Reinforcement learning (RL) shows promise for automated quantum circuit design but often stalls due to a “fidelity trap”: by optimizing only state fidelity, agents overlook entanglement structure and become stranded in suboptimal, overly complex circuits, resulting in significantly reduced search efficiency. In this paper, we propose a scheme that overcomes this barrier by implementing an entanglement-aware learning framework and enhancing the agent's reward function with a direct, quantitative measure of entanglement. This approach offers a more comprehensive physical description of the state space. We demonstrate the efficacy of this principle on three- and four-qubit state-synthesis tasks within an expanded gate set. For this problem, where the fidelity-driven agent systematically fails to discover the minimal-depth circuit, our entanglement-aware agent consistently succeeds. This transformative result is highly robust against variations in initial random seeds and extends to multiqubit systems even in the presence of noise. Our findings establish a generalizable principle that incorporating entanglement as an auxiliary reward can significantly enhance RL-based solutions for a broad class of fidelity-centric tasks in quantum physics and pave the way for scalable, automated discovery on near-term quantum devices.

We report a highly accurate ab initio study of the ionization potential (IP) and electron affinity (EA) of element 119. Electronic correlation effects are treated within the relativistic coupled-cluster theory including excitations up to quadruples. The Gaunt electron-electron interaction and QED corrections are taken into account. The role of high-order correlation effects is analyzed in detail. Our recommended values for the IP and EA are 4.7839(56) and 0.6750(71) eV, respectively. These results tighten previous estimates and provide a reference point for future experiments probing periodic-law trends beyond oganesson.

Here we examine the propagation of relativistic fields in space-time using the viewpoint applied to derive the Rayleigh–Sommerfeld diffraction integral in three-dimensional space. We use this theory to find the propagators for both the Klein–Gordon equation and the Dirac equation. Based on these results, we highlight some apparently overlooked aspects of the Feynman checkerboard model as it is usually applied to the Dirac equation.

We present an alternative approach to the definition of optical helicity in a medium. Our approach resolves the problem that duality transformations which simultaneously combine $\mathbf{E}$ with $\mathbf{H}$ and $\mathbf{D}$ with $\mathbf{B}$ are incompatible with linear constitutive relations. We find that the helicity density in a medium, as the conserved quantity associated with duality transforms, must contain an explicit contribution associated with the polarization and magnetization of the matter, and that it can be expressed naturally in terms of the elementary polarized excitations of the system. In media for which the helicity is conserved, each circular excitation carries a well-defined helicity. However, in a medium for which the helicity is not conserved, we find that the time-varying helicity can be viewed in terms of oscillations between different helicity eigenstates, analogous to neutrino oscillations. Here we explicitly study the helicity in homogeneous and lossless media but we believe that, differently to other choices, this helicity is readily generalizable to media that may be inhomogeneous, lossy, chiral or nonreciprocal.

The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and nonlinearly coupled parametric oscillators, provides a versatile simulator of general classical vector spin models in arbitrary dimension, finding the minimum of the simulated spin Hamiltonian and implementing novel annealing algorithms. In the hyperspin machine, oscillators evolve in time minimizing a cost function that must resemble the desired spin Hamiltonian in order for the system to reliably simulate the target spin model. This condition is met if the hyperspin amplitudes are equal in the steady state. Currently, no mechanism to enforce equal amplitudes exists. Here we bridge this gap and introduce a method to simulate the hyperspin machine with equalized amplitudes in the steady state. We employ an additional network of oscillators (named equalizers) that connect to the hyperspin machine via an antisymmetric nonlinear coupling and equalize the hyperspin amplitudes. We demonstrate the performance of such an equalized hyperspin machine by large-scale numerical simulations up to 10 000 hyperspins. Compared to the hyperspin machine without equalization, we find that (1) the equalized hyperspin machine reaches orders of magnitude lower spin energy and (2) its performance is significantly less sensitive to the system parameters. The equalized hyperspin machine offers a competitive spin Hamiltonian minimizer and opens the possibility to combine amplitude equalization with complex annealing protocols to further boost the performance of spin machines.

In this work we review the Weisskopf-Wigner formalism for spontaneous emission considering the spatial modes of light as well as external atomic degrees of freedom, which we introduce in the theory by modeling the atom as a wave packet in momentum space with a given initial uncertainty. We perform a purity calculation in order to quantify the entanglement encoded in the momentum variables of the atom-photon system. Our purity calculations reveal two high-entanglement regimes depending on the initial atomic momentum uncertainty: (1) the Recoil entanglement regime (which arises in the small momentum uncertainty region) where recoil effects dominate the mechanisms that originate entanglement, and (2) the Doppler entanglement regime (in the large momentum uncertainty region) where homogeneous Doppler shifts in the emitted photon's frequency play the fundamental part in the build up of quantum correlations in the system. Physical considerations are made to explain the nature of each entanglement regime as well as provide their respective thresholds.

The quantum speed limit sets a fundamental restriction on the evolution time of quantum systems. We explore the relationship between quantum imaginarity and the quantum speed limit by utilizing measures such as relative entropy, trace distance, and geometric imaginarity. These speed limits define the fundamental constraints on the minimum time necessary for quantum systems to evolve under various dynamical processes. As applications, the dephasing dynamics and dissipative dynamics are analyzed in detail. The quantum speed limit in stochastic-approximate transformations is also investigated. Our quantum speed limits provide lower bounds on how fast a physical system evolves to attain or lose certain imaginarity, with potential applications in efficient quantum computation designs, quantum control, and quantum sensing.

We study different characterizations of positive (P) divisibility in two-level open quantum systems whose dynamics are governed by a time-local master equation with time-dependent relaxation rates. In the case of phase-covariant dynamics, necessary and sufficient conditions for the P-divisibility of the dynamical map are given in terms of inequalities on such relaxation rates. We propose a geometric P-divisibility criterion based on the Bloch coordinates. The connection to the Breuer-Laine-Piilo (BLP) measure of non-Markovianity is also established. We show how these results can be extended to a Redfield master equation. As an application of such characterizations, we study the open dynamics of a qubit interacting with a single bosonic mode. More precisely, we characterize the properties of the local map of the qubit generated by its interaction with the bosonic mode, playing the role of an extremely reduced bath. Interesting observations are made, opening perspectives for a deeper physical understanding of complete positive divisibility, P-divisibility, and BLP measure.

Traditional quantum speed limits formulated in density matrix space are generally unattainable for a wide class of dynamics and it is difficult to characterize the fastest possible dynamics. To address this, we present two distinct quantum speed limits in Liouville space for completely positive and trace-preserving (CPTP) dynamics. The first bound saturates for time-optimal CPTP dynamics, while the second bound is exact for all states and all CPTP dynamics. Our bounds have a clear physical and geometric interpretation arising from the uncertainty relations for operators acting on Liouville space, and the geometry of quantum evolution in Liouville space. We also obtain the form of the Liouvillian, which generates the time-optimal CPTP dynamics that connects the given initial and target states. To illustrate our findings, we show that the speed of evolution in Liouville space bounds the growth of the spectral form factor and Krylov complexity of states, which are crucial for studying information scrambling and quantum chaos. In another important application, we show that our results can help us understand the counterintuitive phenomenon of the Mpemba effect in nonequilibrium open quantum dynamics, as the minimal relaxation time scale obtained by speed limits is dictated by the eigenmodes of the Liouvillian.

Discrimination of quantum states under local operations and classical communication is an intriguing question in the context of local retrieval of classical information, encoded in the multipartite quantum systems. All the local quantum state discrimination premises considered so far mimic a basic communication setup, where the spatially separated decoding devices are independent of any additional input. Here, exploring a generalized communication scenario, we introduce a framework for input-dependent local quantum state discrimination, which we call local random authentication (LRA). We report that the impossibility of LRA certifies the presence of entangled states in the ensemble, a feature absent from erstwhile nonlocality arguments based on local state discrimination. Additionally, we explore the salient features of this state discrimination prototype for an arbitrary set of orthogonal quantum states and compare them with the traditional notion of local quantum state discrimination. Finally, our results reveal fundamental information-theoretic implications in the local estimation of quantum change-point problems.

Quantifying mixed-state entanglement in many-body systems has been a formidable task. In this work, we quantify the entanglement of states in unresolvable spin ensembles, which are inherently mixed. By exploiting their permutationally invariant properties, we show that the bipartite entanglement of a wide range of unresolvable ensemble states can be calculated exactly. Our formalism is versatile; it can be used to evaluate the entanglement in an ensemble with an arbitrary number of particles, effective angular momentum, and bipartition. We apply our method to explore the characteristics of entanglement in different physically motivated scenarios, including states with definite magnetization and metrologically useful superpositions such as Greenberger-Horne-Zeilinger (GHZ) states and spin-squeezed states. Our method can help understand the role of entanglement in spin-ensemble-based quantum technologies.

Bell nonlocality and quantum steering are recognized as two important physical resources and offer quantum advantages in modern quantum information processing. Inspired by the asymmetric relations of teleportation to Bell nonlocality and quantum steering, in this paper we unify the maximal violation of Bell inequality and the maximal violation of the three-setting linear steering inequality by introducing the concept of average correlation and manage to establish the relation of average correlation to quantum teleportation. Particularly, we propose a necessary and sufficient condition for any two-qubit state with nonclassicality in terms of average correlation for teleportation. Our results suggest that average correlation is not only used to detect the nonclassicality of quantum states, but also can be useful as a potential resource for teleportation.

In this work, we investigate the dynamical process of an open quantum system under the action of quantum cyclic $n$-switch in generalized amplitude-damping channels and depolarizing channels. The quantum cyclic $n$-switch operation is introduced by an external control system. Our results show that the quantum switch can regulate the dynamical behavior of the system dynamics and achieve non-Markovian speedup dynamics. Increasing the dimension of the control system can significantly enhance the evolution speed of the system's non-Markovian dynamics. For the generalized amplitude-damping channels, when the influence of thermal noise is intense, the greater the quantum cyclic $n$-switch is, the lower the initial coherence is, and the more conducive it is to the acceleration of the quantum state evolution speed. In the depolarizing channels, under the action of quantum cyclic $n$-switch, the evolution speed of the system dynamics is directly related to the non-Markovianity and is independent of the initial coherence of the system.

The principal resource in several quantum information-processing tasks is entanglement. Building practically useful versions of such tasks, one often needs to consider multipartite systems. And in such scenarios, it is impossible to eliminate the effects of the environment while distributing the resources. We show how information backflow from the environment due to non-Markovianity in the system dynamics affects the resources in multipartite systems, specifically multiparty entanglement. In particular, we find that the entanglement of multiqubit Greenberger-Horne-Zeilinger cat states saturates with time to a nonzero value for a non-Markovian dephasing noise. The multiqubit $W$ states saturate to a higher value. Such nonzero time-saturated values are washed out if the non-Markovianity in the channel is removed. The multiqubit $W$ states provide a richer set of features, including a nonzero value for an asymptotic number of qubits and an even-odd dichotomy in the entanglement with the number of qubits. Moving to a non-Markovian depolarizing channel, we find that both cat and $W$ states exhibit a revival of entanglement after the collapse.

Despite significant advances in quantum information theory, the well-known entanglement axiom cannot be used to completely distinguish between different types of entanglement. We address this fundamental limitation by proposing generalized entanglement axioms for the complete characterization of entanglement. We firstly extend entanglement axioms under vector majorization—a mathematical framework that extends beyond conventional scalar measures. We then introduce entanglement-measure vectors that enable comprehensive classification of all bipartite pure states under local unitary operations. We further demonstrate how this framework naturally extends to multipartite systems through marginal information analysis. This work establishes a unified, mathematically rigorous methodology for entanglement classification with implications for both quantum foundations and quantum technologies.

We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubitwise commutativity and (full) commutativity. We apply this notion, which we call $k$-commutativity, to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth. We discuss the asymptotic measurement complexity of $k$-commutativity for several families of $n$-qubit Hamiltonians, showing examples with $O\left(1\right)$, $O\left(\sqrt{n}\right)$, and $O\left(n\right)$ scaling.

We investigate how the stabilizer formalism, in particular highly entangled stabilizer states, can be used to describe the emergence of many-body shape collectivity from individual constituents in a symmetry-preserving and classically efficient way. The method that we adopt is based on determining an optimal separation of the Hamiltonian into a stabilizer component and a residual part inducing nonstabilizerness. The corresponding stabilizer ground state is efficiently prepared using techniques of graph states and stabilizer tableaux. We demonstrate this technique in context of the Lipkin-Meshkov-Glick model, a fully connected spin system presenting a second-order phase transition from spherical to deformed state. The resulting stabilizer ground state is found to capture to a large extent both bipartite and collective multipartite entanglement features of the exact solution in the region of large deformation. We also explore several methods for injecting nonstabilizerness into the system, including adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver and imaginary-time evolution (ITE) techniques. Stabilizer ground states are found to accelerate ITE convergence due to a larger overlap with the exact ground state. While further investigations are required, the present work suggests that collective features may be associated with high but simple large-scale entanglement which can be captured by stabilizer states, while the interplay with single-particle motion may be responsible for inducing nonstabilizerness. This study motivates applications of the proposed approach to more realistic quantum many-body systems, whose stabilizer ground states can be used in combinations with powerful classical many-body techniques and/or quantum methods.

We examine the impact of time-dependent gate voltages on entanglement generation in two capacitively coupled charge qubits, with single-electron injection triggered on demand. The gate voltage modulates the tunnel coupling between the qubits and electronic reservoirs, initiating charge transport into the system. The formation of entangled states arises from the competition between interqubit Coulomb interactions and electron-hopping processes. Particular attention is paid to the temporal structure of the gate pulse, which plays a pivotal role in shaping the entanglement dynamics. By exploring a variety of pulse profiles, we uncover regimes of enhanced entanglement and identify optimal driving conditions. Additionally, we investigate how environmental dephasing deteriorates entanglement formation. Within the framework of the density-matrix formalism, we calculate fidelity, linear entropy, and negativity to identify robust operational windows. These results provide insights into controlling quantum correlations in mesoscopic systems and underscore the importance of error-mitigation strategies in realizing high-performance electronic quantum devices.

Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.

A unitary evolution in time may be treated as a curve in the manifold of the special unitary group. The length of such a curve can be related to the energetic cost of the associated computation, meaning a geodesic curve identifies an energetically optimal path. In this work, we employ sub-Riemannian geometry on the manifold of the unitary group to obtain optimally designed Hamiltonians for generating single-qubit gates in an environment with the presence of dephasing noise as well as a two-qubit gate under a time-constant crosstalk interaction. The resulting geodesic equation involves knowing the initial conditions of the parameters that cannot be obtained analytically. We then introduce a random sampling method combined with a minimization function and a cost function to find initial conditions that lead to optimal control fields. We also compare the optimized control fields obtained from the solutions of the geodesic equation with those extracted from the well-known Krotov method. Both approaches provide high-fidelity values for the desired quantum gate implementation, but the geodesic method has the advantage of minimizing the required energy to execute the same task. These findings bring insights for the design of more efficient fields in the arsenal of optimal control theory.