Isolation from the environment leads to the days-long lifetime of noble-gas nuclear spins, but also brings great challenges to the preparation, manipulation, and measurement of nuclear-spin quantum states. Here we find that nuclear spin squeezing, with an ultralong lifetime and huge atomic number, can be efficiently obtained and manipulated based on the coherent spin-exchange interaction between alkali-metal and noble-gas ensembles. Thanks to the considerable advantage of our proposal in preparing the spin squeezing of the macroscopic atomic ensemble with a huge atomic number, even the nuclear spin-squeezed state containing ${10}^{20}$ atoms or more is obtainable with preexisting techniques. Further, the days-long storage and measurement of nuclear spin squeezing can be performed by the coherent manipulation of a magnetic field. This proposal can be implemented in hot atomic ensembles whose ease of access and high adaptability to various environments will significantly facilitate the research and application of nuclear-spin nonclassical states in precision measurement, quantum information, and fundamental physics.

Feedback uses past detection outcomes to dynamically modify a quantum system and is central to quantum control. These outcomes can be stored in a memory, defined as a stochastic function of past measurements. In this work, we investigate the main properties of a general memory function subject to arbitrary feedback dynamics. We show that the memory can be treated as a classical system coupled to the monitored quantum system and that their joint evolution is described by a hybrid bipartite state. This framework allows us to introduce information-theoretic measures that quantify the correlations between the system and the memory. Furthermore, we develop a general framework to characterize the statistics of the memory, such as moments, cumulants, and correlation functions, which can be applied both to general feedback-control protocols and to monitored systems without feedback. As an application, we analyze feedback schemes based on detection events in a two-level system coupled to a thermal bath, focusing on protocols that stabilize either the excited-state population or Rabi oscillations against thermal dissipation.

In this work, we consider a general feedback protocol based on quantum-jump detections, where the last detected jump channel is stored in a memory and subsequently used to implement a feedback action, such as modifying the system Hamiltonian conditioned on the last jump. We show that the time evolution of this general protocol can be described by a Lindblad master equation defined in a hybrid classical-quantum space, where the classical part encodes the stored measurement record (memory) and the quantum part represents the monitored system. Moreover, we show that this representation can be used to fully characterize the counting statistics of a system subject to a general jump-based feedback protocol. We apply the formalism to a three-level system coupled to two thermal baths operating as a thermal machine, and we show that jump-based feedback can be used to convert the information obtained from the jump detections into work. Our framework provides analytical tools that enable the characterization of key statistical properties of any counting observable under jump-based feedback, such as the average current, noise, correlation functions, and power spectrum.

Quantum target ranging, which estimates a target position using entangled photon pairs, is known to offer an error-probability advantage over classical ranging strategies. Yet, realizing this advantage in practice remains challenging, as an existing receiver design relies on collective measurements and requires an impractically large number of quantum memories and linear passive components. In this work, we propose a target ranging protocol with hetero-homodyne detection, providing a practically implementable architecture that achieves quantum advantage in target ranging using only local measurements. Our protocol requires only one heterodyne setup, a single homodyne setup, a delay line, and an efficient classical postprocessing, making the implementation scalable and experimentally feasible. Our results establish a realistic framework for demonstrating quantum advantage in target ranging and contribute toward practical quantum radar systems.

Sharing genuine multipartite entanglement by considering the collective use of copies of biseparable states, which are entangled across all bipartitions but lack genuine multipartite entanglement at the single-copy level, plays a central role in several quantum information processing protocols, and has been referred to as genuine multipartite entanglement activation. We present a protocol for three-qutrit systems showing that two copies of rank-two biseparable states, entangled across every bipartition, are sufficient to generate a genuinely multipartite entangled state with nonzero probability. This contrasts with the three-qubit scenario where many copies of biseparable states might be required for sharing genuine multipartite entanglement. We subsequently generalize our protocols to the case of an arbitrary number of parties. Interestingly, the proposed construction naturally leads to the activation of genuinely nonlocal correlations, yielding a result that is stronger than genuine multipartite entanglement activation alone.

We propose a quantum scrambling Born machine (QSBM) that decouples entanglement generation from the trainable degrees of freedom: a fixed, nontrainable scrambling unitary provides multiqubit entanglement while only single-qubit rotations are optimized. We consider three entangling unitaries (a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution under nearest-neighbor spin-chain Hamiltonians) and show that, for the benchmark distributions and system sizes considered, once the entangler produces near-Haar-typical entanglement the model learns the target distribution with weak sensitivity to the scrambler's microscopic origin. Because the scrambler requires only single-shot calibration, the entire trainable parameter budget is devoted to single-qubit rotations, eliminating the need for trainable multiqubit entangling gates on near-term hardware. Finally, promoting the Hamiltonian couplings to trainable parameters casts the generative task as a variational Hamiltonian problem, with performance competitive with representative classical generative models at matched parameter count.

Quantum error-correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking equilibrium-topology analysis. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. We validate the framework by demonstrating it rediscovers the optimal [[15,7,3]] quantum Hamming code in 20% of independent runs [A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098 (1996); A. Steane, Proc. R. Soc. Lond., Ser. A 452, 2551 (1996)] from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges. Applied across seven objectives [distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surfacelike topologies, connectivity enhancement, and maximization of the quantum Fisher information (which quantifies, via the Cramér-Rao bound, the metrological sensitivity of the encoded codespace)], the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including [[100,50,4]] with distance-4 protection and 50% encoding rate, with tractable cubic per-iteration complexity enabling discovery in under 1 h. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.

Onion routing provides anonymity by layering encryption so that no relay can link sender to destination. A quantum analog faces a core obstacle: Layered quantum encryption generally requires symmetric encryption schemes, whereas classically one would heavily rely on public key encryption. We propose a symmetric-encryption-based quantum onion routing (QOR) scheme by instantiating each layer with the Abelian ideal class group action from the theory of complex multiplication. Session keys are established locally via a Diffie-Hellman key exchange between neighbors in the chain of communication. Furthermore, we propose a “nonlocal” key exchange between the sender and receiver. The underlying problem remains hard even for quantum adversaries and underpins the security of current postquantum schemes. We connect our construction to isogeny graphs and their association schemes, using the Bose-Mesner algebra to formalize commutativity and guide implementation. We give two implementation paths: (i) a universal quantum oracle evaluating the class group action with polynomially many quantum resources and (ii) an intrinsically quantum approach via continuous-time quantum walks, outlined here and developed in a companion paper. A small Qiskit example illustrates the mechanics (by design, not the efficiency) of the QOR.

Calculations of the self-energy corrections to ionization energies of the $3s, 3p_{1/2}$, and $3p_{3/2}$ states in sodiumlike ions with nuclear-charge numbers $Z=30$, 50, 70, and 92 are presented. The calculations are performed using two approaches: the rigorous bound-state QED formalism and the model-QED-operator method. Within the first method, the first and second orders of the QED perturbation theory formulated in the Furry picture are evaluated. Various screening potentials are included into the initial approximation to partially take into account the electron-electron interaction effects already at the lowest order, thereby accelerating the convergence of perturbation series. Within the second approach, different implementations of the model-QED operator, including its incorporation into the relativistic configuration-interaction calculations, are considered. A detailed comparison of the results obtained by these two independent methods is presented, demonstrating good agreement and thus validating the accuracy and efficiency of the model-QED-operator approach for many-electron systems.

We experimentally demonstrate subwavelength spatial confinement of optical excitation using variants of stimulated Raman adiabatic passage (STIRAP) in a ${\text{Pr}}^{3+}\text{:}{\text{Y}}_2{\text{SiO}}_5$ crystal. Building on conventional STIRAP, we implement two more advanced schemes, double STIRAP and tripod STIRAP, which enable enhanced spatial control. At the cost of reduced coherence, double STIRAP provides an almost twofold improvement in resolution compared with conventional STIRAP, which already enables localization nearly two orders of magnitude below the pump beam waist. To resolve such fine structures near the diffraction limit, we employ an autocorrelation-based measurement technique. With this setup, we demonstrate excitation confinement by conventional STIRAP down to $260\pm 40\mathrm{nm}$, thus achieving subwavelength localization. As another powerful variant of adiabatic passage, we apply tripod STIRAP using an additional donut-shaped control beam that suppresses population transfer outside the beam center via coherent population trapping. With tripod STIRAP, we generate excitations as narrow as $350\pm 40\mathrm{nm}$, a factor of 28 below the width of the driving control beam. We demonstrate the scalability of the method by preparing tightly packed grids with up to 41 excitation spots without crosstalk, making the method well-suited for quantum architectures. Our results establish STIRAP variants as robust, versatile tools for coherent, spatially selective optical excitation on a subwavelength scale, opening broad applications in quantum technologies and classical optics.

We investigate the dynamics of a lasing system driven by a current of bosonic (quasi-)particles via a dissipative three-mode mixing process. A semiclassical analysis of this system predicts distinct dynamical regimes, where both the cavity mode and the gain medium can undergo lasing transitions. Of particular interest is an intermediate self-pulsing phase that exhibits the characteristics of an excitable system and converts random input signals into separated, quasi-periodic pulses at the output. By performing exact Monte Carlo simulations, we extend this analysis into the quantum regime and show that despite being dominated by huge bosonic particle number fluctuations, this effect survives even for rather low average photon numbers. Our system thus represents an intriguing model of an excitable quantum many-body system, with practical relevance for quantum detectors or autonomous quantum machines. As an illustration, we discuss the realization of this system with superconducting quantum circuits and its application as a number-resolved avalanche detector for microwave photons.

Hybrid quantum systems harness the distinct advantages of different physical platforms, yet their integration is not always trivial due to potential incompatibilities in operational principles. Here, we theoretically propose and demonstrate a scheme for generating non-Gaussian mechanical states using a strongly driven hybrid system that combines cavity quantum electrodynamics (QED) and cavity optomechanics. Our protocol prepares a non-Gaussian cavity state in the dispersive regime of cavity QED and subsequently transfers it to a mechanical oscillator using the optomechanical interaction enhanced by a coherent cavity drive. While non-Gaussian cavity state control in cavity QED is well established in the dispersive regime, its behavior under strong cavity drive, essential for cavity optomechanics, remains largely unexplored. To bridge this gap, we develop an efficient simulation framework to model cavity-QED dynamics in the high-photon-number regime. We show that a strong cavity drive can coherently displace the cavity state with minimal perturbations, effectively decoupling it from the qubit. The resulting large coherent cavity field enhances the optomechanical coupling strength, enabling high-fidelity transfer of non-Gaussian features from the cavity states to the mechanical mode. These results reveal different dynamical features of driven cavity QED and open a pathway toward realizing non-Gaussian mechanical quantum memories and sensors.

Considering an $N$-level system interacting factorizably with a continuous spectrum, we derive expressions for the bound states and the dynamical evolution within this single-excitation Friedrichs model by using the projection operator formalism. First, we establish explicit criteria to determine the number of bound states whose existence suppresses the complete spontaneous decay of the system. Second, we derive the open system's decay dynamics, which is naturally described by an energy-independent non-Hermitian Hamiltonian in the Markovian limit. As an example, we apply our framework to a two-level atomic chain side-coupled to a photonic lattice, uncovering a rich variety of decay dynamics and realizing an anti-$\mathcal{PT}$-symmetric Hamiltonian in the system's evolution.

We formulate a continuous-variable quantum computing (CVQC) algorithm to study Berry's phase on photonic quantum computers. We demonstrate that CVQC allows the simulation of charged particles with orbital angular momentum under the influence of an adiabatically changing $\vec{B}$ field. Although formulated entirely in the CVQC setting, our construction uses only passive linear-optical operations (beam splitters and phase shifts), which act identically in single-photon photonic architectures. This enables experimental realization on the quandela ascella platform, where we observe the Berry's phase phenomenon with interferometric measurement. We also generalize the framework to more rapid nonadiabatic evolution. By concatenating Aharonov-Anandan cycles for opposing magnetic fields we demonstrate that one can engineer a circuit in which dynamical phases and leading nongeometric errors cancel by symmetry, leaving the intrinsically robust geometric phase contribution.

The quantum $\mathrm{\Lambda }$ system is a ubiquitous structure in many quantum technologies, where two stable, lower-energy levels are coupled indirectly via an unstable, higher-energy level that is much more susceptible to decoherence and relaxation. In this paper, we solve the problem of finding a control driving field that leads to a desired final condition while minimizing the average population on the unstable level in finite time. We formulate the problem as an optimal control problem where the cost to be minimized is a combination of the energy of the control and the average population in the highest level. Our formulation applies to density matrix states, enabling control of mixed states and ensembles, which are essential for realistic settings such as thermal preparations, sensors, and scalable quantum information platforms. We utilize the Pontryagin Maximum Principle, symmetry reduction, and a number of auxiliary techniques to reduce the problem of finding the optimal control to a feasible numerical procedure. We prove several properties of the optimal control functions, such as normality and smoothness, and derive the system of differential equations that must be satisfied by the optimal pair of control and trajectory. We present a case study involving a Hadamard-like transformation for illustration. We discuss robustness of the control functions to the presence of unmodeled dynamics.

Highly charged ions (HCIs) combine compact electronic structure with strong relativistic effects, offering both robustness against external perturbations and enhanced sensitivity to variations of the fine-structure constant. Recent advances in sympathetic cooling and trapping enable precision measurements of highly charged ions; however, fully exploiting their potential requires accurate theoretical predictions. In particular, reliable calculations of clock wavelengths are essential for experimentally locating HCI clock transitions. Here, we treat ${\mathrm{Cf}}^{17+}$ as a univalent ion and perform calculations within the relativistic coupled-cluster framework, iteratively including nonlinear single-double contributions and valence and core triple excitations. We also assess quantum-electrodynamic corrections and basis-set and partial-wave truncation effects. Our results establish the impact of different correlation contributions on the low-lying energy spectrum and provide a quantitatively reliable prediction of the $5f_{5/2}\to 6p_{1/2}$ clock transition, highlighting the critical role of core-valence correlations and iterative triples for precision spectroscopy and optical clock development.

We report the experimental demonstration of the odd- and even-order harmonics predicted by [Chen et al., Phys. Rev. A 102, 053703 (2020)] and [S. Ashhab, J. R. Johansson, A. M. Zagoskin, and F. Nori, Phys. Rev. A 75, 063414 (2007)]. Using a cesium-atom magnetic-resonance platform under strong periodic driving, we observe a distinct transition in the time-domain signal between armchair- and sawtooth-like plateaus. Analysis of the Fourier amplitude spectrum reveals strict symmetry constraints within the monochromatic field region, where odd- and even-order harmonics can only occur individually. By implementing a bichromatic driving scheme, the selection rules in the case of a monochromatic field are broken, enabling the coexistence of odd- and even-order harmonics. This bichromatic harmonic engineering mechanism provides a physically meaningful means of control for periodically driven quantum systems. Our work establishes an experimental atomic magnetic-resonance platform for revealing symmetry-controlled harmonic engineering in a periodically driven quantum system, providing a generic physical paradigm that is conceptually relevant to bichromatic Floquet-control protocols in other quantum platforms.

We investigate the below-threshold harmonic (BTH) generation of the ${\mathrm{H}}_2^{+}$ molecule driven by a femtosecond infrared (IR) laser pulse in the presence of an extreme-ultraviolet (XUV) field—a process referred to as XUV-induced Rabi flopping. Rabi flopping (RF) is not confined to the three-level system interacting solely with an XUV pulse; it also manifests itself in the dressed cascade multilevel system when an IR field is introduced alongside the XUV pulse. By constructing a five-level Hamiltonian coupled with the molecular Perelomov-Popov-Terent'ev model and comparing with ab initio simulations, we reveal that both the one-photon RF between the two lowest states and the multiphoton RF involving higher excited states occur simultaneously in the dressed cascade multilevel system. Distinct odd and even harmonics emitted from dressed excited states due to multiphoton RF, as well as Rabi splittings, are observed in the BTH spectra. The laser-induced coherence of dressed states leads to quantum interference among excitation pathways that govern the optical response, providing a different approach for coherently controlling BTH generation in the RF regime under combined IR-XUV laser irradiation.

We study tunneling ionization of aligned ${\mathrm{H}}_2^{+}$ in strong near-circular laser fields numerically and analytically. The calculated attoclock offset angles differ for different alignments. By developing a strong-field model to quantitatively describe the alignment-related effects of two-center interference and near-nucleus Coulomb potential during tunneling, we can reproduce this phenomenon. We show that both effects significantly affect the offset angle and corresponding ionization time delay of aligned molecules. This model enables us to analytically separate these two effects, allowing us to clearly identify the Coulomb-induced time delay corresponding to dynamic time. Overall, there is an angle difference of about $1^{\circ }$ and a time-delay difference of about 5 as between the two typical cases of parallel and perpendicular alignments. This can be attributed to the subtle difference in the laser-dressed near-nucleus Coulomb potential in these cases. For more complex molecules such as ${\mathrm{N}}_2$, our simulations show that the wave function of the valence electron also plays an important role in the alignment-dependent offset angle and time delay. Our results may be useful for probing attosecond tunneling dynamics of aligned molecules.