The capability of the quantum approximate optimization algorithm (QAOA) in solving combinatorial optimization problems has been intensively studied in recent years due to its application in the quantum-classical hybrid regime. Despite having difficulties that are innate in the variational quantum algorithms (VQA), such as barren plateaus and the local minima problem, QAOA remains one of the applications that is suitable for the recent noisy intermediate scale quantum (NISQ) devices. Recent works have shown that the performance of QAOA largely depends on the initial parameters, which motivate parameter initialization strategies to obtain good initial points for the optimization of QAOA. On the other hand, optimization strategies focus on the optimization part of QAOA instead of the parameter initialization. Instead of having absolute advantages, these strategies usually impose trade-offs to the performance of the optimization problems. One such example is the layerwise optimization strategy, in which the QAOA parameters are optimized layer by layer instead of the full optimization. The layerwise strategy costs less in total compared to the full optimization, in exchange of lower approximation ratio. In this work, we propose the iterative layerwise optimization strategy and explore the possibility for the reduction of optimization cost in solving problems with QAOA. Using numerical simulations, we found that by combining the iterative layerwise strategy with proper initialization strategies, the optimization cost can be significantly reduced in exchange for a minor reduction in the approximation ratio. We also show that in some cases, the approximation ratio given by the iterative layerwise strategy is even higher than that given by the full optimization.

Working with trapped atoms at a close distance to each other, we show that one can implement entangling gates based on nonindependent qubits using a single pulse per qubit, or a single structured pulse. The optimal parameters depend on approximate solutions of Diophantine equations, causing the fidelity to never be exactly one, even under ideal conditions, although the errors can be made arbitrarily smaller at the cost of stronger fields. We fully characterize the mechanism by which the gates operate and study the effects of thermal motion and intensity fluctuations in the laser beams for different physical implementations of the gates. If instead of one pulse, we control the system with a two-pulse sequence, a plethora of mechanisms become possible where one can choose the optimal parameters from a wide range of values to achieve high-fidelity gates that are more protected from the effects of laser intensity fluctuations.

Modern resonance spectroscopic experiments on the measurement of transition frequencies in atoms have reached a level where a meticulous description of all aspects of the studied processes has become obligatory. The precision achieved has led to the fact that the determination of the transition frequency on the basis of measured data is substantially refined by theoretical treatment of the observed spectral line profile. Thus, a large impact of effects arising beyond the resonance approximation, in particular due to the effect of quantum interference, is found experimentally. We show that the picture becomes even more complicated when the observed spectral line profile is “identified” with one of the processes—emission or absorption. An accurate determination of the transition frequency requires a description of the absorption line profile inseparable from the emission process, and vice versa. The theoretical aspects discussed in this paper create prerequisites for more accurate experiments.

Ab initio interaction potential for the electronic ground state of the argon dimer has been developed. The potential uses previously calculated accurate Born-Oppenheimer interaction energies while significantly improving the description of relativistic effects by including the two-electron Darwin and orbit-orbit corrections. Moreover, leading-order quantum electrodynamics corrections to the potential are calculated, and long-range retardation of the electromagnetic interactions is taken into account. Spectroscopic properties of the argon dimer are reported, such as the bond dissociation energy, positions of rovibrational levels, and rotational and centrifugal-distortion constants. Our potential supports eight rotationless vibrational states, and the existence of a ninth level can neither be confirmed nor ruled out at the current accuracy level. Finally, thermophysical properties of the argon gas, including pressure and acoustic virial coefficients, as well as transport properties—viscosity and thermal conductivity—are evaluated using the developed potential. For the virial coefficients, the obtained ab initio values are somewhat less accurate than the most recent experimental results. However, the opposite is true for the transport properties, where the theoretical results calculated in this work have significantly smaller uncertainties than the data derived from measurements.

Spectral-line-broadening models have been moving towards including full Coulomb interactions between the atom and plasma, replacing the commonly used dipole approximation. The effects of the full Coulomb interaction have been thoroughly explored for plasma electrons, resulting in redshifts of spectral lines in high-energy-density plasmas. We explore the impact of a full Coulomb treatment on ion broadening. Penetrating collisions due to ions do not significantly impact the linewidths. The most significant aspect is the appearance of quasimolecular resonances in the far line wings, such as those previously observed in white-dwarf spectra. We identify several problems with the existing models. The most direct implementation causes the quasimolecular features to appear at the wrong photon energies. It is possible to include the detailed molecular structure, but this currently requires the Anderson-Talman approximation, which ignores the $N$-body properties of the plasma. We find that $N$-body effects can substantially broaden these quasimolecular features and even shift them, depending on the plasma conditions. We conclude that penetration of ions into the spatial extent of the radiator wave function does not strongly affect the usual diagnostics and may have a moderate to weak effect on opacity. The Rosseland mean opacity is weighted towards low-opacity regions of a spectrum, where these quasimolecular features are found.

We investigate the twisted state of an atom and the possible effect of such a state on the properties of the photons emitted as a result of an electron transition in that atom. We first propose a framework for describing the twisted atomic state and then explore possible differences in the nuclear recoil effects in the twisted atom compared to those in the plane-wave atom. We conclude that if the initial atomic state is twisted, then the photon distribution is altered. We point out that, in a certain observation scheme, one can detect a feature of this twist in the distribution of the emitted photons, even in zero order in $m/M$.

The $3d$ states in the $n=3$ level of H-like ${\mathrm{Ar}}^{17+}$ ions, to which direct excitation from the $1s$ ground state is optically forbidden, were prepared by the ladder-type ($1s_{1/2}\to 2p_{3/2}\to 3d$) double excitation with three-dimensional resonant coherent excitation (3D-RCE). 455 and 390 MeV/u ${\mathrm{Ar}}^{17+}$ ions were excited by a combination of two different crystal fields induced by the arrangement of crystal planes as they passed through a 1.0-$\mu \mathrm{m}$-thick Si crystal. We observed resonance profiles in the charge-state distribution of the ions after passing through the thin crystal and in yields of Lyman $\alpha$ and $\beta$ x rays. The $2p_{3/2}\to 3d$ transitions were confirmed by depletion of the Lyman $\alpha$ x-ray yield. The observed resonance profile and its dependence on the polarization of the crystal field are in reasonable agreement with theoretical simulations based on the density matrix approach. These results pave the way for the formation of highly excited states of highly charged heavy ions, where the direct transition from the $1s$ ground state is optically forbidden.

We calculate the weak-coupling resistivity of the two-dimensional Bose Hubbard model, comparing with the more familiar fermionic case. At high temperature the resistivity is linear in $T$, while in the low-temperature normal state it is exponentially suppressed. We explore the density dependence and calculate the momentum relaxation rate.

Cold-atom gravimetry is susceptible to environmental factors and noise resulting from the expansion of the atom cloud, thereby impacting the quality of gravity signals. An amplitude-modulated mirror-pulse scheme for cold-atom gravimeters is proposed to enhance the stability of the gravity measurement. The amplitude-modulated pulse is calculated based on the combined optimal control method of differential evolution and gradient ascent pulse engineering. This combination imparts high robustness to the amplitude-modulated pulse against detuning and coupling strength. Numerical modeling of the atom gravimeter with a cloud of 3 $\mathrm{\mu }\mathrm{K}{}^{87}\mathrm{Rb}$ atoms suggests that, compared with the rectangular pulse, the amplitude-modulated mirror pulse reduces the uncertainty of the gravity value extracted from a single interference fringe, increases the contrast of the interference fringe by about 1.5 times, and improves the stability of the gravity measurement. Additionally, by imposing constraints on pulse-shape smoothness, the phase-noise transfer function of the gravimeter using the amplitude-modulated mirror pulse closely approximates the performance of the rectangular pulse.

While in linear optics the subject of structured light has been a fruitful field of both theoretical and applied research, its development in the arena of nonlinear optics has been underexplored. In this paper, we construct frozen-wave-type structured optical beams in Kerr nonlinear media, emphasizing the self-defocusing case, and we use them to guide and control Gaussian optical beams. The results presented in this study support the expectation that structured light in nonlinear media can open new avenues of theoretical research and applications, particularly in the realms of light controlling light and for all-optical photonics.

In open, driven systems where parity-time symmetry is preserved, phenomena that defy conventional wisdom emerge near exceptional points, promising advances in photonics. While most studies focus on two-level systems of a conventional exceptional point, unconventional exceptional points as well as reentrant phases have been discovered in separate studies of higher-dimensional phase spaces. In this article, we present a minimal, analytical model that encompasses several key phenomena in higher-dimensional phase spaces, including reentrant $\mathcal{PT}$ phases, higher-order exceptional points, and anisotropic exceptional points. Using the exact analytical solution, we identify a topological index as the unifying origin of these different phenomena. The simplicity of the model may furthermore facilitate experimental implementations for enhanced sensing and efficient polariton devices.

We study the coherent population trapping resonance induced by the radiation of a microwave-current-modulated diode laser. The situation is considered when a harmonic phase modulation of the microwave field is used to generate the error signal for the frequency stabilization of atomic clocks. We demonstrate that in this case the resonance acquires a multipeak structure. If it is asymmetric and the components of the multipeak structure are not fully resolved, then the resonance frequency nonlinearly depends on the laser field intensity. The peaks become separated at an increase in the frequency of the phase modulation, providing a linear dependence of the frequency on the intensity of the laser field. This theoretical prediction is confirmed experimentally. Other advantages of the high-frequency modulation regime are also discussed.

Monochromatically driven two-level systems (i.e., Rabi models) are ubiquitous in various fields of physics. Though they have been exactly solved, the physical pictures in these exact solutions are not clear. Recently, approximate analytical solutions with neat physics have been obtained by using the counter-rotating hybridized rotating wave (CHRW) method, which has been proven to be effective over a wider range of parameters than the previous analytical solutions. However, the CHRW depends on a parameter $\xi$, which has no solution in some regimes. Here, we combine the double-unitary-transformation approach with the generalized Van Vleck nearly degenerate perturbation theory, and present approximate analytical results with clear physics for almost all parameter regimes, which agree well with the numerical solutions and the previous experimental results. Moreover, the dynamic frequencies of the Rabi model are regular, and the frequency with the highest Fourier amplitude changes from the Rabi frequency to $2n\omega$ with driving frequency $\omega$ and integer $n$, as the driving intensity increases from weak to deep-strong. In addition, we further explore the Floquet dynamics of the dissipative open Rabi model. Remarkably, the dissipations are tunable in the rotating frame, and the approximate analytical results obtained by our method are in good agreement with the numerical results in the strong driving regime. These results pave the way to quantum control using strong and deep-strong driving with applications in quantum technologies.

The nonincreasing feature of temporal quantum steering under a completely positive trace-preserving (CPTP) map, as proposed by Chen et al. [Phys. Rev. Lett. 116, 020503 (2016)], has been considered as a practical measure of non-Markovianity. In this paper we utilize an all-optical scheme to simulate a non-Markovian collision model and to examine how Gaussian steering can be used as a tool for quantifying the non-Markovianity of a structured continuous-variable (CV) Gaussian channel. By modifying the reflectivity of the beam splitters (BSs), we are able to tune the degree of non-Markovianity of the channel. After analyzing the non-Markovian degree of the dissipative channel within two steering scenarios, we discovered that the Gaussian-steering-based non-Markovian measure depends the specific scenario because of the asymmetry of Gaussian steering. We also compared the Gaussian-steering-based non-Markovianity to the one based on violation of divisibility of a CPTP map.

Continuous-variable source-independent quantum random-number generators (CV-SI-QRNGs) generate high-speed secure random numbers without any assumptions about source. Recently, Smith et al. [Phys. Rev. A 99, 062326 (2019)] proposed a CV-SI-QRNG with phase-randomized local oscillator (LO) protocol, which does not require additional active optical components, thus reducing the complexity of the CV-SI-QRNG setup and attracting widespread attention. However, the trusted but imperfect sampling device used in CV-SI-QRNG has not yet been fully investigated, which will lead to performance degradation and security problems. In this work, we investigate the influence of imperfect sampling devices on the CV-SI-QRNG with phase-randomized LO, including the finite-sampling bandwidth, finite-sampling precision, and finite-size effect. Simulation results show that practical imperfections in the sampling device will affect the estimation of lower bound on the conditional min-entropy and reduce the extractable randomness. To improve the performance of CV-SI-QRNG and prevent such information leakages, we also provide some corresponding countermeasures. Our work highlights the influences of imperfect sampling devices on the performance and security of practical CV-SI-QRNG systems, which helps to improve their robustness and practicality.

The quantum walk is a quantum counterpart of the classical random walk that exhibits nonclassical behaviors and outperforms the classical random walk in various aspects. It has been known that a single particle can be propagated by a discrete-time quantum walk with a quadratic time scaling in the variance of position distribution, beating the linear time scaling in a classical random walk. In this paper, we consider the discrete-time quantum walk for multiple particles in a one-dimensional lattice, and investigate the optimization of the joint coin state to enhance the spatial propagation of the particles in the lattice. We study the asymptotic evolution of position distribution for multiple particles in the long-time limit, and analytically optimize the joint coin state to derive the maximum variance of the position distribution between the particles after the evolution of the quantum walk. An interesting result is that an optimized coin state always possesses specific exchange symmetry which can be characterized by a graph consisting of two disconnected complete subgraphs and the exchange symmetry can significantly influence the position correlations between the particles, showing the critical role of coin symmetry in the propagation of multiple particles by the quantum walk. We further study the entanglement of the optimized coin states to show the relation of the coin correlations to the particle position distribution.

Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time evolution and noise seem to rule out unbiased quantum simulation in the near term. We prove that classical postprocessing, i.e., long-time filtering of an offline time series, exponentially improves the circuit depth needed for quantum time evolution. We apply the filtering method to the construction of a hybrid quantum-classical algorithm to estimate energy gap, an important observable not governed by the variational theorem. We demonstrate, within an operating range of filtering, the success of the algorithm in a proof-of-concept simulation for finite-size scaling of a minimal spin model. Our findings set the stage for unbiased quantum simulation to offer memory advantage in the near term.

Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics systems. As a test case, we take pulses for single-qudit swap gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be $\lesssim 0.1\%$ of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.

We explore the potential impact of the recently introduced correlated approximate catalytic procedure on quantum information processing tasks, particularly focusing on phase and subchannel discrimination protocols. Our findings reveal that the correlated catalyst substantially enhances the efficiency of these protocols, thus improving the reliability of message decoding and information transmission in the context of phase discrimination and subchannel discrimination problem. In addition, we introduce fidelity of modified bipartite coherence swapping protocol. Empowered by the correlated catalyst, we are able to increase the fidelity of the coherence swapping protocol.