We provide, to our knowledge, first and unambiguous evidence of the existence of cluster crystals formed by a binary mixture of ultrasoft, cluster-forming particles. In an effort to reduce the high dimensionality of the parameter space of binary mixtures, we have restricted ourselves to a symmetric, equimolar system, introducing as the pivotal parameter the scaling factor $\zeta$ that characterizes the cross interaction. Our investigations are based on a commonly used model for ultrasoft particles and on classical density functional theory, which, within a mean-field framework, allows for mixed clusters composed of particles of both species. Minimizing the free energy functional predicts three competing cluster crystal structures, namely, a bcc and a tetragonal lattice that reduces under certain conditions to an fcc lattice. The emerging phase diagram is rather intricate, but is well understood in terms of an energetic competition between the two sublattices. Complementary molecular dynamics simulations confirm the stability of the predicted structures and allow to trace the particles in their migration processes through the crystal.

Recently, there has been considerable interest in studying quantum sensing near the critical points of a system evolving unitarily and undergoing a phase transition. However, there are many quantum systems in which dissipation is very important. The quantum phase transition in such systems results as a result of competition between nonlinearity, drive, and dissipation. These quantum phase transitions belong to the class of nonequilibrium phase transitions. In this work, we present a detailed study of quantum sensing of the system parameters near the critical points of a dissipative phase transition. We illustrate the key results by considering a coherently driven nonlinear Kerr medium interacting with environment. The first-order quantum phase transition is characterized by the closing of the gap in eigenvalues of the underlying Liouvillian. The steady-state sensing away from the critical point has standard quantum limit scaling with respect to the effective system size, whereas Heisenberg scaling is found at the critical point. The latter is subject to a critical slowing down. We have also examined sensing of system parameters using the metastable states and find better sensing performance at intermediate timescales, i.e., when the system has not yet settled in steady state. Detailed results on the scaling behavior in different time domains are given.

We construct a model of a three-dimensional helical second-order topological superconductor formed by an array of weakly coupled Rashba nanowires. We identify the parameter regime in which there are energy gaps in both the bulk and surface energy spectra, while a pair of helical ${\mathbb{Z}}_{2q}$ parafermionic modes (with $q$ being an odd integer) remains gapless along a closed path of one-dimensional hinges. The precise trajectory of these hinge modes is dictated by the hierarchy of interwire couplings and the boundary termination of the sample. In the noninteracting limit $q=1$, the system hosts gapless Majorana hinge modes.

Crystallites form in supercooled liquids as particles rearrange into ordered structures, driven by thermal fluctuations or external stimuli. While the thermodynamics of heterogeneous crystallization under boundary constraints is well described by classical nucleation theory, the kinetics of symmetry formation—particularly in systems far from the transition point—remains poorly understood. In this study, we investigate the heterogeneous crystallization of a colloidal system across a wide range of effective supercooling degrees by varying the volume fraction. Using confocal microscopy, we capture the motion and local structures of particles in situ with high spatial and temporal resolution. Our results reveal a consistent crystallization pathway across different supercooling levels: Rotational symmetry forms prior to translational symmetry, with normal modes of local structures playing distinct roles in each stage of crystallization. Notably, the liquid-to-precursor transformation is robust even under deep supercooling, suggesting minimal influence of supercooling on rotational order development. In contrast, the precursor-to-solid transformation is significantly accelerated in denser systems, indicating that translational order is strongly governed by the degree of supercooling. These findings provide insights into the interplay between thermodynamics and kinetics in heterogeneous crystallization and offer guidance for controlling phase transitions across a broad range of disciplines.

Droplets are ubiquitous in nature and industry, yet their behavior is not yet fully understood, particularly for extreme conditions not typically encountered in viscous classical fluids. In this study, we investigated the oscillations of a superfluid ${}^4\mathrm{He}$ pendant droplet formed beneath a cup by superfluid film flow. We controlled the mobility of the droplet's edge by attaching cylinders of varying diameter to the underside of the cup, so that the droplet was suspended from the bottom of the cylinder. For wide cylinders or in the absence of a cylinder, the lowest point of the droplet oscillated vertically, while the edge oscillated along the surface, with only a slight dependence of the oscillation period on the droplet volume, which contradicts the common assumption in classical fluids that larger droplets oscillate with a longer period. For narrow cylinders, the droplet oscillated vertically, while the edge remained fixed at the cylinder's edge, and the oscillation period increased monotonically with increasing droplet volume, displaying the expected behavior. These observations demonstrate that free motion of the droplet's edge contributes to anomalous volume-independent oscillation of pendant droplets. We propose that the marginal volume dependence arises from the stability of superfluid pendant droplets in a region between two instabilities. This behavior is significant only for fluids that completely wet the substrate and possess a mobile edge, a condition rarely observed in classical fluids but naturally occurring in superfluids. Hence, these findings reveal unique properties of droplets in superfluid ${}^4\mathrm{He}$ not seen in classical fluids.

We introduce a chiral Schrödinger cat qubit, a bosonic quantum code generalizing Kerr cat qubits that exploits higher-order nonlinearities. Compared to standard Kerr cats, the chiral cat qubit allows additional correction of bit-flip errors within the Hilbert space of a single bosonic oscillator. This property results from optical bistability, i.e., the simultaneous presence of multiple long-lived states. Two of them define the code logical basis and two define an error manifold. Thanks to the chiral structure of the phase space of this system, the error manifold can be engineered to “capture” bit-flip events in the code space (a bit-flip trap), without affecting the quantum information stored in the system. Therefore, it is possible to perform detection and correction of errors. We demonstrate how this topological effect can be particularly efficient in the presence of large dephasing. We provide concrete examples of the performance of the code and show the possibility of applying quantum operations rapidly and efficiently. Beyond the interest in this single technological application, our work demonstrates how the topology of phase space can enhance the performance of bosonic codes.

Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work, we propose measuring an algorithm's performance using the mutual information between the output and the actual value. The task of optimizing this mutual information using a single query is similar to a basic task of quantum communication, where one attempts to maximize the mutual information of the sender and receiver. We make this analogy precise by splitting the algorithm between two agents, obtaining a communication protocol. The oracle's target property plays the role of a message that Alice encodes into a quantum state, which is subsequently sent over to Bob. The first part of the algorithm performs this encoding, and the second part measures the state and aims to deduce the message from the outcome. Moreover, we formally consider the oracle as a separate subsystem, whose state records the unknown oracle identity. Within this construction, Bob's optimal measurement basis minimizes the quantum correlations between the two subsystems. We also find a lower bound on the mutual information, which is related to quantum coherence. These results extend to multiple-query nonadaptive algorithms. As a result, we describe the optimal nonadaptive algorithm that uses at most a fixed number of queries, for any oracle classification problem. Crucially, this mutual-information perspective was shown elsewhere [A. Levi et al., Quantum Sci. Technol. 11, 015029 (2026)] to have practical utility for algorithmic design, providing the theoretical foundation to optimize iterative subroutines in hybrid quantum-classical schemes. Within the present work, we apply this framework to analyze the stage-by-stage information flow and track partial progress in several standard quantum algorithms, including the Deutsch-Jozsa, Bernstein-Vazirani, and Shor-Kitaev algorithms.

We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.

Optical clocks have achieved remarkable estimated fractional frequency uncertainties reaching the ${10}^{-18}$ level and below, enabling applications in fundamental physics, general relativity, and geodesy. However, the challenge of verifying the international consistency of optical clocks remains critical as efforts intensify toward redefining the SI second based on an optical transition or transitions. We report on a two-month international clock comparison campaign involving seven optical clocks in four national metrology institutes (INRIM, LNE-OP, NPL, and PTB) connected via the optical fiber network established in Europe. The campaign resulted in optical frequency ratios with uncertainties ranging from $7.7\times {10}^{-18}$ to $6.1\times {10}^{-17}$. Among the results, the ${}^{171}\mathrm{Yb}^{+}\left(\mathrm{E}3\right)$ clocks at NPL and PTB demonstrated agreement within an uncertainty of $7.7\times {10}^{-18}$, marking the first international verification of two independently developed optical clocks below one part in ${10}^{17}$. The operation of the ${}^{199}\mathrm{Hg}$ clock at LNE-OP (formerly LNE-SYRTE) resulted in frequency ratios with improved uncertainties with ${}^{171}\mathrm{Yb}^{+}\left(\mathrm{E}3\right), {}^{171}\mathrm{Yb}$, and ${}^{87}\mathrm{Sr}$ optical clocks. These results provide input for the redefinition of the second and underscore how fiber-linked clock networks can advance metrology and scientific applications.

Ultrafast strong-field laser-plasma physics is shown to offer a promising framework for relativistic nonlinear quantum electrodynamics (QED). As one of its key advantages, this approach to relativistic nonlinear QED does not require an external beam of relativistic particles. Instead, high-energy electrons are produced in this setting as a part of ultrafast strong-field laser-plasma interactions. An intense ultrashort laser pulse generates and accelerates dense electron bunches to relativistic energies, giving rise to photon-pair emission confined to the nanometer scale in space and the attosecond scale in time. As a lowest-order nonlinear QED process, relativistic electrons in laser-driven plasmas are shown to give rise to attosecond bursts of two-photon emission, providing an ultrabroadband source of correlated photon pairs. As a physically insightful estimate, the rate of this two-photon emission is expressed via a product ${\alpha }^2\gamma {\omega }_{\text{turn}}$, where $\alpha$ is the fine-structure constant, $\gamma$ is the Lorentz factor, and ${\omega }_{\text{turn}}$ is the local relativistic curvature frequency. Photon pairs with strongest correlations, providing a resource for photon entanglement, are emitted at a much lower rate, estimated as ${\alpha }^2{\gamma }^2{\omega }_{\text{turn}}{E}_{\perp }/E_S$, where $E_{\perp }$ is the laser electromagnetic field, determining the transverse Lorentz force, and $E_S$ is the Schwinger critical field. Our study offers a clear framework for isolating quantum aspects of laser-driven relativistic plasma electrodynamics from their classical counterparts, enabling a physically justifiable approach to the analysis of nonlinear QED phenomena in complex laser-plasma interactions driven by ultrashort high-intensity laser pulses. With purely quantum-field effects isolated via ${\alpha }^2$ and $E_{\perp }/E_S$ factors, the role of classical plasma analysis in this framework is to simulate spatially and temporally resolved electron trajectories, thus providing direct in situ probes for local $\gamma$ and ${\omega }_{\text{turn}}$ factors of plasma electrons. At laser intensities corresponding to relativistic laser amplitudes $a_0\sim 20–200$, accessible at multipetawatt laser facilities, laser-solid interactions drive electrons to $\gamma \sim 100$, and their correlated attosecond photon-pair emission emerges as a previously unexplored quantum light source competing with classical coherent synchrotron emission.

While machine learning holds great promise for quantum technologies, most current methods focus on predicting or controlling a specific quantum system. Metalearning approaches, however, can adapt to new systems for which little data are available, by leveraging knowledge obtained from previous data associated with similar systems. In this paper, we metalearn dynamics and characteristics of closed and open two-level systems, as well as the Heisenberg model. Based on experimental data of a Loss-DiVincenzo spin qubit hosted in a Ge/Si core/shell nanowire for different gate voltage configurations, we predict qubit characteristics, i.e., $g$ factor and Rabi frequency using metalearning. The algorithm we introduce improves upon previous state-of-the-art metalearning methods for physics-based systems by introducing techniques such as adaptive learning rates and a global optimizer for improved robustness and increased computational efficiency. We benchmark our method against other metalearning methods, a vanilla transformer, and a multilayer perceptron, and demonstrate improved performance.

Spin squeezing in atomic ensembles enables atom interferometry with sensitivities below the shot-noise limit, but the associated entanglement is highly susceptible to loss, making imperfections in atom optics a central limitation. Bragg diffraction is an established technique for driving transitions between atomic momentum states and enables large-momentum transfer through higher-order diffraction while preserving the internal state. However, it is intrinsically limited by two competing mechanisms: Short light pulses induce parasitic diffraction into off-resonant orders beyond an effective two-level description, while long pulses face velocity selectivity. We derive analytical expressions in a second-quantized framework for the atom optics and phase uncertainty of a Mach-Zehnder interferometer including these effects. We demonstrate that sub-shot-noise scaling is achieved only in a regime of intermediate pulse duration. Furthermore, we show that deleterious effects of higher-order diffraction are partially mitigated by optimizing the input quantum state.

Inorganic structural chemistry leads naturally to a theory for crystal structure prediction formalized by a generalized disjunctive programming, which is formulated using continuous and Boolean variables to involve the algebraic equations, disjunctions, and logic propositions. Since the feasibilities of continuous variables change drastically depending on Boolean variables and vice versa, iterative optimization of continuous and Boolean variables efficiently transforms a randomly generated initial structure into an optimal solution. Boolean variables are introduced to elucidate the “combinatorial backbone” of the original continuous optimization problem, which corresponds to the graphs describing crystal structures with clear chemical meanings. Since many subgraphs are discovered in numerous graphs generated through structural optimizations, on-the-fly learning of the feasibilities of them accelerates the discovery of the optimal solutions. This theory enables designing a wide variety of crystal structures with small computations based on only the atomic radii and feasible coordination numbers of each atom.

We propose a hybrid quantum computing architecture composed of alternating fluxonium and transmon qubits, which are coupled via transmon tunable couplers. We show that this system offers excellent scaling properties, characterized by engineered zero $ZZ$ crosstalk in the idle regime, a substantial reduction of level-crowding challenges through the alternating arrangement of different qubit types within the lattice, and parameter regimes that circumvent the capacitive loading problem commonly associated with fluxoniums. In numerical simulations, we show a parametrically driven CZ gate that achieves a closed-system infidelity that is orders of magnitude below the coherence limit for gate durations $\gtrsim 30\mathrm{ns}$ using a two-tone flux pulse on the tunable coupler. Furthermore, we show that this gate scheme retains its fidelity in the presence of multiple spectator qubits, making it a scalable solution for large lattices. Moreover, for the implementation of error correcting codes, our approach can leverage the long coherence times and large nonlinearities of fluxoniums as data qubits, while fixed-frequency transmons with established readout techniques can serve as measurement ancillae.