Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of approximately 50 qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and, therefore, how much infidelity is suffered) in generating highly entangled states. Here, we describe recent hardware upgrades to Quantinuum’s H2 quantum computer, enabling it to operate on up to 56 qubits with arbitrary connectivity and 99.843(5)% two-qubit gate fidelity. We define a class of circuits with random geometries that become hard to classically simulate in very low depth and implement them utilizing the flexible connectivity of H2. A careful analysis demonstrating the fast saturation of classical simulation complexity with depth indicates that H2 can yield data well beyond the reach of state-of-the art classical simulation methods at unprecedented fidelities. We find that the considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the quantum charge-coupled device architecture as continued progress is made toward building larger machines.

Reinforcement learning (RL) algorithms have transformed many domains of machine learning. To tackle real-world problems, RL often relies on neural networks to learn policies directly from pixels or other high-dimensional sensory input. By contrast, many theories of RL have focused on discrete state spaces or worst-case analysis, and fundamental questions remain about the dynamics of policy learning in high-dimensional settings. Here, we propose a solvable high-dimensional RL model that can capture a variety of learning protocols, and we derive its typical policy learning dynamics as a set of closed-form ordinary differential equations. We obtain optimal schedules for the learning rates and task difficulty—analogous to annealing schemes and curricula during training in RL—and show that the model exhibits rich behavior, including delayed learning under sparse rewards, a variety of learning regimes depending on reward baselines, and a speed-accuracy trade-off driven by reward stringency. Experiments on variants of the Procgen game “Bossfight” and Arcade Learning Environment game “Pong” also show such a speed-accuracy trade-off in practice. Together, these results take a step toward closing the gap between theory and practice in high-dimensional RL.

The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here, we provide a comprehensive picture of how local dissipation due to effective chemical events manifests on large scales in active matter. We start from a microscopic model for a single catalytic particle involving explicit solute molecules and show that it undergoes directed motion. Leveraging stochastic thermodynamics, we calculate the average entropy production rate for interacting particles. We then show how the model of active Brownian particles emerges in a certain limit, and we determine the entropy production rate on the level of the hydrodynamic equations. Our results augment the model of active Brownian particles with rigorous expressions for the dissipation that cannot be inferred from their equations of motion, and we illustrate consequences for wall aggregation and motility-induced phase separation. Notably, our bottom-up approach agrees with the “naive” result from Onsager’s principle for the local dissipation rate.

The Hubbard model is believed to capture the essential physics of cuprate superconductors. However, recent theoretical studies suggest that it fails to reproduce a robust and homogeneous superconducting ground state. Here, using resonant inelastic x-ray scattering and density matrix renormalization group calculations, we show that magnetic excitations in the prototypical cuprate ladder ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ are inconsistent with those of a simple Hubbard model. The magnetic response of hole carriers, contributing to an emergent branch of spin-flip excitations, is strongly suppressed. This effect is the consequence of strong $d$-wavelike pairing, enhanced by nearly an order of magnitude through a large nearest-neighbor attractive interaction and persisting up to at least 260 K. The close connection between the physics of cuprate ladders and that of the two-dimensional compounds suggests that such an enhanced hole pairing may be a universal feature of superconducting cuprates.

We report evidence for superconductivity with onset temperatures up to 11 K in thin films of the infinite-layer nickelate parent compound ${\mathrm{NdNiO}}_2$. A combination of oxide molecular beam epitaxy and atomic hydrogen reduction yields samples with high crystallinity and low residual resistivities, a substantial fraction of which exhibit superconducting transitions. We survey a large series of samples with a variety of techniques, including electrical transport, scanning transmission electron microscopy, x-ray absorption spectroscopy, and resonant inelastic x-ray scattering, to investigate the possible origins of superconductivity. We propose that superconductivity could be intrinsic to the undoped infinite-layer nickelates but suppressed by disorder due to a possibly sign-changing order parameter, a finding which would necessitate a reconsideration of the nickelate phase diagram. Another possible hypothesis is that the parent materials can be hole doped from randomly dispersed apical oxygen atoms, which would suggest an alternative pathway for achieving superconductivity.

Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued by both a continuum of environments and temporal instabilities. These induce noisy quantum and classical correlations at the level of the circuit. The relevant spatiotemporal effects are difficult enough to understand, let alone combat. There is presently a lack of either scalable or complete methods to address the phenomena responsible for scrambling and loss of quantum information. Here, we make deep strides to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, assumes no parameters values, and is written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing also for easy modularization and simplification based on the expected physics of the system. This is then demonstrated through both extensive numerical studies and implementations on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. Finally, we conclude our analysis with applications thereof to the efficacy of control techniques to counteract these effects—including noise-aware circuit compilation and optimized dynamical decoupling. We find significant improvements are possible in the diamond norm and average gate fidelity of arbitrary SU(4) operations, as well as related decoupling improvements in contrast to off-the-shelf schemes.

In this report, we apply a suite of ultrafast spectroscopic techniques and advanced calculations to reveal the interplay between electronic and lattice degrees of freedom in ferroelectric ${\mathrm{BiFeO}}_3$. Using transient sum frequency generation spectroscopy, which is sensitive to electronic polarizations, we observe a transient electronic dipole reduction upon optical excitation which recovers at 0.5 and 10 ps timescale. The time-dependent density functional theory calculation reveals that both ligand-metal charge transfer and local excitation transition occurred upon photo excitation. To reveal the nature of electronic dipole restoration, we employ transient extreme ultraviolet (EUV) spectroscopy—an element-specific ultrafast technique that follows charge dynamics of Bi, Fe, and O altogether. The transient EUV dynamics observed both ultrafast free charge carrier relaxation to excitons, as well as polaron formation. However, a timescale comparison suggests that only the polaron formation is responsible for the 0.5 ps electronic dipole restoration, whereas the faster electronic relaxation does not contribute to the ferroelectric property changes. Multireference configuration interaction calculation further corroborates this result by showing both Fe and Bi atoms shift from the ground state equilibrium—leading to the polaron formation. Our result disentangles the multidegrees of freedom in ultrafast ferroelectric modulation and identifies the pivotal motion—a local polaron formation—for the fast ferroelectric recovery. It provides crucial insights on the specific lattice distortion that could modulate properties or phase transitions of condensed matter materials.

Defects in crystals can have a transformative effect on the properties and functionalities of solid-state systems. Dopants in semiconductors are core components in electronic and optoelectronic devices. The control of single color centers is at the basis of advanced applications for quantum technologies. Unintentional defects can also be detrimental to the crystalline structure and hinder the development of novel materials. Whatever the research perspective, the identification of defects is a key, but complicated, and often long-standing issue. Here, we present a general methodology to identify point defects by combining isotope substitution and polytype control, with a systematic comparison between experiments and first-principles calculations. We apply this methodology to hexagonal boron nitride ($h$-BN) and its ubiquitous color center emitting in the ultraviolet spectral range. From isotopic purification of the host $h$-BN matrix, a local vibrational mode of the defect is uncovered, and isotope-selective carbon doping proves that this mode belongs to a carbon-based center. Then, by varying the stacking sequence of the host $h$-BN matrix, we unveil different optical responses to hydrostatic pressure for the nonequivalent configurations of this ultraviolet color center. We conclude that this defect is a carbon dimer in the honeycomb lattice of $h$-BN. Our results show that tuning the stacking sequence in different polytypes of a given crystal provides unique fingerprints contributing to the identification of defects in 2D materials.

Network flows are pervasive, including the movement of people, transportation of goods, transmission of energy, and dissemination of information; they occur on a range of empirical interconnected systems, from designed infrastructure to naturally evolved networks. Despite the broad spectrum of applications, because of their domain-specific nature and the inherent analytic complexity, a comprehensive theory of network flows is lacking. We introduce a unifying treatment for network flows that considers the fundamental properties of packet symmetries, conservation laws, and routing strategies. For example, electrons in power grids possess interchangeability symmetry, unlike packages sent by postal mail, which are distinguishable. Likewise, packets can be conserved, such as cars in road networks, or dissipated, such as Internet packets that time out. We introduce a hierarchy of analytical field-theoretic approaches to capture the different scales of complexity required. Mean-field analysis uncovers the nature of the transition through which flow becomes unsustainable upon unchecked growth of demand. Mesoscopic field theory accurately accounts for complicated network structures, packet symmetries, and conservation laws and yet is capable of admitting closed-form solutions. Finally, the full-scale field theory allows us to study routing strategies ranging from random diffusion to shortest path. Our theoretical results indicate that flow bottlenecks tend to be near sources for interchangeable packets and near sinks for distinguishable ones, and that dissipation hinders the maximum sustainable throughput for interchangeable packets but can enhance throughput for distinguishable packets. Finally, we showcase the flexibility of our multiscale theory by applying it in two distinct domains of road networks and the C. elegans neuronal network. Our work paves the way for a more unifying and comprehensive theory of network flows.

Quantized lattice vibrations (i.e., phonons) in solids are robust and unambiguous fingerprints of crystal structures and of their symmetry properties. In metals and semimetals, strong electron-phonon coupling may lead to so-called Kohn anomalies in the phonon dispersion, providing an image of the Fermi surface in a nonelectronic observable. Kohn anomalies become prominent in low-dimensional systems, in particular, in graphene, where they appear as sharp kinks in the in-plane optical phonon branches. However, in spite of intense research efforts on electron-phonon coupling in graphene and related van der Waals heterostructures, little is known regarding the links between the symmetry properties of optical phonons at and near Kohn anomalies and their sensitivity towards the local environment. Here, using inelastic light scattering (Raman) spectroscopy, we investigate a set of custom-designed graphene-based van der Waals heterostructures, wherein dielectric screening is finely controlled at the atomic-layer level. We demonstrate experimentally and explain theoretically that, depending exclusively on their symmetry properties, the two main Raman lines of graphene react differently to the surrounding environment. While the 2D line, which is due to near-zone-edge optical phonons, undergoes changes due to the neighboring dielectric environment, the in-plane, zone-center optical phonons are symmetry protected from the influence of the latter. These results shed new light on the unique electron-phonon coupling properties in graphene and related systems and provide invaluable guidelines to characterize dielectric screening in van der Waals heterostructures and moiré superlattices.

The high coercive field (${\mathcal{E}}_c$) of hafnia-based ferroelectrics presents a major obstacle to their applications. The ferroelectric switching mechanisms in hafnia that dictate ${\mathcal{E}}_c$, especially those related to domain nucleation in the nucleation-limited-switching (NLS) model and domain-wall motion in the Kolmogorov-Avrami-Ishibashi (KAI) model, have remained elusive. We develop a deep-learning-assisted multiscale approach, incorporating atomistic insights into the critical nucleus, to predict both NLS- and KAI-type coercive fields. The theoretical NLS-type ${\mathcal{E}}_c$ values agree with previous experimental results as well as our own measurements and also exhibit the correct thickness scaling for films between 3 and 20 nm. Combined theoretical and experimental investigations reveal that the giant ${\mathcal{E}}_c$ in hafnia-based ferroelectrics arises from the ultrathin geometry, which confines switching to the NLS mechanism. We predict that the theoretical lower limit for KAI-type ${\mathcal{E}}_c$ is $0.1\mathrm{MV}/\mathrm{cm}$ arising from mobile domain walls. The activation of KAI-type switching to achieve lower ${\mathcal{E}}_c$ is supported by our experimental demonstration of a low coercive field of $1\mathrm{MV}/\mathrm{cm}$ in 60 nm ferroelectric $({\mathrm{HfO}}_2{)}_n/({\mathrm{ZrO}}_2{)}_n$ ($n=3$ unit cells) superlattices. These findings establish a comprehensive framework for understanding ferroelectric switching in hafnia and highlight the potential of geometry and domain-wall engineering to achieve low-${\mathcal{E}}_c$ devices.

The generation of topologically nontrivial magnetic configurations has been a pivotal topic in both basic and applied nanomagnetism research. Localized noncoplanar magnetic defects such as skyrmions or merons were found to interact strongly with currents, making them interesting candidates for future spintronics applications. So far, mostly systems with a high rotational symmetry have been investigated where skyrmions were axially symmetric. Here, we study a low-symmetry system by spin-polarized scanning tunneling microscopy and an atomistic spin model using parameters based on first-principles calculations. We demonstrate how a delicate balance between energy terms generates both topologically trivial and nontrivial domain walls, depending on their nonequivalent crystallographic direction. The topological walls consist of alternating merons and antimerons, and the topological charge is 1 for every 6-nm length of the wall. The incorporation of holes in the films facilitates the transition from an in-plane ferromagnetic ground state to a spin-spiral state. Both domain walls and spirals transition into isolated elongated magnetic skyrmions in applied magnetic fields. These findings establish low-symmetry systems as a versatile platform for spin-texture engineering.

Experiments show that light-matter strong coupling affects chemical properties, though the underlying mechanism remains unclear. A major challenge is to perform reliable and affordable simulation of molecular behavior when many molecules are collectively coupled to the same optical mode. This paper presents an ab initio quantum electrodynamics coupled cluster method for the collective strong coupling regime. The model describes electronic and electron-photon correlation within a molecular subsystem, while a simplified description of the collective polaritonic excitations allows for a realistic microscopic light-matter coupling. The developed framework provides a computationally tractable route to accurately simulate a molecule in a collective environment, which is unfeasible when several molecules are treated explicitly. We investigate the properties of the argon dimer under strong light-matter coupling. In the single-molecule regime (large light-matter coupling), the potential energies are substantially modified, weakening the excimer bond. In contrast, in the collective regime (small light-matter coupling, large number of molecules), the ground state potential energy surface and the first vibrational levels of the excited state do not change significantly. However, collective strong coupling produces an abrupt transition in the vibrational landscape of the excimer, causing higher vibrational levels to behave similarly to the vibrations in the ground state. We expect the excimer formation to be inhibited by light-matter strong coupling and conclude that chemical properties are altered via distinct mechanisms in the collective and single-molecule regimes. We also discuss fundamental aspects of polaritonic chemistry, such as resonance conditions and sudden changes of the molecular properties when a critical collective coupling strength is achieved.

Coherent phonons, light-induced coherent lattice vibrations in solids, provide a powerful route to engineer structural and electronic degrees of freedom using light. In this manuscript, we formulate an ab initio theory of the displacive excitation of coherent phonons (DECP), the primary mechanism for light-induced structural control in semimetals. Our study—based on the ab initio simulations of the ultrafast electron and coherent-phonon dynamics in the presence of electron-phonon interactions—establishes a predictive computational framework for describing the emergence of light-induced structural changes and the ensuing transient band-structure renormalization arising from the DECP mechanism. We validate this framework via a combined theoretical and experimental investigation of coherent phonons in the elemental semimetal antimony. Via a Fourier analysis of time- and angle-resolved photoemission spectroscopy measurements, we retrieve information about transient spectral features and quasiparticle renormalization arising from the coherent $A_{1g}$ phonon as a function of momentum, energy, time, and fluence. The qualitative and quantitative agreement between experiment and theory corroborates the first-principles approach formulated in this study. We further apply this formalism to investigate the coherent-phonon dynamics in the topological Weyl semimetal Td-${\mathrm{WTe}}_2$. Besides reproducing the entire spectrum of coherent phonons observed in experiments, our simulations clearly indicate that the shear $A_{1g}$ mode—the mode orchestrating a light-induced phase transition in Td-${\mathrm{WTe}}_2$—is strongly driven by the DECP mechanism and, thus, provide a conclusive explanation for the driving mechanism underpinning the phase transition. Besides advancing the fundamental understanding of electron-phonon interactions mediated by coherent phonons, this study opens new opportunities for predictively engineering structural and electronic degrees of freedom in semimetals via the DECP mechanism.

In optics and photonics, a small number of building blocks—like resonators, waveguides, arbitrary couplings, and parametric interactions—allow the design of a broad variety of devices and functionalities, distinguished by their scattering properties. These devices include transducers, amplifiers, and nonreciprocal devices, like isolators or circulators. Usually, the design of such a system is handcrafted by an experienced scientist in a time-consuming process, where it remains uncertain whether the simplest possibility has indeed been found. In our work, we develop the discovery algorithm autoscatter, which automates this challenge. By optimizing the continuous and discrete system properties, our automated search identifies the minimal resources required to realize the requested scattering behavior. In the spirit of artificial scientific discovery, it produces a complete list of interpretable solutions and leads to generalizable insights, as we illustrate in several examples. autoscatter opens the door towards the automated discovery of scattering setups for photonics, microwaves, and optomechanics, with possible future extensions to periodic structures, sensing, and electronic devices.

Quantum key distribution (QKD) provides information-theoretic security for communication. The mode-pairing (MP) protocol emerges as a promising solution for long-distance QKD by eliminating the need for a global phase reference while maintaining the repeaterlike rate-loss scaling. Recent implementations have demonstrated its potential, but they either rely on costly ultrastable lasers or struggle with phase fluctuations from commercial lasers, particularly over long distances. As a result, surpassing the repeaterless bound with a practical system remains a challenge. In this work, we demonstrate a practical high-performance MP-QKD system using commercial lasers. To address phase fluctuations, we propose a frequency-tracking scheme based on fast Fourier transformation, enabling us to extend the pairing length to $2\times {10}^5$ pulses ($160\mathrm{\mu }\mathrm{s}$). We propose a model to carefully analyze the phase noise and optimize the system parameters. Our system achieves an optimal secret key rate of $47.8\mathrm{bit}/\mathrm{s}$ over 403 km of standard fiber (76.5 dB loss), exceeding the repeaterless bound by a factor of 2.92. Furthermore, we compare MP-QKD and twin-field QKD under various practical conditions and clarify the distinct application scenarios of the two protocols. These results confirm the feasibility of MP-QKD using cost-effective commercial technologies, paving the way for scalable quantum communication networks.

We study topologically stable defect structures in systems where the defect line classification in three dimensions and associated algebra of interactions (the fundamental group) are governed by the non-Abelian eight-element group, the quaternions $Q_8$. The non-Abelian character of the defect algebra leads to a topological rigidity of bound defect pairs, and trivalent junctions which are the building blocks of multijunction trivalent networks. We realize such structures in laboratory chiral nematics and analyze their behavior analytically, along with numerical modeling.

Systems of spins with strong dipolar interactions and controlled dimensionality enable new explorations in quantum sensing and simulation. In this work, we investigate the creation of strong dipolar interactions in a two-dimensional ensemble of nitrogen-vacancy (NV) centers generated via plasma-enhanced chemical vapor deposition on (111)-oriented diamond substrates. We find that diamond growth on the (111) plane yields high incorporation of spins, both nitrogen and NV centers, where the density of the latter is tunable via the miscut of the diamond substrate. Our process allows us to form dense, preferentially aligned, 2D NV ensembles with volume-normalized ac sensitivity down to ${\eta }_{\mathrm{ac}}=810\mathrm{pT}\mathrm{\mu }{\mathrm{m}}^{3/2}{\mathrm{Hz}}^{-1/2}$. Furthermore, we show that (111) affords maximally positive dipolar interactions among a 2D NV ensemble, which is crucial for leveraging dipolar-driven entanglement schemes and exploring new interacting spin physics.

Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors. High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment. However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings. While virtual gates offer a practical solution, determining all the required cross-capacitance matrices accurately and efficiently in large quantum dot registers is an open challenge. Here, we establish a modular automated virtualization system (MAViS)—a general and modular framework for autonomously constructing a complete stack of multilayer virtual gates in real time. Our method employs machine learning techniques to rapidly extract features from two-dimensional charge stability diagrams. We then utilize computer vision and regression models to self-consistently determine all relative capacitive couplings necessary for virtualizing plunger and barrier gates in both low- and high-tunnel-coupling regimes. Using MAViS, we successfully demonstrate accurate virtualization of a dense two-dimensional array comprising ten quantum dots defined in a high-quality $\mathrm{Ge}/\mathrm{SiGe}$ heterostructure. Our work offers an elegant and practical solution for the efficient control of large-scale semiconductor quantum dot systems.

The insulating magnetic pyrochlore ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ has gained attention as a quantum spin-ice candidate with dipole-octupole character that arises from the crystal-electric-field ground-state doublet for the ${\mathrm{Ce}}^{3+}$ Kramers ion. This dipole-octupole character permits both spin-ice phases based on magnetic dipoles and those based on more-exotic octupoles. This work reports low-temperature neutron diffraction measurements on single-crystal ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ with $Q$ coverage both at low $Q$, where the magnetic form factor for dipoles is near maximal, and at high $Q$, covering the region where the magnetic form factor for ${\mathrm{Ce}}^{3+}$ octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$, which each showed temperature-dependent diffuse diffraction at high $Q$, interpreted as arising from octupolar correlations. Our measurements use an optimized single-crystal diffuse scattering instrument that allows us to screen against strong Bragg scattering from ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. The temperature-difference neutron diffraction reveals a low-$Q$ peak consistent with dipolar spin-ice correlations reported in previous work, and an alternation between positive and negative net intensity at higher $Q$. These features are consistent with our numerical-linked-cluster calculations using pseudospin interaction parameters previously reported for ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$, ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, and ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$. Importantly, neither the measured data nor any of the NLC calculations show evidence for increased scattering at high $Q$ resulting from octupolar correlations. We conclude that at the lowest attainable temperature for our measurements ($T=0.05\mathrm{K}$), scattering from octupolar correlations in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ is not present in the neutron diffraction signal on the level of our observation threshold of around 0.1% of the low-$Q$ dipole scattering. We compare these results to those obtained earlier on powder ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$, and to low-energy inelastic neutron scattering from single-crystal ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$.