Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parametrized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators that form the backbone of the method can become unstable or biased due to the presence of nodes, a ubiquitous feature of quantum wave functions. In the continuum, this results in heavy-tailed estimators with potentially divergent variances, while in discrete Hilbert spaces the sampling distribution can miss parts of the support needed to form unbiased estimators. These statistical pathologies lead to unreliable optimization trajectories in stochastic reconfiguration or incorrect variational dynamics in time-dependent variational Monte Carlo (t-VMC) and severely limit the power of the numerical simulations. We introduce blurred sampling to address these difficulties. The method has a number of rigorous properties that make it well behaved, effective, and computationally efficient. Additionally, it is a postprocessing approach that can be used without modifying the underlying sampler and incurs only minimal overhead. We demonstrate its effectiveness in a broad range of problems—including ground-state optimization in both continuum and discrete settings as well as in time-dependent variational Monte Carlo, where it resolves previously identified failure modes—and further apply it to large-scale problems in spin dynamics. This work establishes a broadly applicable framework for robust VMC and t-VMC calculations.

By combining the assumptions of Bell locality with those of generalized noncontextuality, we define classes of noncontextuality inequalities for correlations arising in a bipartite Bell circuit. These classes are distinguished by which subsets of the full set of operational identities are taken as input to the principle of noncontextuality; certain natural subsets form a hierarchy that provides a way of understanding and classifying different forms of quantum correlations, including entanglement, steering, and nonlocality. Each level of this hierarchy gives rise to a corresponding class of noncontextuality inequalities whose violation witnesses one of these forms of bipartite quantum resourcefulness, thereby yielding different sufficient conditions for entanglement. The resulting entanglement certification paradigm requires no prior characterization of the measurements, delivers a verdict independent of tomographic gauge freedom, and can certify any entangled state without auxiliary entangled sources. To illustrate the power of this paradigm, we show that noncontextuality inequalities can certify entanglement for families of two-qubit isotropic states for which certification by Bell or steering inequalities is known to be impossible. We also show that, compared with the Bell test, this approach certifies a much larger fraction of entangled states, while the associated membership problem is computationally more tractable. On the experimental side, we describe techniques to ensure nontrivial operational identities in the presence of noisy and imperfect implementations. We also identify the sufficient condition under which these techniques are valid, namely, a particular notion of tomographic completeness of the implemented Bell circuit, which ensures that the operational identities are independent of tomographic gauge. Finally, we provide an experimental demonstration of the superior performance of this entanglement certification technique using polarization-entangled photons.

Quantum symmetrization is the task of transforming a nonstrictly increasing list of $n$ integers into an equal superposition of all permutations of the list (or more generally, performing this operation coherently on a superposition of such lists). This task plays a key role in initial state preparation for first-quantized simulations. Motivated by an application to fermionic systems, various algorithms have been proposed to solve a weaker version of symmetrization in which the input list is strictly increasing, but the general symmetrization problem with repetitions in the input list has not been well studied. We present the first efficient quantum algorithms for the general symmetrization problem. If $m$ is the greatest possible value of the input list, our first algorithm symmetrizes any single classical input list using $\tilde{O}(\log n)$ depth and $O(n\log n+\log m)$ ancilla qubits, and our second algorithm symmetrizes an arbitrary superposition of input lists using $\tilde{O}({\log }^{3}n)$ depth and $O(n\log n)$ ancilla qubits. Our algorithms enable efficient simulation of bosonic quantum systems in first quantization (in particular, we describe a simulation of the Bose-Hubbard model with complexity $\mathrm{poly}(n,\log m)$) and can prepare (superpositions of) Dicke states of any Hamming weight in $\tilde{O}(\log n)$ depth (respectively, $\tilde{O}({\log }^{3}n)$ depth) using $O(n\log n)$ ancilla qubits. We also propose an $\tilde{O}({\log }^{3}n)$-depth quantum algorithm to transform second-quantized states to first-quantized states. Using this algorithm, QFT-based quantum telescope arrays can image brighter photon sources, extending quantum interferometric imaging systems to a new regime.

In the past decade, photoinduced superconductinglike behaviors have been reported in a number of materials driven by intense pump fields. Of particular interest is the high-$T_c$ cuprate ${\mathrm{YBa}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\mathrm{x}}$ (YBCO), where such effect has been reported up to the so-called pseudogap temperature $T^{*}\sim 300–400\mathrm{K}$. In a recent tour-de-force experiment, a transient magnetic field which is proportional to and in the same direction of an applied field has been observed outside the sample, suggestive of flux exclusion due to the Meissner effect. In this paper, we present an alternative interpretation of these experiments based on a mechanism that we term the flux-Floquet instability of the sine-Gordon (SG) model. We take as our premise the model of preformed Cooper pairs in the pseudogap phase. Starting from the local superconducting order parameter in equilibrium, we introduce an extended SG model to describe the dynamics of the relative phase between the layers of a bilayer. We demonstrate that a combination of external magnetic field and strong terahertz drive used in experiments by Fava et al. results in a novel Floquet instability in the model. This instability leads to currents at the edges of the bilayer formed by defects or grain boundaries, with the current flowing in the opposite direction of the equilibrium screening current, producing a giant paramagnetic magnetization in the same direction as the applied field. We show how this scenario can fit most of the available data. To the extent that this model can account for the data, we conclude that the experiments have the important consequence of revealing the presence of local pairing in the pseudogap phase. While the bulk of this paper addresses the experiment on YBCO, our results reveal a new instability in the SG equation that is of fundamental interest, with potential applications such as providing a mechanism for generating large magnetic fields at ultrafast timescales in Josephson devices.

Excitons, the correlated electron-hole pairs governing optical and transport properties in organic semiconductors, have long resisted direct experimental access to their full quantum-mechanical wave functions. Here, we use femtosecond time-resolved photoemission orbital tomography (trPOT) combining high-harmonic probe pulses with time- and momentum-resolved photoelectron spectroscopy to directly image the momentum-space distribution and ultrafast dynamics of excitons in $\alpha$-sexithiophene thin films. We introduce a model that enables reconstruction of the exciton wave function in real space, including both its spatial extent and its internal phase structure. The reconstructed wave function reveals coherent delocalization across approximately three molecular units and exhibits a characteristic phase modulation, consistent with ab initio calculations within the framework of many-body perturbation theory. Time-resolved measurements further indicate an approximately 25% contraction of the exciton radius within 400 fs, suggesting self-trapping driven by exciton-phonon coupling. These results establish trPOT as a general and experimentally accessible approach for resolving exciton wave functions—with spatial, phase, and temporal sensitivity—in a broad class of molecular and low-dimensional materials.

Preparation of quantum thermal states of many-body systems is a key computational challenge for quantum processors, with applications in physics, chemistry, and classical optimization. We provide a simple and efficient algorithm for thermal state preparation, combining engineered bath resetting and modulated system-bath coupling to derive a quantum channel approximately satisfying quantum detailed balance relations. We show that the fixed point $\widehat{\sigma }$ of the channel approximates the Gibbs state as $\parallel \widehat{\sigma }-{\widehat{\sigma }}_{\beta }\parallel \sim {\theta }^2$, where $\theta$ is the system-bath coupling and ${\widehat{\sigma }}_{\beta }\propto e^{-\beta {\widehat{H}}_S}$. We provide extensive numerics, for the example of the 2D quantum Ising model, confirming that the protocol successfully prepares the thermal state throughout the finite-temperature phase diagram, including near the quantum phase transition. Simulations for free-fermion systems provide further evidence for the accuracy of the protocol for large system sizes in the weak-coupling limit. Our algorithm provides a path to efficient quantum simulation of quantum-correlated states at finite temperature with current and near-term quantum processors.

Quantifying the irreversibility and dissipation of nonequilibrium processes is crucial to understanding their behavior, assessing their possible capabilities, and characterizing their efficiency. We introduce a physical quantity that quantifies the irreversibility of stochastic Langevin systems from the observation of individual molecules’ displacements. Categorizing these displacements into a few groups based on their initial and final positions allows us to measure irreversibility precisely without the need to know the forces and magnitude of the fluctuations acting on the system. For short times, our model-free estimate of irreversibility is related to entropy production by a conditional fluctuation theorem. For short times and, in general, for stationary protocols, our estimate provides a lower bound to the average entropy production. We validate the method on single-molecule force spectroscopy experiments of proteins subject to force ramps. We show that irreversibility is sensitive to detailed features of the energy landscape underlying the protein folding dynamics and suggest how our methods can be employed to unveil key properties of protein folding processes.

Quantum routers (QRouters) are essential components of bucket-brigade quantum random access memory (QRAM), enabling quantum applications such as Grover’s search and quantum machine learning. Despite significant theoretical advances, achieving scalable and coherent QRouters experimentally remains challenging. Here, we demonstrate coherent quantum routers using a superconducting quantum processor, laying a practical foundation for scalable QRAM systems. The quantum router at the core of our implementation utilizes the transition composite gate scheme, wherein auxiliary energy levels temporarily mediate conditional interactions. By leveraging two-qubit primitives in its construction, the quantum router preserves straightforward initialization and calibration while significantly reducing circuit depth and duration relative to traditional gate-based decompositions. Moreover, by encoding routing addresses in the nonadjacent qutrit states $|0⟩$ and $|2⟩$, our design inherently enables erasure-detection capability, providing efficient postselection to mitigate routing errors. Experimentally, we achieve an average fidelity of 94.8% across three individual QRouters, and we validate scalability through a two-layer quantum routing network achieving a fidelity of 82.4%. Our results represent a significant advancement in quantum routing technology, providing enhanced fidelity, built-in error resilience, and practical scalability crucial for the development of future QRAM and large-scale quantum computing architectures.

Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today’s leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a general semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying measurements from fidelity-constrained sources, (iii) computing dimensionality in genuine multiparticle entangled states, (iv) benchmarking dimensionality for state preparation devices, and (v) finding uncertainty relations for nearly anticommuting observables. These applications reflect both the usefulness and versatility of the methodology, as well as its potential for broader relevance in the field.

Long-term stability in materials is commonly associated with resistance to external perturbations. Yet metastable defect populations may relax spontaneously even in the absence of environmental stimuli, reshaping macroscopic properties over extended timescales. Here, we show the real-space visualization of intrinsic aging of $n$-type ${\mathrm{Mg}}_3{(\mathrm{Sb},\mathrm{Bi})}_2$ under inert and room-temperature conditions after two-year storage by atomic-scale characterizations. Density-functional-theory calculations and machine-learning molecular dynamics simulations prove that the aging originates from relaxation of a metastable Mg-rich state, in which low vacancy-formation energies and migration barriers enable thermodynamically favorable and kinetically accessible Mg redistribution. Multiscale characterizations further reveal that grain boundaries (GBs) act as fast-diffusion pathways and effective sinks, establishing a hierarchical Mg redistribution process from grain interiors to GBs and surfaces. These results identify intrinsic defect physics as one of the fundamental stability constraints in functional materials and underscore the importance of controlling defect thermodynamics and transport pathways for achieving practically durable materials.

In the study of electronic structure, the wave function view dominates the current research landscape and forms the theoretical foundation of modern quantum mechanics. In contrast, valence bond (VB) theory represents chemical bonds as shared electron pairs and can provide an intuitive, particle-based insight into chemical bonding. In this work, using a newly developed periodic dynamic Voronoi Metropolis sampling (PDVMS) method, we project classical many-body electronic configurations from the neural network wave function and apply VB theory to construct a complementary particle-view paradigm. The powerful neural network wave function can achieve near-exact ab initio solutions for the ground state of both molecular and solid systems. It allows us to definitively characterize the ground state of benzene by reassessing the competition between its two VB structures. Extending PDVMS to solids, we also predict a spin-staggered VB structure in graphene, which explains emergent magnetic properties in graphene-based nanostructures. Furthermore, this particle view provides insight into the optimization process of the neural network wave function itself. Our work thus introduces a framework for analyzing many-body electronic structure in molecules and solids, opening new avenues for investigating this complex problem and its associated exotic phenomena.

The generation of non-Gaussian quantum states is a key requirement for universal continuous-variable quantum information processing. We report the experimental generation of large-amplitude squeezed coherent-state superpositions (squeezed cat states) on free-space optical pulses, reaching an amplitude of $\alpha =2.47$, which, to our knowledge, exceeds all previously reported values. Our protocol relies on the controlled mixing of the Fock states $|1⟩$ and $|2⟩$ through a tunable beam splitter, followed by heralding via homodyne detection. The resulting state displays three well-resolved negative regions in its Wigner function and achieves a fidelity of 0.53 with the target state $\propto \widehat{S}(z)(|\alpha ⟩-|-\alpha ⟩)$, with $\alpha =2.47$ and squeezing parameter $z=0.56$. These results constitute a significant milestone for temporal breeding protocols and for the iterative generation of optical Gottesman-Kitaev-Preskill states, opening perspectives for scalable and fault-tolerant photonic quantum architectures.

Superionic conductors are fascinating systems representing a state of matter intermediate between solids and liquids, yet their underlying physics remain poorly understood. Correlations in jump dynamics have been theoretically proposed as a key mechanism underlying superionic diffusion, but a direct experimental demonstration remains elusive. Here, we report the direct observation of collective cation hopping in the argyrodite compound ${\mathrm{Cu}}_7{\mathrm{PS}}_6$, using single-crystal neutron scattering to access the full four-dimensional space-time correlations of ionic motion. By leveraging the rarely used coherent scattering channel in quasielastic neutron scattering, together with diffuse scattering, we reveal pronounced short-range dynamical correlations between diffusing Cu ions, providing direct experimental evidence of collective hopping in a superionic phase. Machine-learned molecular dynamics simulations quantitatively reproduce all our measurements and pinpoint the dominant collective hopping mechanism. Furthermore, we establish through both experiments and simulations that the collective diffusive hops originate from the breakdown of low-energy phonons dominated by the Cu motions in the parent ordered phase, demonstrating a key link between phonon precursors and the activation of facile collective hops. This work presents the first direct experimental evidence of collective hopping in superionic argyrodites and identifies wave-vector-resolved soft phonons as its physical origin, advancing the microscopic understanding of ionic transport in superionic solids.

Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of ${}^{174}\mathrm{Yb}$ in $6sns{{}^{1}S}_0$ Rydberg states across nearly two decades in principal quantum number $n$ and 3 orders of magnitude in molecular binding energy. Using the Coulomb Green’s function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy $s$-wave scattering length and the positions of two spin-orbit split $p$-wave shape resonances. Our results provide strong evidence that the ${\mathrm{Yb}}^{-}$ anion exists only as a metastable resonance. We additionally show the sensitivity of ULRM spectra to the atomic quantum defects, using this to determine the quantum defect of the $6s23f{{}^{1}F}_3$ state. Together, these findings establish Yb ULRMs as a powerful probe of electron-Yb interactions and lay essential groundwork for future Rydberg experiments with divalent atoms.

Ab initio auxiliary-field quantum Monte Carlo (AFQMC) is a systematically improvable many-body method, but its application to extended solids has been severely limited by unfavorable computational scaling and memory requirements that obstruct rigorous access to the thermodynamic and complete-basis-set limits. By combining tensor hypercontraction with $\mathbf{k}$-point symmetry, we reduce the computational and memory scaling of ab initio AFQMC for solids to $\mathcal{O}(N^3)$ and $\mathcal{O}(N^2)$, respectively, with an arbitrary basis, comparable to diffusion Monte Carlo. This enables simultaneous, controlled extrapolation of full-system AFQMC calculations to the thermodynamic and complete-basis-set limits across insulating, metallic, and strongly correlated solids, without embedding, local approximations, empirical finite-size corrections, or composite schemes. Our results establish AFQMC as a general-purpose, systematically improvable alternative to diffusion Monte Carlo and coupled-cluster methods for predictive ab initio simulations of solids, enabling accurate energies and magnetic observables within a unified framework.

The appearance of fractional Chern insulators in moiré systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wave functions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moiré systems. We first show that at the level of individual Bloch wave functions, the real-space Chern number, akin to a Pontryagin index, is a fragile marker. It generically vanishes except for specific limits where the Bloch functions exhibit fine-tuned zeros within the unit cell, such as the chiral limit of twisted bilayer graphene (TBG) or the adiabatic regime of twisted homobilayer transition metal dichalcogenides (TMDs). We then show that these limitations do not apply to textures associated with ensembles of Bloch wave functions, such as entire bands or the ensemble of states at a given energy. The Chern number of these textures defines a robust topological index protected by a spectral gap. We find that symmetries constrain it to be nonzero for both twisted TMDs and TBG across all twist angles and levels of corrugation, which can be verified in scanning tunneling microscopy measurements. By projection to the band ensemble texture, a single-component Hamiltonian under fictitious magnetic field emerges in broad regime, enabling a direct comparison of multicomponent bands to Landau-level wave functions. We also study real-space topology within the topological heavy fermion model of TBG, finding that the real-space topological features are supported only by the light $c$ electrons.

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of large systems. While the ETH apparently holds across a wide range of interacting quantum systems, in this work, we show that it may require generalization in the presence of thermal first-order phase transitions. We introduce a class of all-to-all spin models, featuring first-order thermal phase transitions that stem from two distinct local maxima of entropy (two mean-field solutions that we dub “branches”) that exchange dominance in the many-body density of states as the energy is varied. We argue that, for energies in the vicinity of the thermal phase transition, eigenstate expectation values do not need to converge to the same thermal value. The system has a regime with coexistence of two classes of eigenstates corresponding to the two branches with distinct expectation values at the same energy density and another regime with Schrödinger-cat-like eigenstates that are interbranch superpositions; these two regimes are separated by an eigenstate phase transition. We propose a more general form of the ETH Ansatz, support our results by semiclassical calculations and an exact diagonalization study of a microscopic spin model, and argue that the structure of eigenstates in the vicinity of thermal first-order phase transitions can be experimentally probed via nonequilibrium dynamics.

Ferroelectric domain walls are described as interfacial regions between oppositely polarized domains, where the original bulk distortions are suppressed or reconstructed at energetic cost. Here, we demonstrate that $\mathrm{Pca}{2}_1$ ${\mathrm{HfO}}_2$ exhibits a distinct ferroelectric domain wall where the polarization-reversal boundaries remain structurally bulk compatible and exceptionally low in energy. The central mechanism is a pair-condensation—the simultaneous condensation of the two trilinearly coupled phonon modes located at opposite termini of a single phonon branch. We show that this pair condensation not only establishes the microscopic origin of layer-selective ferroelectricity in bulk but also governs the exceptionally low energy of the 180° domain walls. Specifically, the simultaneous reversal and complementary energetic responses of the paired condensed modes compensate the domain-wall energy cost and facilitates a wall-centered structure where bulk motifs are locally recovered rather than suppressed. This bulklike domain wall is corroborated by the agreement between density-functional-theory calculations and annular-bright-field-STEM measurements of oxygen displacements. This logic extends to suboptimal and higher-energy domain walls which emerge as accessible structural bridges via the selective, energy-minimizing reversal of individual condensed phonon modes. By unifying these structural and energetic observations under the principle of pair condensation, this work provides a generalized predictive framework for engineering domain-wall physics in multimode functional materials.

The origin of superconductivity in magic-angle twisted bilayer graphene has been a subject of intense debate. While some experimental evidence indicated an unconventional pairing mechanism which should be sensitive to Coulomb screening, experimental attempts to tune the critical temperature by screening Coulomb interactions so far have remained unsuccessful, possibly indicating a conventional phonon-mediated pairing. Here we study a double-layer electronic system consisting of two twisted graphene bilayers in immediate proximity of each other but remaining electronically decoupled. By increasing the carrier density in one bilayer, we completely suppressed both the superconductivity and the correlated-insulator state in the adjacent magic-angle graphene. The observation of such an effect from screening offers support for an unconventional mechanism of Cooper pairing in magic-angle twisted bilayer graphene, shedding new light on the underlying physics governing their properties.

We present a general, systematic, and quantitative theory of electromagnetism and chirality in crystalline solids. Symmetry is its basic guiding principle, enabling us to consider macroscopic multipole densities without reference to any specific microscopic configurations. We use a formal analogy between space inversion $i$ and time inversion $\theta$ to identify two complementary, comprehensive classifications of crystals, based on five categories of electric and magnetic multipole order—called polarizations—and five categories of chirality. The five categories of polarizations (parapolar, electropolar, magnetopolar, antimagnetopolar, and multipolar) embody the variety of ways in which electromagnetic multipole order can be realized in solids, thus expanding the familiar notion of electric dipolarization in ferroelectrics and magnetization in ferromagnets to higher-rank multipole densities characterizing, e.g., altermagnets and alterelectrics. Group theory also permits the absolute, gauge-invariant quantification of these multipole densities. The five categories of chirality (parachiral, electrochiral, magnetochiral, antimagnetochiral, and multichiral) extend the notion of enantiomorphism—conventionally associated with the lack of spatial mirror symmetries—to include all possibilities for creating nonsuperposable images by applying the inversions $i$, $\theta$, and $i\theta$. In particular, multichiral systems lack all inversion symmetries and therefore have four different enantiomorphs. Each category of chirality is shown to arise from particular superpositions of electric and magnetic multipole densities. Our theory has great predictive power by relating electric and magnetic multipolar order with, e.g., distinctive features in the crystal structure, the electronic band structure, property tensors, and response tensors of quantum materials. These findings are critical for a large community working on fundamental and applied aspects of novel quantum materials.