white noise and imperfections in state preparation, measured by critical visibility. Additionally, we analyze parametrized families of Bell inequalities to identify optimal parameters for different robustness criteria. This study demonstrates that different Bell inequalities exhibit varying degrees of robustness depending on the desired properties, such as the type of noise resistance or the target level of negative CVNE. By bridging the gap between Bell inequalities and CVNE, our research enhances understanding of the quantum properties of entangled systems and offers insights for practical quantum information processing tasks.

Quantum computing offers several new pathways toward finding many-body eigenstates, with variational approaches being some of the most flexible and near-term oriented. These require particular parametrizations of the state and, for solving multiple eigenstates, must incorporate orthogonality. In this work, we use techniques from manifold optimization to arrive at solutions of the many-body eigenstate problem via direct minimization over the Stiefel and Grassmannian manifolds, avoiding parametrizations of the states and allowing for multiple eigenstates to be simultaneously calculated. These Riemannian manifolds naturally encode orthogonality constraints and have efficient quantum representations of the states and tangent vectors. We provide example calculations for quantum many-body molecular systems and discuss different pathways for solving the multiple eigenstate problem.

Dephasing is a main noise mechanism that afflicts quantum information, it reduces visibility, and destroys coherence and entanglement. Therefore, it must be reduced, mitigated, and, if possible, corrected to allow for demonstration of quantum advantage in any application of quantum technology, from computing to sensing and communications. Here we discuss a hardware scheme of error filtration to mitigate the effects of dephasing in optical quantum metrology. The scheme uses only passive linear optics and ancillary vacuum modes, without need of single-photon sources or entanglement. It exploits constructive and destructive interference to partially cancel the detrimental effects of statistically independent sources of dephasing. We apply this scheme to preserve coherent states and to phase stabilize stellar interferometry, showing that a significant improvement can be obtained by using only a few ancillary modes.

We investigate optimized quantum state preparation for quantum metrology applications in noisy environments. Using the qfi-opt package, we simulate a low-depth variational quantum circuit (VQC) composed of a sequence of global rotations and entangling operations applied to a chain of qubits that are subject to dephasing noise. The parameters controlling the VQC are numerically optimized to maximize the quantum Fisher information, which characterizes the ultimte metrological sensitivity of a quantum state with respect to a global rotation. We find that, regardless of the details of the entangling operation implemented in the VQC, the optimal quantum states can be broadly classified into a trio of qualitative regimes, i.e., catlike, squeezedlike, and product states, associated with different dephasing rates. Our findings are relevant for designing optimal state-preparation strategies for next-generation quantum sensors exploiting entanglement, such as time and frequency standards and magnetometers, aimed at achieving state-of-the-art performance in the presence of noise and decoherence.