Solving large-scale quadratic unconstrained binary optimization (QUBO) problems is critical in various fields, including physics, finance, and engineering. However, these problems remain intractable on conventional computing architectures. Alternative solvers, such as Ising machines (IMs) based on networks of coupled electronic, mechanical, or photonic parametric oscillators (POs), have recently been developed. PO-based IMs aim to find the ground state of an Ising Hamiltonian, which encodes the solution to a QUBO problem. However, their analog nature and their energy-minimization process based on gradient descent make PO-based IMs inherently susceptible to identifying inaccurate solutions. In this work, we introduce and validate a QUBO solver—the analog Floquet solver (AFS)—which enhances the dynamics of PO-based IMs by leveraging Floquet states that emerge spontaneously in POs coupled to high-quality-factor resonances. These states enable the AFS to embed periodic time modulation into its energy-minimization process, allowing it to escape local minima during the search for QUBO problem solutions. As a result, the AFS significantly increases the likelihood of identifying accurate solutions compared to conventional PO-based IMs. More generally, this work defines a new paradigm in analog computing—spanning both classical and quantum realms—that can be physically realized with existing technologies across diverse physical domains.

The interplay among electronic correlation, topology, and time-reversal symmetry often leads to exotic quantum states of matter, as highlighted by the discoveries of fractional Chern insulators in twisted bilayer ${\mathrm{MoTe}}_2({\mathrm{tMoTe}}_2)$. Among the fractional Chern insulators (FCIs) in ${\mathrm{tMoTe}}_2$, the most robust is at a hole filling factor of $\mathit{\nu }=-\frac{2}{3}$ per moiré unit cell. Here, employing pump-probe circular dichroism measurement on ${\mathrm{tMoTe}}_2$ at twist angles $\theta =3.9°$ and 3.7°, we show that a correlated state at $\mathit{\nu }=-\frac{4}{3}$ exhibits an unusual Ising antiferromagnet behavior. The $\mathit{\nu }=-\frac{4}{3}$ state with no net magnetization undergoes first order phase transitions at extremely low magnetic fields of $|{\mu }_{0}H|\sim 2–6\mathrm{mT}$ to partially valley polarized states. This behavior is notably absent for all other correlated states in ${\mathrm{tMoTe}}_2$ and also disappears for $\mathit{\nu }=-\frac{4}{3}$ at higher or lower twist angles ($\theta =4.0°$ or 3.3°). The observed magnetic signature is consistent with a theoretically proposed fractional topological insulator (FTI), consisting of two copies of ${\mathit{\nu }}_{\pm }=-\frac{2}{3}$ FCIs with opposite chirality in the ${\mathit{K}}^{\pm }$ valleys. The experimental results are supported by interacting continuum model calculations that reveal the extreme closeness in energy ($\mathrm{\Delta }\mathrm{E}<1\mathrm{meV}$) between the putative FTI (${\mathit{\nu }}_{\pm }=-\frac{2}{3}$ and ${\mathit{\nu }}_{\mp }=-\frac{2}{3}$) and partially valley polarized states (${\mathit{\nu }}_{\pm }=-1$ and ${\mathit{\nu }}_{\mp }=-\frac{1}{3}$). Our findings present a candidate FTI with time-reversal symmetry and call for advanced transport and imaging measurements to establish the quantized helical edge modes.

The discovery of superconductivity in bulk bilayer nickelates under high pressure, and its subsequent stabilization in compressively strained thin films at ambient pressure, has established a new platform for exploring high-$T_{\mathrm{c}}$ superconductivity beyond the cuprates. Central to this development is the prominent role of the $3d_z^2$ orbital in shaping the low-energy electronic structure, imposing constraints on microscopic theories and fueling debate over the superconducting mechanism. Here we report a systematic in situ angle-resolved photoemission spectroscopy study of compressively strained bilayer nickelate thin films spanning Ca doping, oxygen stoichiometry and film thickness. Despite variations in oxygen-vacancy disorder and surface termination, the electronic structure remains robust and exhibits a systematic strain-driven evolution consistent with an intermediate-correlation regime. In particular, we demonstrate a Ca-doping-induced electronic structure evolution that is consistent with Fermi-level crossing of the $\gamma$ band and is decoupled from the presence of superconductivity, suggesting that, while important for the $\gamma$ band to be near the Fermi level, the debated $\gamma$ crossing and the resulting Fermi pocket may not be a prerequisite for superconductivity. Together, our results establish key spectroscopic constraints on the minimal fermiology and correlation strength relevant to superconductivity in bilayer nickelates, providing an experimental foundation for microscopic theories of their pairing mechanism.

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master equation methods. These path integrals allow one to readily impose space-time symmetries, including Lorentz invariance or diffeomorphism invariance. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the stochastic path integral of classical stochastic dynamics while respecting symmetry principles. We introduce a path integral formulation of general relativity where the space-time metric is treated classically. The theory is a candidate for a fundamental theory that reconciles general relativity with quantum mechanics. The theory is manifestly covariant, and may be inequivalent to the theory derived using master equation methods. We prove that entanglement cannot be created via the classical field, reinforcing proposals to test the quantum nature of gravity via entanglement generation.

Knits and crochets are mechanical metamaterials with a long history that can typically be produced from a single yarn. Despite the simplicity of the manufacturing process, they exhibit a wide range of structural configurations with diverse mechanical properties and application potentials. Although there has been recent growing interest in textile-based metamaterials, a rigorous topological characterization of what makes a structure knittable has been lacking. Here, we introduce a general criterion based on topological constraints that distinguish knits and crochets from other textile structures. We demonstrate how the introduction of topological defects and their propagation makes this classification practical. Our approach highlights a fundamental link between manufacturing processes and structural fragility. Within this framework, we show how the rationalization of defect propagation unlocks the design of fabrics with controllable damage resistance.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks. Existing approaches rely on deterministic state transfer, or probabilistic protocols that require active control or measurements and postselection. Here, we demonstrate a fundamentally different, fully autonomous process, where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir. In our experiment, a Josephson parametric converter produces a Gaussian, continuous-variable entangled state of propagating microwave fields that drives two spatially separated superconducting transmon qubits into a stationary, discrete-variable entangled state. We also show how qubit tomography unlocks a direct and sensitive verification of two-mode squeezing in the microwave domain. These results establish networks of qubits interfaced with distributed continuous-variable entangled states as a powerful platform for foundational studies and quantum-technology applications.

Remote entanglement between widely separated qubits is a fundamental quantum phenomenon and a critical resource for quantum information applications. Generating entanglement between independent qubits separated by arbitrary, potentially large distances requires propagating quantum states and is typically achieved using pulsed protocols combining distinct steps of local entanglement generation followed by distribution. This necessity raises an intriguing question: Can remote entanglement be stabilized indefinitely, instead of periodically regenerated and redistributed only after decay? Here, we demonstrate that this is indeed possible, reporting autonomous stabilization of entanglement between two separate superconducting-qubit devices. Combining nonreciprocal waveguide coupling and local driving, we experimentally realize a symmetry-based coherent quantum-absorber scheme in a cascaded network. We quantify the degree of entanglement through quantum state tomography, finding that the protocol’s entangling power is severely limited by imperfections that break the required symmetry. We show, however, that a modified protocol based on an alternate symmetry is far more robust, enabling us to achieve a concurrence approaching 0.5, a limit set by only local loss in the network. Our results enable on-demand delivery of high-fidelity entanglement in modular quantum processors and networks and pave the way for autonomously protecting distributed quantum information.

Recent studies of two-dimensional layered materials under external electric fields have gained significant attention, as such fields offer a powerful, noninvasive approach to actively modulate surface interactions at the molecular level, enabling real-time and reversible tuning of material properties. In this article, we use fully atomistic molecular dynamics simulations based on machine-learning potentials to predict the dependence of chemifriction on external electric fields in defected layered contacts. By controlling the rate of polar bond formation and rupture, friction can be either increased or decreased depending on the field strength and direction. To extend these atomistic insights to the experimentally relevant low-velocity regime, we develop a physically motivated stochastic model that bridges atomic-scale mechanisms with macroscopic friction behavior. Although demonstrated for hexagonal boron nitride junctions, the proposed mechanism of electrotunable chemifriction is expected to be general and applicable to a broad range of layered materials with polar interlayer bonding.

The quest to identify quantum advantages lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets attempting to foretell the future, yet the boundary between visionary insight and unfounded fantasy is perilously thin. In this Perspective, we examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, and communication. We explore five keystone properties, predictability, typicality, robustness, verifiability, and usefulness that define an ideal quantum advantage, and envision what new quantum advantages could arise in a future with ubiquitous quantum technology. We prove that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide, the ultimate power of quantum technologies may emerge from advantages we cannot yet conceive.

The process of scientific discovery relies on an interplay of observations, analysis, and hypothesis generation. Machine learning is increasingly being adopted to address individual aspects of this process. However, it remains an open challenge to fully automate the heuristic, iterative loop required to discover the laws of an unknown system by exploring it through experiments and analysis, without tailoring the approach to the specifics of a given task. Here, we introduce sciexplorer, an agent that leverages large language model tool-use capabilities to enable exploration of systems without any domain-specific blueprints and apply it to physical systems that are initially unknown to the agent. We test sciexplorer on a broad set of models spanning mechanical dynamical systems, wave evolution, and quantum many-body physics. Despite using a minimal set of tools, primarily based on code execution, we observe impressive performance on tasks such as recovering equations of motion from observed dynamics and inferring Hamiltonians from expectation values. The demonstrated effectiveness of this setup opens the door toward similar scientific exploration in other domains, without the need for fine-tuning or task-specific instructions.

We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose code space is stabilized by Clifford operators. We formulate a path-integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus establishing a connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.

Soft solids and their surface deformations control the response of many natural and artificial systems. Yet, their underlying properties are vigorously debated, particularly for polymer networks. While molecular-scale theories predict no interfacial changes with macroscopic deformation, multiple experiments suggest otherwise. To settle this issue, we measure displacement fields near the interface of a silicone gel, in the limit of small deformations. We discover an unexpected multiscale response. The shear modulus decreases smoothly by half with $20\mathrm{\mu }\mathrm{m}$ of the interface. At the same time we observe a surface excess elasticity, that depends on history and outer medium composition. These results reveal the fundamentally multiscale nature of polymeric surfaces, and call for further experimental and theoretical investigations into the basic understanding of soft solid interfaces.

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

The relaxation dynamics of glass-forming liquids shows at a temperature $T_c$, somewhat above the glass-transition temperature $T_g$, a crossover, indicating the conjunction of two different dynamical regimes. For temperatures slightly above $T_c$, experiments and computer simulations have extensively probed this dynamics on the particle level and identified several universal scaling laws that are often compatible with the predictions of ideal mode coupling theory, while for temperatures below $T_c$, the nature of the relaxation dynamics, and hence the reason for the crossover, has so far remained elusive. Here we use large-scale computer simulations to investigate how in the low-temperature regime the relaxation mechanism differs from the one at higher temperatures. Our analysis reveals unexpected scaling laws that allow us to give a surprisingly simple description of the relaxation dynamics at very low $T$’s. Space-time correlation functions show that the cage-escape process involves rare but large particle displacements. These displacements give rise to distinctive subdiffusive power laws in the mean squared displacement and the intermediate scattering function, and also rationalize the origin of the universal excess wing found in the dynamic susceptibility. This insight advances our understanding on the dynamics of glass-forming systems at temperatures that are close to the experimental glass transition.

The tin-vacancy center in diamond (SnV) has emerged as a compelling building block for realizing next-generation quantum networks thanks to its excellent optical and spin properties. Coupling to photonic crystal cavities (PCCs) promises to further enhance the SnV light-matter interface and unlock a diverse range of entanglement generation protocols. Recent pioneering experiments showing Purcell enhancement of SnV centers in PCCs underscore this potential. However, optical coupling that is coherent—the key ingredient for use in quantum protocols—has so far remained elusive. Here, we demonstrate above-unity coherent cooperativity of SnV centers embedded in photonic crystal cavities. We fabricate free-standing PCCs using a quasi-isotropic undercut. Across two samples, we conduct room-temperature characterizations, measuring resonances for 327 cavities, with an average quality factor exceeding $Q=1.1(4)\times {10}^4$. Two cavity-coupled emitters are examined in detail, exhibiting quality factors up to $Q=25.4(4)\times {10}^3$ and Purcell-reduced lifetimes corresponding to cooperativities up to $C=20.3(11)$. Furthermore, the single SnVs are observed to strongly modulate the cavity transmission with an extinction contrast up to 98.8(4)%% on resonance. Finally, SnV linewidth measurements reveal above-unity coherent cooperativities in both devices, with the highest value being $C_{\mathrm{coh}}=8.3(12)$. These results open the door to using cavity-coupled SnV centers as efficient, coherent light-matter interfaces for future quantum networks.

BosonSampling is the leading candidate for demonstrating quantum computational advantage in photonic systems. While we have recently seen many impressive experimental demonstrations, there is still a formidable distance between the complexity-theoretic hardness arguments and current experiments. One of the largest gaps involves the ratio of particles to modes—all current hardness evidence assumes a “dilute” regime in which the number of linear optical modes scales at least quadratically in the number of particles. By contrast, current experiments operate in a “saturated” regime with a linear number of modes. In this paper, we bridge this gap, bringing the hardness evidence for experiments in the saturated regime to the same level as had been previously established for the dilute regime. This involves proving a worst-to-average-case reduction for computing the permanent, which is robust both to large numbers of row repetitions and also to distributions over matrices with correlated entries. We also apply similar arguments to give evidence for hardness of Gaussian BosonSampling in the saturated regime.

Abrupt learning, long performance plateaus followed by rapid convergence, is a common phenomenon in recurrent neural networks (RNNs) trained on working-memory tasks. In such cases, the networks develop transient slow regions in state space that extend the effective timescales of computation. However, the mechanisms driving sudden performance improvements and their causal role remain unclear, largely because we lack an analytical dynamical-systems framework. To address this gap, we introduce the ghost mechanism, a general process by which finite-dimensional continuous-time dynamical systems exhibit transient slowdown near the remnant of a saddle-node bifurcation. By reducing the high-dimensional dynamics near ghost points, we derive a one-dimensional canonical form that analytically captures learning as a process controlled by a single scale parameter. Using this model, we study a form of abrupt learning emerging from ghost points and identify a critical learning rate that scales as an inverse power law with the timescale of the learned computation. Beyond this rate, learning collapses through two interacting modes: (i) vanishing gradients and (ii) oscillatory gradients near minima. These features can lock the system into high confidence but incorrect predictions when parameter updates trigger a no-learning zone, a region of parameter space where gradients vanish. We validate these predictions in low-rank RNNs, where ghost points precede abrupt transitions and further demonstrate their generality in full-rank RNNs trained on canonical working-memory tasks. Our theory offers two approaches to address these learning difficulties: Increasing trainable ranks stabilizes learning trajectories, while reducing output confidence mitigates entrapment in no-learning zones. Overall, the ghost mechanism reveals how the computational demands of a task constrain the optimization landscape, demonstrating that well-known learning difficulties in RNNs partly arise from the dynamical systems they must learn to implement.

The paradigm of considering open quantum systems—i.e., focusing only on the system of interest, and treating the rest of the world as an effective environment—has proven to be a highly effective way to understand a range of quantum systems, across areas of study such as quantum optics, cold atoms, superconducting qubits, and impurities in solid-state systems. A common approach in many of these contexts has been to consider simplified approaches based on the Born and Markov approximations. While these approximations are indeed often appropriate in contexts such as quantum optics, the widespread application of these approximations has been driven more by simplicity than by accuracy. In particular, these Markovian treatments will fail in many cases, such as when coupling to the environment is not weak, when the environment is structured and has resonances, when the system couples to low-frequency modes of the environment, or when the questions of interest involve the propagation of information through the environment. Despite the fact that many real problems are non-Markovian, the Markov approximation is still widely used, as it is often assumed that a fully non-Markovian treatment is too complex to be practical. In this Perspective we discuss a recently developed set of techniques that address this challenge. Centering our discussion around the notion of the process tensor, we demonstrate that the generality of the process tensor concept, coupled with efficient tensor-network methods, opens the door to the description of a wide range of observable non-Markovian processes in a wide range of open quantum systems.

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of ${10}^{19}$ and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.