We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a generalization of symmetry for open quantum systems. For Abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has nontrivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.

We show that no Einstein-Podolsky-Rosen (EPR)–like bipartite entanglement can be distilled from a tripartite Haar random state $|\mathrm{\Psi }{⟩}_{ABC}$ by local unitaries or local operations when each subsystem $A$, $B$, or $C$ has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance, showing a doubly exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $\epsilon$-net argument and concentration of measure. Viewing $|\mathrm{\Psi }{⟩}_{ABC}$ as a bipartite quantum error-correcting code $C\to AB$, this implies that neither output subsystem $A$ nor $B$ supports any nontrivial logical operator. We also establish general constraints on the structure of tripartite entanglement in Haar random states, showing that W- or Greenberger-Horne-Zeilinger–like entanglement cannot be distilled and that nontrivial global symmetries are absent. Finally, we discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief.

Kerr-cat qubits have been experimentally shown to exhibit a large noise bias, with one decay channel suppressed by several orders of magnitude. In superconducting implementations, increasing the microwave drive on the nonlinear oscillator that hosts the Kerr-cat qubit should, in principle, further enhance this bias. Instead, experiments reveal that above a critical drive amplitude the tunneling time, which is the less dominant decay channel, ceases to increase and even decreases. Here, we show that this breakdown arises from the multimode nature of the circuit implementation. Specifically, additional modes, including the buffer mode used to deliver the stabilizing drive and higher modes of the Josephson junction array, can induce multiphoton resonances that sharply degrade Kerr-cat coherence. We uncover this mechanism by retaining the full circuit nonlinearities and treating the strong drive exactly within a Floquet-Markov framework that accounts for quasidegeneracies of the Kerr-cat spectrum. Our results not only provide an explanation for the sudden reduction of the tunneling time, but also demonstrate that the Kerr-cat qubit can be very robust in the presence of a carefully engineered electromagnetic environment. Beyond the Kerr-cat qubit, the tools developed here open the door to study a broad range of drive-induced phenomena in dissipative superconducting circuits, in both resonant and off-resonant driving regimes. Examples include inelastic scattering in circuits with arbitrary anharmonicity and drive strength as well as subharmonically driven devices such as parametric amplifiers and couplers and other protected qubits whose coherence is governed by quasidegeneracies.

Hysterons provide a minimal description of memory in driven matter: bistable elements with distinct switching thresholds whose collective dynamics generate hysteresis, avalanches, and history-dependent switching. Experimental realizations have so far been dominated by solid-state mechanical systems, where bistability is usually encoded structurally through buckling, snap-through, or geometric incompatibility. Here we realize hysteron physics through a hydrodynamic route. A single elastic fiber anchored in a microfluidic channel becomes bistable through nonlinear elastohydrodynamic feedback: Viscous loading deforms the fiber, deformation reshapes hydraulic resistance, and flow redistribution modifies the loading. This feedback produces a fluidic hysteron whose onset is organized by a cusp catastrophe in geometric control parameters. A parallel bypass channel acts as a geometric load line that reshapes, and can even eliminate, bistability while simultaneously mediating long-ranged hydraulic interactions between fibers. In arrays, varying a single geometric parameter drives a transition from a noninteracting Preisach regime with return-point memory to an interacting regime with configuration-dependent thresholds, mixed-direction switching paths, and projected trajectories that cross the independent-Preisach envelope. These results establish a passive hydrodynamic route to hysteron networks, in which memory emerges from flow-structure feedback and global hydraulic constraints.

We construct an effective field theory (EFT) that captures the universal behavior of out-of-time-order correlators (OTOCs) at late times in generic quantum many-body systems with conservation laws. The EFT hinges on a generalization of the strong-to-weak spontaneous symmetry-breaking pattern adapted to out-of-time-order observables and reduces to conventional fluctuating hydrodynamics when time-ordered observables are probed. We use the EFT to explain different power-law behavior observed in OTOCs at late times and show that many OTOCs are entirely fixed by conventional transport data at leading order. Nevertheless, we show that a specific combination of OTOCs is sensitive to novel transport parameters not visible in regular time-ordered correlators. We test our predictions in Hamiltonian and Floquet spin chains in one spatial dimension.

Optical cavities are a foundational technology for controlling light-matter interactions. While interfacing a single cavity to either an atom or ensemble has become a standard tool, the advent of single-atom control in large atomic arrays has spurred interest in a new frontier of “many-cavity QED,” featuring many independent resonators capable of separately addressing individual quantum emitters. In this fast-evolving landscape, the cavity array microscope was recently introduced—employing free space intracavity optics to engineer a two-dimensional array of tightly spaced cavity ${\mathrm{TEM}}_{00}$ modes with wavelength-scale waists, ideally suited for interfacing with atom arrays. Here, we realize the next generation of this architecture, achieving hundreds of degenerate cavity modes with improved, uniform finesse, and explore the technical features of the system which will enable further scalability. In particular, we study imperfections, including optical aberrations, field of view constraints, array nondegeneracies, and losses from optical elements. We identify the sensitivity to these various factors and exposit the control knobs and techniques necessary to align and operate the system in a stable manner. Ultimately, we lay out a pathway toward operation with tens of thousands of independent cavities while maintaining compatibility with existing atom arrays, paving the way to myriad applications including highly parallelized remote entanglement generation, fast and nondestructive midcircuit readout, and the implementation of hybrid atom-photon Hamiltonians.

Key to solving many societally relevant problems in materials science, quantum chemistry, and nuclear physics is understanding their fundamental microscopic quantum behavior. All of these problems can be phrased as fermionic (e.g., electrons, quarks) and bosonic particles (e.g., lattice vibrations, photons) interacting with each other. However, solving these systems of strongly interacting fermions and bosons is out of reach for classical computers and also non-error-corrected qubit-only quantum computers. In this paper, we introduce a hybrid qubit and bosonic-oscillator quantum-simulation framework, which is so efficient that it could simulate some of these strongly correlated problems even without error correction. Specifically, we leverage the available universal bosonic gate set with $\mathcal{O}(1)$ operations per gate as a function of the bosonic cutoff. This enables our framework to provide exact decompositions of higher-order fermion-boson interactions, including notoriously challenging terms such as $(2+1)\mathrm{D}$ gauge theories. We show how to compile dynamics, ancilla-free partial error detection, nonlocal observable measurements, and ground-state energy estimation using both qubit-boson variational quantum eigensolvers and quantum signal processing. We introduce a “post-qubit quantum advantage” experiment which is out of reach for both near-term qubit-only quantum computers and classical computers. We justify this proposal by estimating bosonic gate fidelities through high–boson-occupation Lindblad simulation and by comparing to qubit-only algorithms. For the latter, we develop a new qubit-based algorithm for simulating a beam splitter with a boson number cutoff $N_{\max }$, which scales as $\tilde{\mathcal{O}}(N_{\max }^{1+o(1)})$, asymptotically outperforming previously known qubit methods. However, to reach the same circuit fidelity as qubit-boson hardware with 99.9% per-gate fidelity, a qubit quantum computer using the best-known method would still need fidelities of at least 99.9999%, likely requiring substantial error correction. Our framework can be used in superconducting hardware, which we focus on, as well as trapped-ion and neutral-atom hardware. This work establishes digital hybrid qubit-boson quantum simulation as a promising and advantageous method for solving the many challenging, strongly correlated, fermion-boson models of relevance to science and technology.

Moiré superlattices in van der Waals heterostructures, arising from lattice mismatch or twist angle, provide a powerful platform for engineering correlated electronic and excitonic states. Moiré excitons form when electrons and holes are individually modulated by the moiré potential yet remain bound by Coulomb interaction, resulting in exciton wave functions with a highly nontrivial and rich real-space structure. However, achieving in situ and dynamic control over the interplay between excitonic Coulomb interaction and the moiré potential remains a central challenge. Here, we demonstrate that hydrostatic pressure provides a continuous and effective means of enhancing the moiré potential and tuning moiré excitons in ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$ moiré heterobilayers. As pressure increases, intralayer moiré excitons exhibit systematic redshifts as the moiré potential deepens. Crucially, above $\sim 3\mathrm{GPa}$ the system enters a strong-moiré regime, where a new higher-energy intralayer moiré exciton emerges that is not accessible otherwise. Combining dual-gate optical spectroscopy with Bethe-Salpeter equation calculations, we reveal that this emerging moiré exciton state arises from strong pressure-induced hybridization between two distinct exciton series: Wannier-Rydberg and charge-transfer excitons. Enhanced exciton-electron and exciton-exciton interactions observed in doping-dependent photoluminescence further evidence the strengthened moiré potential under pressure. Our work establishes a pioneering paradigm of moiré excitonic wave function engineering, enabling the on-demand creation of tailored excitonic species in moiré superlattices.

Superconductivity in three dimensions is almost universally governed by Ginzburg-Landau mean-field theory, with critical fluctuations typically confined to within a few percent of the transition temperature ($T_{\mathrm{c}}$). We report that the heavy-fermion superconductor ${\mathrm{UTe}}_2$ exhibits superconducting fluctuations that extend over a temperature range as wide as $T_{\mathrm{c}}$ itself—the largest observed for any three-dimensional superconductor. Through ultrasound measurements of the elastic moduli and sound attenuation, we find that ${\mathrm{UTe}}_2$ transitions from a mean-field-like state at ambient pressure to a fluctuation-dominated state at higher pressures. This regime is marked by elastic softening and an increase in sound attenuation that onsets well above $T_{\mathrm{c}}$, with the attenuation remaining anomalously high deep in the superconducting state. Our analysis suggests that these features stem from an extremely low superfluid phase stiffness. This results in a kinetic inductance as high as that of granular aluminum, but achieved in the clean limit. We propose a model where this exotic state is driven by dominant interband pairing mediated by ferromagnetic fluctuations, leading to “local” Cooper pairs with a coherence length of only a few lattice constants.

Heat generation and conduction at moving interfaces are ubiquitous and fundamentally important. However, despite decades of progress on thermal transport across static interfaces, insights into moving interfaces remain rare due to the complex and ever-changing nature of most sliding contacts. Here, we take advantage of structural superlubricity and achieve simultaneous mechanical manipulation and thermal measurement of the heterointerface between gold micromesas and single-crystal graphite. We uncover a robustly high thermal conductance which is orders of magnitude higher than that in conventional moving contacts and remarkably insensitive to arbitrary interfacial rotation and thousands of cycles of sliding. In conjunction with atomistic simulations, we reveal the critical role of full atomic contact associated with the interfacial superlubricity and the stacking-insensitive out-of-plane phonon modes that dominate heat transfer. Altogether, our findings highlight diverse superlubric heterointerfaces as a pristine platform for exploring phonon dynamics in moving systems and managing heat in emerging devices including twistronics and slidetronics.

Predicting future observations plays a central role in machine learning, biology, economics, and many other fields. It lies at the heart of organizational principles such as the variational free-energy principle and, based on the second law of thermodynamics, has even been shown to be necessary for reaching the fundamental energetic limits of information processing on a tape. While the usefulness of the predictive paradigm is undisputed, complex adaptive systems that interact with their environment are more than just predictive machines: They have the power to act upon their environment and cause change. In this work, we develop a framework to analyze the thermodynamics of information processing in percept-action loops, a model of agent-environment interaction, allowing us to investigate the thermodynamic implications of actions and percepts on equal footing. To this end, we introduce the concept of work capacity defined as the maximum rate at which an agent can expect to extract work from its environment. Our results reveal that work-efficient agents must balance prediction and forgetting. This highlights a fundamental departure from the thermodynamics of passive observation, suggesting that prediction and energy efficiency may be at odds in active learning systems.

Recent advances in quantum simulators allow direct experimental access to ensembles of pure states generated by measuring part of an isolated quantum many-body system. These projected ensembles encode fine-grained information beyond thermal expectation values and provide a new window into quantum thermalization. In chaotic dynamics, projected ensembles exhibit universal statistics governed by maximum-entropy principles, known as deep thermalization. At infinite temperature, this universality is characterized by Haar-random ensembles. More generally, physical constraints such as finite temperature or conservation laws lead to Scrooge ensembles, which are maximally entropic distributions of pure states consistent with these constraints. Here, we introduce Scrooge $k$-designs, which approximate Scrooge ensembles, and we use this framework to sharpen the conditions under which Scrooge-like behavior emerges. We first show that global Scrooge designs arise from long-time chaotic unitary dynamics alone, without measurements. Second, we show that measuring a complementary subsystem of a scrambled global state drawn from a global Scrooge $2k$-design induces a local Scrooge $k$-design. Third, we show that a local Scrooge $k$-design arises from an arbitrary entangled state when the complementary system is measured in a scrambled basis induced by a unitary drawn from a Haar $2k$-design. These results show that the resources required to generate approximate Scrooge ensembles scale only with the desired degree of approximation, enabling efficient implementations. Complementing our analytical results, numerical simulations identify coherence, entanglement, nonstabilizerness, and information scrambling as essential ingredients for the emergence of local Scrooge-like behavior. Together, our findings advance theoretical explanations for maximally entropic, information-stingy randomness in quantum many-body systems.

For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive, often relying on operational definitions without fundamental principles. Here, we fill this gap by proposing an approach based on three axioms: (i) local recoverability, (ii) absence of long-range correlations, and (iii) spatial uniformity. States that satisfy these axioms are fixed points; requiring the axioms only after coarse-graining promotes each fixed point to an equivalence class, i.e., a phase, presenting the first step toward the axiomatic classification of mixed-state phases of matter: the mixed-state bootstrap program. From these axioms, a rich set of topological data naturally emerges; importantly, these data are robust under relaxation of axioms. For example, each topological mixed state supports locally indistinguishable classical and/or quantum logical memories with distinct responses to topological operations. These data label distinct mixed-state phases, allowing one to distinguish them. We further uncover a hierarchy of secret-sharing constraints: In non-Abelian phases, reliable recovery—even of information that looks purely classical—demands a specific coordination among spatial subregions, a requirement different across non-Abelian classes. This originates from non-Abelian fusion rules that can stay robust under decoherence. Finally, we performed large-scale numerical simulations to corroborate stability: Weakly decohered fixed points respect the axioms once coarse-grained. Surprisingly, the axiom violations at different length scales exhibit an exact crossing at the critical point, enabling its identification without any rescaling or data-collapse ambiguities. These results lay the foundation for a systematic classification of topological states in open quantum systems.

A spin nematic order, analogous to a nematic liquid crystal, characterizes the spontaneous breaking of spin-space rotational symmetry while preserving time-reversal ($T$) symmetry. On the other hand, the order parameter characterizing the $T$-symmetry breaking is the composite three-spin order, i.e., the scalar spin chirality (SSC) ${\chi }_{ijk}=⟨S_i·(S_j\times S_k)⟩$, where $S_i$, $S_j$, $S_k$ are spins at neighboring sites $i$, $j$, $k$, respectively, and nonzero SSC is known to induce anomalous Hall effect (AHE). Although a spin nematic phase has been suggested in the frustrated magnets and the square-lattice iridate, how a spin nematic phase might affect magneto-transport properties is unknown. Here we use polarized neutron scattering to show that tetragonal lattice $A{\mathrm{MnBi}}_2$ ($A=\mathrm{Ca}$, Yb) is a strictly $c$-axis-aligned collinear antiferromagnet ($C$-type) with $T_N\approx 270$ and 290 K. On cooling from 450 K to $T_N$, low-energy spin excitations in ${\mathrm{YbMnBi}}_2$ spontaneously change from isotropic to anisotropic in spin space within the tetragonal plane, forming a dynamic spin nematic phase around 400 K due to heavy Yb-induced spin-orbit coupling, before gapping out below $T_N$. Similar polarized neutron scattering measurements on ${\mathrm{CaMnBi}}_2$ reveal isotropic paramagnetic scattering without a spin nematic phase above $T_N$. Under an in-plane external magnetic field, the ${\mathrm{Yb}}^{3+}$ moments may interact with the dynamic spin nematic phase to induce nonzero SSC, giving rise to AHE and anomalous Nernst effect (ANE) in ${\mathrm{YbMnBi}}_2$ that is absent in ${\mathrm{CaMnBi}}_2$ above $T_N$. Theoretical analysis of Ginzburg-Landau theory based on the symmetry indicates that the coupling terms between the nematic order and SSC of 5 order in the spin operators are allowed under an external magnetic field $B$. This could explain the rapid increase of AHE as a function of $B$ in ${\mathrm{YbMnBi}}_2$. Our results, therefore, provide compelling evidence for dynamic SSC-induced AHE and ANE in the paramagnetic phase of a compensated collinear antiferromagnet, opening a new avenue for the physics of composite orders of multiple spins for room-temperature spintronics without magnetic order.

We experimentally and theoretically study the thermodynamically optimal control of interacting multiparticle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that transport the system between prescribed trap configurations within a fixed time in the most energy efficient way. For Markovian systems with conservative pairwise interactions, we establish a general result in the low-noise limit: optimal particle trajectories are linear in space and time, corresponding to steady straight-line motion, irrespective of the specific interaction potential, even for nonlinear forces. Thus, conservative interactions do not modify the geometry of the optimal paths. This property breaks down in the presence of strong noise or nonconservative interactions. For the paradigmatic case of hydrodynamic coupling, we demonstrate experimentally that optimal control can involve curved trajectories that significantly reduce the energetic cost by exploiting collectively generated fluid flows. The emergence of curved paths as optimal solutions highlights a fundamental distinction between noninteracting and interacting systems and reveals a cooperative mechanism for energy-efficient control.

Quasicrystals extend topological concepts beyond periodic systems, but their exploration in mechanical wave systems remains elusive. Here, we experimentally realize two-dimensional quasicrystal water waves with fivefold rotational symmetry via the interference of multiple quasiplane waves. Although topologically indistinguishable in real space, these patterns are uniquely classified by higher-dimensional topological charge vectors that obey an angular-momentum-like conservation law. Using the water-wave amplitude and its in-plane gradient, we construct a synthetic three-dimensional vector field and demonstrate the emergence of skyrmions in water-wave quasicrystals. These skyrmions exhibit dynamically evolving boundaries and orientations, i.e., deformation and propagation due to phasonlike motion during the evolution of the quasicrystal water-wave field. Remarkably, the associated phase singularities can generate forces and torques that stably trap and drive the rotation of floating particles. We demonstrate in experiments the simultaneous manipulation of particles at multiple trapping sites in different ways, opening a path toward programmable control of particle dynamics. By bridging higher-dimensional topology with water-wave quasicrystals and skyrmions, our work not only advances the physics of topological hydrodynamics but also establishes a platform for on-demand particle control in aqueous environments, which is promising for applications in biomedicine, microfluidics, and lab-on-a-chip technologies.

We introduce a variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multidimensional Wigner phase-space representation and employs a variational multi-Gaussian Ansatz, whose accuracy is systematically controlled by the number of Gaussian components. The variational equations of motion are derived from the Dirac-Frenkel principle and evaluated efficiently by combining the analytical structure of Gaussian functions with automatic differentiation. As a key physical application, we study a driven-dissipative two-dimensional Bose-Hubbard lattice with two-boson coherent driving and two-body losses. Using our dynamical approach, we compute the finite-size scaling of the Liouvillian spectral gap—extracted from the relaxation dynamics—which vanishes in the thermodynamic limit. Our results reveal critical slowing down with dynamical exponents of the 2D quantum Ising universality class, demonstrating the power of our method to capture complex quantum dynamics in large open systems.

We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site level, in contrast to Sachdev-Ye-Kitaev chains. It is analytically tractable for large local Hilbert space dimension and weak intersite coupling. In this limit, we show that energy dynamics is described by a classical master equation and is diffusive. We also show that the spectral form factor can be expressed exactly in terms of the solution to this master equation. For a two-site system, we obtain closed-form expressions for both the two-point correlator of energy density and the spectral form factor, in essentially perfect agreement with numerical simulations. For an $L$-site system we show at late times how a linear ramp emerges in the spectral form factor, as universally expected from level repulsion in chaotic quantum systems. Conversely, at earlier times we identify two distinct mechanisms for an increase of the spectral form factor above its ramp value. One of these is associated with energy diffusion and is effective until the Thouless time, which varies as $L^2$. The other involves contributions like those that would appear if the system were composed of many uncoupled subsystems: They generate a large enhancement of the spectral form factor and are suppressed on a timescale varying as $(\ln L{)}^2$. Besides being exact for the limit considered, we believe our approach provides the natural approximation even for small local Hilbert space dimension and strong intersite coupling. We present a numerical study of a spin-half chain, finding an early-time enhancement of the spectral form factor which is qualitatively similar to that in our solvable model.

Topology can imbue lattice systems with special properties, notably, the presence of robust eigenstates living at their boundary. Through dimensional reduction, the robust bulk band topology of, e.g., the integer quantum Hall system can be mapped onto similarly robust charge-pumping dynamics of a topological pump living in one lower dimension. Recent studies have uncovered a rich influence of interactions on the dynamics of topological pumps in nonlinear systems, including the robust pumping of self-bound solitons. These striking observations in classical nonlinear photonics have raised a number of questions, chiefly if and how this phenomenology persists in strongly correlated quantum systems and in the few-body limit. Here, using few- and many-atom arrays, we explore how dipolar interactions impact the dynamics of topological population pumping along a Rydberg synthetic dimension. In the few-body limit, we find that dipolar interactions lead to self-bound states that are efficiently pumped along the synthetic dimension, described by an emergent pair-state topological pump. We find that this interaction-assisted pumping persists in many-atom arrays, with a sharpened dependence on the dipolar interaction strength that stems from the enhanced spatial connectivity. These Rydberg-based studies on interaction-assisted topological pumping help connect observations from classical nonlinear photonics to the few-body quantum limit and pave the way for studies of new strongly correlated topological phenomena.