The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions for combinatorial optimization problems on current noisy intermediate-scale quantum (NISQ) devices. The primary focus of ongoing research is to exhibit its speed advantage over classical algorithms. However, the performance of QAOA is restricted at lower depths, while higher depths are limited by current experimental techniques. We propose an algorithm that amalgamates the capabilities of QAOA and the real-space renormalization group transformation. Numerical simulations indicate that our proposed algorithm can deliver precise solutions for specific randomly generated instances using QAOA at shallow depths, even at the lowest depth. This algorithm is particularly suitable for current NISQ devices, offering the potential to demonstrate a quantum advantage.

Building on previous research on frequency allocation optimization for superconducting circuit quantum processors, this work incorporates several techniques to improve overall solution quality. We introduce constraints and imposed edgewise differences help to improve the optimization results. We also introduce optimization variables for the orientation of each edge, defined as the direction from the control qubit to the target qubit, to be chosen during optimization. To scale up to larger processors, multimodule designs are employed with various boundary conditions, thereby enhancing the collective yield. These enhancements allow for greater flexibility in processor design by eliminating the need for handpicked orientations. We support the efficient assembly of large processors with dense connectivity by choosing the best boundary conditions. Examples demonstrate that, at low computational cost, this optimization approach finds a frequency configuration for a square chip with over 1000 qubits and over 10% yield at much larger dispersion levels than required by previous approaches.

The polarization tensor of graphene derived in the framework of the Dirac model using the methods of thermal quantum field theory in ($2+1$) dimensions is recast in a mathematically equivalent but more compact and convenient in computations form along the real frequency axis. The obtained unified expressions for the components of the polarization tensor are equally applicable in the regions of the on- and off-the-mass-shell electromagnetic waves. The advantages of the presented formalism are demonstrated on the example of nonequilibrium Casimir force in the configuration of two parallel graphene-coated dielectric plates, one of which is either hotter or colder than the environment. This force is investigated as a function of temperature, the energy gap, and chemical potential of graphene coatings with the account of the effects of spatial dispersion. In addition to the thermodynamically nonequilibrium Casimir and Casimir-Polder forces, the obtained form of the polarization tensor can be useful for investigation of many diverse physical phenomena in graphene systems, such as surface plasmons, reflectances, electrical conductivity, radiation heat transfer, and so on.

We report the determination of the Landé $g_J$ factor and Zeeman coefficients for the ground-state of ${}^{171}{\mathrm{Yb}}^{+}$, relevant to microwave quantum frequency standards (QFSs). The $g_J$ factor is obtained by using two independent methods, the multiconfiguration Dirac-Hartree-Fock and multireference configuration-interaction methods, yielding a consistent value of $2.002615\left(70\right)$. The first- and second-order Zeeman coefficients are determined as $14010.78\left(49\right)\mathrm{Hz}/\mu \mathrm{T}$ and $31.0869\left(22\right)\mathrm{mHz}/\mu {\mathrm{T}}^2$, respectively, based on the calculated $g_J$ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the ${}^{171}{\mathrm{Yb}}^{+}$ microwave QFSs. The results reported in this work also offer potential for improved constraints on variations in fundamental constants through frequency comparisons and advancing trapped-ion quantum computers based on the ground-state hyperfine splitting of ${}^{171}{\mathrm{Yb}}^{+}$.

The strong collective interaction of atoms with an optical cavity causes normal mode splitting of the cavity's resonances, whose width is given by the collective coupling strength. At low optical density of the atomic cloud, the intensity distribution of light in the cavity is ruled by the cavity's mode function, which is determined solely by its geometry. In this regime the dynamics of the coupled atom-cavity system is conveniently described by the open Dicke model, which we apply to calculating normal mode splitting generated by periodically ordered clouds in linear and ring cavities. We also show how to use normal mode splitting as a witness for Wannier-Bloch oscillations in the tight-binding limit. At high optical density the atomic distribution contributes to shaping the mode function. This regime escapes the open Dicke model, but can be treated by a transfer matrix model provided the saturation parameter is low. Applying this latter model to an atomic cloud periodically ordered into a one-dimensional lattice, we observe the formation of photonic bands gaps competing with the normal mode splitting. We discuss the limitations of both models and point out possible pathways to generalized theories.

We theoretically and computationally investigate the role that the spatial spread of atoms plays in the transmission and reflection of weak light from atom arrays. In particular, we investigate whether coherent wave functions for the atoms' positions leads to different results from a thermal distribution with the same spatial spread. We find that the coherence is not relevant when the light is weak and the electronic states evolve on timescales shorter than the oscillation period of the atoms in their traps. Full numerical calculations and derivations using the sudden approximation show that reflection and transmission agree with the simple averaging over atom positions for these conditions. For parameters outside these restrictions, the simple spatial averaging may lead to inaccurate results.

Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite systems. In this framework, we consider a quantum battery made up of many interacting subsystems and study the maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting functional parallel ergotropy. Focusing on the bipartite case, we first observe that parallel ergotropy outperforms work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum available work and the second agent B, subsequently, extracts what is left on the other part. For the agents, this showcases the need of cooperating for an overall benefit. Second, from the informational point of view, we observe that the parallel capacity of a state can detect entanglement and compare it with the statistical entanglement witness that exploits fluctuations of stochastic work extraction. Additionally, we face the technical problem of computing parallel ergotropy. We derive analytical upper bounds for specific classes of states and Hamiltonians and provide recipes to obtain numerical upper bounds via semidefinite programming in the generic case. Finally, extending the concept of parallel ergotropy, we demonstrate that system's free-time evolution and application of local unitaries allow one to saturate the gap with the ergotropy of the whole system.

Probing a quantum system disrupts its state in a phenomenon known as backaction. In this work we investigate the conditions for this disruption to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes comprised of projective measurements and probes which more generally transfer quantum information from the system to a quantum computer. The latter case is relevant to the recently introduced quantum-enhanced experiments in which quantum postprocessing is performed on a quantum computer and which can offer an exponential sampling advantage over projective measurements and classical postprocessing. Our framework explicitly considers the effects of an environment using a model of unitary evolution which couples the system, apparatus, and environment. Information dynamics is investigated using the Rényi and von Neumann entropies of the evolving state, and we construct a replica theory for studying these quantities. We identify the possible replica symmetries an experiment can possess and discuss the meaning of their spontaneous symmetry breaking. In particular, we identify a minimum subgroup whose spontaneous symmetry breaking results in an entanglement transition. This symmetry is only possible when the information in the apparatus is as informative about the dynamics of the system as the information transferred to the environment. We call this requirement the information exchange symmetry and quantify it by a relationship between the entropies. We then introduce a generalized notion of spontaneous symmetry breaking such that the entanglement transition can be understood as the spontaneous breaking of the information exchange symmetry and without referring to the replica theory. Information exchange symmetry breaking is then shown to generalize the phenomenology of the measurement-induced phase transition (MIPT). We apply this theory to a quantum-enhanced experiment probing the unitary dynamics of a Haar brickwork quantum circuit, and we determine that the universality class of the critical point is distinct from that for the MIPT. This notion of information exchange symmetry breaking generalizes the MIPT and provides a framework for understanding the dynamics of quantum information in quantum-enhanced experiments.

The nonlinear interaction of x rays with matter is at the heart of understanding and controlling ultrafast molecular dynamics from an atom-specific viewpoint, providing new scientific and analytical opportunities to explore the structure and dynamics of small quantum systems. At increasingly high x-ray intensity, the sensitivity of ultrashort x-ray pulses to specific electronic states and emerging short-lived transient intermediates is of particular relevance for our understanding of fundamental multiphoton absorption processes. In this work, intense x-ray free-electron laser (XFEL) pulses at the European XFEL are combined with a gas cell and grating spectrometer for a high-intensity transmission spectroscopy study of multiphoton-induced ultrafast molecular fragmentation dynamics in ${\mathrm{CF}}_4$. This approach unlocks the direct intrapulse observation of transient fragments, including neutral atoms, by their characteristic absorption lines in the transmitted broadband x-ray spectrum. The dynamics with and without initially producing fluorine $K$-shell holes are studied by tuning the central photon energy. The absorption spectra are measured at different FEL intensities to observe nonlinear effects. Transient isolated fluorine atoms and ions are spectroscopically recorded within the ultrashort pulse duration of a few tens of femtoseconds. An isosbestic point that signifies the correlated transition between intact neutral ${\mathrm{CF}}_4$ molecules and charged atomic fragments is observed near the fluorine $K$ edge. The dissociation dynamics and the multiphoton absorption-induced dynamics encoded in the spectra are theoretically interpreted. Overall, this study demonstrates the potential of high-intensity x-ray transmission spectroscopy to study ultrafast molecular dynamics with sensitivity to specific intermediate species and their electronic structure.

Recognized as an astrophysical molecule, $\mathrm{Mg}{\mathrm{C}}_2$ has garnered significant attention. In this study, we employed the DW-SA-CASSCF/icMRCI+Q/AV(Q+d)Z (Dynamic-weighting-state-averaged-complete active space self-consistent field/Internally contracted multi reference configuration interaction with Davidson correction based on augmented valence quadruple zeta with added diffuse and polarization functions) method to compute high-precision ab initio energy points. A neural-network approach was subsequently utilized to fit the global potential energy surface of the $\mathrm{Mg}{\mathrm{C}}_2$ molecule in its $\tilde{X}{}^1{A}_1$ state. In contrast to previous methods, the optimization of neural-network parameters in this study was carried out using the trust region framework (TRF). The TRF algorithm exhibits superior performance in parameter optimization and demonstrates reduced dependency on neuron parameters compared to the Levenberg-Marquardt algorithm. Utilizing the obtained potential energy surface, three reaction pathways for $\mathrm{MgC}\left(X{}^3{\mathrm{\Sigma }}^{-}\right)+\mathrm{C}\left({}^{3}P_g\right)\to \mathrm{Mg}+{\mathrm{C}}_2$ were identified, confirming that this reaction proceeds as a barrierless exothermic process. To further verify the accuracy of the fitted potential energy surface, the reaction cross section was calculated under the initial condition $v=0,j=0,20,50,80,120$ for this reaction. By integrating the cross section with the relative translational energy, rate coefficients were determined under various initial conditions. Under the initial condition $v=0,j=0$, the rate coefficient is at its maximum, and the trend of the rate coefficient with temperature first decreases and then increases. At a temperature of 100 K, the rate coefficient reaches its minimum value. At low temperatures, the rate coefficient is very high, which is consistent with the characteristics of a barrierless exothermic reaction.

We report a 40 parts per ${10}^9$ measurement of the positronium $1{}^3{S}_1\to 2{}^3{S}_1$ interval using pulsed two-photon optical spectroscopy. The transition is detected via field ionization of atoms excited from the $2S$ to the $20P$ Rydberg state. Precise Monte Carlo line-shape simulations allow for the accounting of effects such as Doppler and ac Stark shifts, while an optical heterodyne measurement of the excitation laser pulse is used to correct for laser frequency chirp. A value of $1233607210.5\pm 49.6\mathrm{MHz}$ is obtained. This scheme allows for the measurement of the velocity distribution of positronium atoms to correct for the second-order Doppler effect. This is a major source of systematic uncertainty expected for future measurements of this transition with a cw laser; thus, our technique paves the way toward a new generation of a high-precision determination of this interval in positronium.

In this study, we theoretically investigated x-ray spectra from the radiative decay of muonic deuterium molecules in resonance states $\mathrm{dd}{\mu }^{*}$, which plays an important role in a new kinetic model of muon catalyzed fusion ($\mu \mathrm{CF}$). The resonance states are Feshbach resonances located below the $\mathrm{d}\mu (n=2$) $+$ d threshold energy and radiatively decay into the continuum or bound states. The x-ray spectra having characteristic shapes according to the radial distribution of the two nuclei are obtained using precise three-body wave functions. We carefully examined the convergence of the x-ray spectra and achieved agreements between the length- and velocity-gauge calculations. We revealed a nonadiabatic kinetic energy distribution of the decay fragments, indicating that the radiative decay becomes a heating source of muonic atoms. We also investigated the decay branch that directly results in bound-state muonic molecules. Some resonance states $\mathrm{dd}{\mu }^{*}$ and $\mathrm{dt}{\mu }^{*}$ are found to have high branching ratios to the bound state where intramolecular nuclear fusion occurs. The formation of the muonic molecules in the bound states from metastable muonic atoms can be a fast track in the $\mu \mathrm{CF}$ cycle, which skips a slow path to form the bound state from the ground-state muonic atoms and increases the $\mu \mathrm{CF}$ cycle rate. Although the spectra from the radiative decays are located in the energy range of 1.5–1.997 keV, which is close to the $\mathrm{K}\alpha$ x-ray of 1.997 keV from muonic deuterium atoms, state-of-the-art microcalorimeters can distinguish them.

Fragmentation dynamics in the Coulomb explosion of hydrocarbons, specifically methane, ethane, propane, and butane, are investigated using time-dependent density functional theory (TDDFT) simulations. The goal of this work is to elucidate the distribution of fragments generated under laser-driven Coulomb explosion conditions. Detailed analysis reveals the types of fragments formed, their respective charge states, and the optimal laser intensities required for achieving various fragmentations. Our results indicate distinct fragmentation patterns for each hydrocarbon, correlating with the molecular structure and ionization potential. Additionally, we identify the laser parameters that maximize fragmentation efficiency, providing valuable insights for experimental setups. This research advances our understanding of Coulomb explosion mechanisms and offers a foundation for further studies in controlled molecular fragmentation.

Multiphoton interference measurements in attosecond physics, e.g., the reconstruction of attosecond beating by interference of two-photon transitions (RABITT), are the typical methods of choice to experimentally access the photoionization delay in atoms and molecules. The exact relation between the measurable multiphoton delays and the theoretical single-photon delays is typically modeled by correction terms, continuum-continuum delays, obtained from a high-energy limit of the theory. However, these are unreliable at photoelectron kinetic energies smaller than about 10 eV, and do not have photoemission angular dependence. In this work we develop an accurate analytic alternative that gives accurate correction terms even at very low energies. Our method is computationally very straightforward, predicts correct multiphoton photoelectron angular distributions as well as the expected angular dependence of the continuum-continuum delay. We validate the approach theoretically against state-of-the-art ab initio calculations as well as experimentally with a two-harmonic RABITT setup, which properly separates different higher-order multiphoton pathways and offers a promising way of analyzing congested molecular photoionization spectra.

We experimentally and theoretically study the nonadiabatic strong-field ionization of prealigned nitrogen molecules in an elliptically polarized laser pulse with an attoclock configuration. We observe an obvious oscillation of the most probable radial electron momentum with respect to the molecular alignment angle. Using a semiclassical model, we identify the influence of the molecular orbital and the long-range Coulombic potential on the alignment-dependent final radial momentum. We show that the oscillation of the radial electron momentum results from the effect of the alignment-dependent nonadiabatic initial transverse momenta at the tunnel exit that is induced by a spatial offset along the tunneling direction when the electron starts to tunnel, which depends on the molecular orientation. Our work deepens the understanding of how the molecular orbital affects the nonadiabatic tunneling process of the electron in strong laser pulses.

Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative—of which a class of superdeterministic models are an example—overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modeling. In their comment [Phys. Rev. A 109, 026201 (2024)], Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavored by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modeling framework and from the fact that we referred to this framework as “classical” in order to contrast it with an intrinsically quantum alternative. In this Reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist hierarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.

We analyze the geometry of the ground-state manifold in parameter-dependent many-body systems with quantum phase transitions (QPTs) and describe finite-size precursors of the singular geometry emerging at the QPT boundary in the infinite-size limit. In particular, we elucidate the role of diabolic points in the formation of first-order QPTs, showing that these isolated geometric singularities represent seeds generating irregular behavior of geodesics in finite systems. We also demonstrate that established approximations, namely the mean-field approximation in many-body systems composed of mutually interacting bosons and the two-level approximation near a diabolic point, are insufficient to provide a reliable description of geometry. The outcomes of the general analysis are tested and illustrated by a specific bosonic model from the Lipkin-Meshkov-Glick family.

We present an innovative, platform-independent concept for multiparameter sensing where the measurable parameters are in series, or cascaded, enabling measurements as a function of position. With temporally resolved detection, we show that squeezing can give a quantum enhancement in sensitivity over that of classical states by a factor of $e^{2r}$, where $r\approx 1$ is the squeezing parameter. As an example, we have modeled an interferometer that senses multiple phase shifts along the same path, demonstrating a maximal quantum advantage by combining a coherent state with squeezed vacuum. Further classical modeling with up to 100 phases shows linear scaling potential for adding nodes to the sensor. The approach can be applied to remote sensing, geophysical surveying, and infrastructure monitoring.