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.

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.

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.

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.

As an instance of geometrical frustration with nonmagnetic degrees of freedom, we explore the physics of local spin $S\ge 1$ moments on the pyrochlore lattice that interact via pure quadrupolar couplings. In the presence of spin-orbit coupling, there are nine allowed couplings between nearest-neighbor quadrupoles. We determine the semiclassical phases and survey the phase diagram of the model. One may view the Hamiltonian as being composed of two copies of the well-studied dipolar model with couplings between the copies, and we find that each easy-plane dipolar phase has two quadrupolar counterparts. As geometrical frustration is important over broad swathes of the parameter space, there are many classical quadrupolar liquids and regions with order-by-disorder selection of discrete states. Order by disorder with quadrupoles admits cubic terms in the Landau theory whose effects appear in Monte Carlo simulations and flavor-wave calculations for fixed spin $S$. We showcase a number of examples of quadrupolar spin liquids, including one realizing a rank-3 symmetric tensor gauge theory exhibiting sixfold pinch point singularities. We discuss remarkable differences between the quadrupolar physics of different spin quantum number. We also discuss connections to the non-Kramers rare earth pyrochlore materials.

A hallmark of classical ergodicity is the complete loss of memory of the initial conditions due to eventual uniform covering of a priori available phase space. In quantum counterparts of such systems, however, this classical ergodic ideal is fundamentally limited: Here, we introduce the concept of a quantum birthmark, a permanent signature left by the initial state and its early-time evolution in a general quantum system, which gives rise to nonergodic behavior persisting even in the infinite-time limit. We present a birthmark framework outlining a ubiquitous memory effect for an arbitrary, nonstationary state composed of two factors conspiring together: the universal and the revival enhancement. The former sets the minimal amplification carried by the time evolution of a quantum state based on global symmetries, whereas the latter incorporates the further enhancement stemming from the early dynamics, particularly prominent in the presence of recurrences that occur before the Heisenberg time. As a concrete example, we identify quantum birthmarks in the venerable stadium billiard, where they can be significantly enhanced by quantum scars. Finally, we discuss the broader implications of quantum birthmarks, including their role as a natural extension of all types of scarring theories to generic nonstationary quantum systems and prospects for experimental observation. Generally, our work opens an unexplored avenue for understanding the elusive quantum nature of ergodicity.

Extended Wigner’s friend scenarios (EWFSs) model agents themselves as unitarily evolving quantum systems, going beyond the standard use of quantum theory where agents are treated classically. Several no-go results suggest deep challenges in this setting: Frauchiger and Renner argued that quantum agents reasoning using quantum theory would arrive at logical paradoxes, while the local-friendliness theorem raises difficulties for maintaining objective notions of measurement events and causal reasoning in EWFSs. This prompts a key question: Can the ability to make and test scientific predictions and reason consistently still be maintained if quantum theory applies universally, even to agents and their memories? We answer this positively by developing a general quantum circuit framework for EWFSs without assuming absolute measurement outcomes. We formalize Heisenberg cuts in terms of distinct choices of channels in the circuit, labeled by “settings,” and show that Frauchiger-Renner-type paradoxes are fully resolved by making explicit the conditioning on these channels or settings. We provide concrete reasoning rules for quantum agents that ensure logical, probabilistic, and causal consistency. Our framework captures all perspectives in an EWFS within a single causal structure while allowing events to be fundamentally subjective, and we show how objective events and predictions nevertheless emerge in current real-world quantum experiments. Thus, we demonstrate a relational yet operational framework that overcomes key challenges in EWFSs without altering the Born rule, unitarity, or classical logic and probability for outcomes. This establishes a formal platform to analyze and compare different EWFS arguments and extend quantum information methods consistently into the Wigner’s friend domain.

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.

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.

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.

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.

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.

Analog quantum simulators offer a route to exploring strongly correlated many-body dynamics beyond classical computation, but their predictive power remains limited by the absence of quantitative error estimation. Establishing rigorous uncertainty bounds is essential for elevating such devices from qualitative demonstrations to quantitative scientific tools. Here we introduce a general framework for bounded-error quantum simulation, which provides predictions for many-body observables with experimentally quantifiable uncertainties. The approach combines Hamiltonian and Lindbladian Learning—a statistically rigorous inference of the coherent and dissipative generators governing the dynamics—with the propagation of their uncertainties into the simulated observables, yielding confidence bounds directly derived from experimental data. We demonstrate this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions. We analyze error bounds on two levels. First, we learn an open-system model from experimental data collected in an initial time window of quench dynamics, simulate the corresponding master equation, and quantitatively verify consistency between theoretical predictions and measured dynamics at long times. Second, we discuss short-time error bounds directly from experimental measurements alone, without relying on classical simulation—crucial for entering regimes of quantum advantage. In both cases, the learned models reproduce the experimental evolution within the predicted bounds, demonstrating quantitative reliability and internal consistency. By integrating statistical learning, open-system modeling, and precise experimental control, bounded-error quantum simulation provides a scalable foundation for trusted analog quantum computation, bridging the gap between experimental quantum platforms and predictive many-body physics. The techniques presented here directly extend to digital quantum simulation.

Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multitime correlation functions. We consider the dynamics of higher-order out-of-time-order correlators (OTOCs) in a minimal circuit model for quantum dynamics. This model mimics the dynamics of a structured subsystem locally coupled to a maximally random environment. We prove the exponential decay of all higher-order OTOCs and fully characterize the relevant timescales, showing how local operators approach free independence at late times. We show that the effects of the environment on the local subsystem can be captured in a higher-order influence matrix, which allows for a Markovian description of the dynamics provided an auxiliary degree of freedom is introduced. This degree of freedom directly yields a dynamical picture for the OTOCs in terms of free cumulants from free probability, consistent with recent predictions from the full eigenstate thermalization hypothesis. This approach and the relevant influence matrix are expected to be applicable in more general settings and present a first step to characterizing quantum memory in higher-order OTOCs.

We show the emergence of random matrix theory (RMT) spectral correlations in the chaotic phase of generic, periodically kicked, interacting, quantum many-body systems by analytically calculating the spectral form factor (SFF), $K(t)$, up to two leading orders in time, $t$. We explicitly consider the presence or absence of time-reversal ($\mathcal{T}$) symmetry to investigate all three Dyson symmetry classes, namely, the circular orthogonal ensemble (COE) for $\mathcal{T}$-invariant systems with ${\mathcal{T}}^2=1$, the circular unitary ensemble (CUE) in the absence of $\mathcal{T}$ symmetry, and the circular symplectic ensemble (CSE) for $\mathcal{T}$-invariant systems with ${\mathcal{T}}^2=-1$. Our derivation applies the random phase approximation to perform ensemble averages, and we give its justification for generic many-body interactions. We express the SFF as a sum of contributions of certain diagrams. While the number of diagrams that contribute to the SFF in the first and second orders in $t$ for the COE and CUE classes is finite, the number of such diagrams is exponentially large in $t$ for the CSE class. Thus, we have developed a new diagrammatic technique that uses reduced diagrams to incorporate contributions from many diagrams. For the COE class, we show that beyond Thouless time $t^{*}$, the SFF takes the form $K(t)\simeq 2t-2t^2/\mathcal{N}$ up to second order in time, where $\mathcal{N}$ is the Hilbert space dimension. For the CUE class, we show that $K(t)\simeq t$ beyond $t^{*}$, and there is no universal term in the second order, unlike the COE case. For the CSE class, we show that $K(t)\simeq 2t+2t^2/\mathcal{N}$ up to two orders in time beyond $t^{*}$. The above findings of the SFF up to second order in time are in agreement with the RMT predictions for these classes. In all three cases, the scaling of $t^{*}$ with system size $L$ is determined by the eigenvalues of a doubly stochastic matrix $\mathcal{M}$. For strongly interacting fermionic chains, $\mathcal{M}$ is $SU(2)$ invariant in all three cases, leading to $t^{*}\propto L^2$ in the presence of $U(1)$ symmetry. In the absence of $U(1)$ symmetry, we find $t^{*}\propto L^0$, due to the gapped, nondegenerate, second-largest eigenvalue of $\mathcal{M}$, or $t^{*}\propto \ln (L)$, due to the gapped second-largest eigenvalue with degeneracy proportional to $L^{\zeta }$, $\zeta >0$. Our calculation of the SFF is plausible in higher space dimensions as well, where similar system-size scalings of $t^{*}$ can be obtained.