Scalable quantum computers and quantum networks require the combination of quantum processing nodes with efficient light-matter interfaces to distribute quantum information in local or long-distance quantum networks. Neutral-atom arrays have both been coupled to Rydberg states to enable high-fidelity quantum gates in universal processing architectures, and to optical cavities to realize interfaces to photons. However, combining these two capabilities and coupling atom arrays to highly excited Rydberg states in the mode of an optical cavity has been an outstanding challenge. Here we present a novel cavity-coupled Rydberg array that achieves this long-standing goal. We prepare, detect, and control individual atoms in a scalable optical tweezer array, couple them strongly to the optical mode of a high-finesse optical cavity and excite them in a controlled way to Rydberg states. We show that high-cooperativity coupling to an optical cavity—demonstrated via the dispersive shift of the resonance of the cavity in presence of the atoms—and strong Rydberg interactions—demonstrated via the collective enhancement of Rydberg coupling in the atomic array—can be achieved in our setup at the same spatial location. Our presented experimental platform opens the path to several new directions, including the realization of quantum network nodes, quantum simulation of long-range interacting, open quantum systems, and photonic-state engineering leveraging high-fidelity Rydberg control.

The discovery of high-temperature superconductivity in bilayer and trilayer nickelates has spurred intense interest in the Ruddlesden-Popper nickelates, yet the fundamental properties of the ${\mathrm{NiO}}_2$ layer remain obscured by interlayer coupling. It is therefore imperative to investigate the electronic properties of their single-layer counterpart—though not superconducting—to isolate the intrinsic physics of the Ni-O layer. In this work, we present a systematic study of the single-layer nickelate ${\mathrm{La}}_{1.4}{\mathrm{Sr}}_{0.6}{\mathrm{NiO}}_4$ using high-resolution angle-resolved photoemission spectroscopy and theoretical calculations. We reveal strong electron correlation effects manifested by high-energy kinks in band dispersions and a pronounced orbital-dependent band renormalization. Interestingly, we observe a quasi-one-dimensional electronic structure characterized by straight Fermi surface sheets along the diagonal momentum directions. Such a squarelike Fermi surface topology facilitates non-Fermi-liquid behavior consistent with the Luttinger liquid model, as evidenced by the power-law spectral function, robust temperature scaling, and spectroscopic features reminiscent of spin-charge separation. Our results therefore not only point toward an exotic Luttinger liquid phase emerging from the unexpected dimensional reduction in an intrinsically quasi-two-dimensional nickelate but also provide a new perspective for understanding the intriguing physics in multilayer nickelates.

Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions confined in an externally applied trapping potential self-organize into “Coulomb crystals” due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and most eigenmodes of motion involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by locally tuning the confining potential for each ion. A single motional quantum, or phonon, can be coherently shared among two or three ions located at the vertices of an equilateral triangle $30\mathrm{\mu }\mathrm{m}$ on a side. We tune the motional eigenmodes about closed contours in configuration space and observe that, if the contour adiabatically encircles a conical intersection present in the motional eigenvalue surfaces, the single-phonon wave function acquires a topological Berry phase that is independent of the contour shape. We characterize these phases by single-phonon interference and study how phase changes occur when the motional mode tuning becomes nonadiabatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array provides unique access to quantum multibody effects.

In this work, we realize the $3+1\mathrm{D}$ noninvertible ${\mathbb{Z}}_N$ chiral symmetry generator as an operator in a many-body lattice Hilbert space. A crucial ingredient in our construction is the use of infinite-dimensional U(1) rotor site Hilbert spaces. Specifically, our Hilbert space is that of a U(1) lattice gauge theory coupled to a charge 1 scalar in the Villain formulation, which allows for direct access to monopoles and for a simple definition of a magnetic ${\mathbb{Z}}_N$ one-form symmetry $Z_m^{(1)}$, at the lattice Hamiltonian level. We construct the generator of the ${\mathbb{Z}}_N$ chiral symmetry as a locality-preserving unitary operator not in the entire Hilbert space but only in the subspace of $Z_m^{(1)}$-invariant states. Using a lattice-level duality based on gauging $Z_m^{(1)}$, we find a dual description of this subspace, as the subspace of a charge $1/N$ gauge theory invariant under an electric one-form symmetry $Z_e^{(1)}$. We show that, in this dual formulation, the chiral symmetry generator extends unitarily to the entire Hilbert space but has a mixed anomaly with the $Z_e^{(1)}$ symmetry.

How the detailed entanglement structure emerges from quantum dynamics remains a fundamental challenge motivated by recent advances in quantum simulators and information processing. As a central milestone, the small-incremental-entangling (SIE) theorem bounds the entanglement-entropy growth rate but does not control the entanglement spectrum itself. In this work, we define the spectral-entangling strength, which quantifies how strongly an operator can reshape the distribution of Schmidt coefficients across a bipartition. We then prove a spectral-SIE theorem: for Rényi index $\alpha \ge 1/2$, the growth rate of Rényi-entanglement entropies admits a universal bound. Remarkably, our bound at $\alpha =1/2$ is both qualitatively and quantitatively optimal; below this threshold ($\alpha <1/2$), no universal speed limit on entanglement growth can exist. This result yields a sharp $1/s^2$ threshold in the tail of the ordered squared Schmidt coefficients, or equivalently in the entanglement-spectrum weights (with $s$ the Schmidt index). It enables rigorous truncation-based-error control and establishes a quantitative link between entanglement-spectrum structure and computational complexity. As a practical highlight, for one-dimensional power-law interactions $1/r^{\eta }$ with $\eta >2$, this implies matrix-product-state approximations with bond dimension polynomial in ($n/\epsilon$) for ground states, real-time evolved states, and Gibbs states, thereby closing the quasipolynomial gap, where $n$ is the system size, and $\epsilon$ denotes the target approximation error in the relevant state or operator norm. By controlling Rényi entanglement, we further obtain a rigorous a priori truncation-error bound for the time-dependent density-matrix renormalization-group scheme analyzed here. Overall, we extend the SIE paradigm from bounding entanglement entropies to constraining the entanglement spectrum itself.

Active matter sustains emergent flows at the expense of preserving structural order. The feedback between structure and viscous flows typically disrupts crystalline and liquid-crystalline organization by amplifying the very deformations they generate. Yet this destabilizing paradigm has recently been challenged by experiments showing that inertial fluid flows can stabilize few-body bound states of active spinners. Whether inertial active matter can sustain genuine cohesion and order at the many-body level, however, remains elusive. Here we investigate two-dimensional assemblies of macroscopic spinners operating at high Reynolds number and uncover two phase transitions leading to the emergence of a dilute percolating fluid and a dense spin-textured crystal. At low density, inertial flows generate two competing interactions: anisotropic attractions and transverse Magnus forces that continuously break and reconfigure bonds. Together they drive a percolation transition toward a dynamically rearranging holey liquid reminiscent of the empty-liquid states observed in equilibrium patchy colloids. At high density, the feedback between spin alignment and particle positions suppresses transverse rearrangements and yields a first-order transition toward a spin-ordered crystal. Our results demonstrate that, beyond the overdamped limit, hydrodynamic feedback can promote rather than destroy collective order, revealing a distinct regime of many-body active matter governed by inertial flows.

Liquid mixtures can separate into phases with distinct composition. This phenomenon has recently come back to prominence due to its role in complex biological liquids, such as the cytoplasm, which contain thousands of components. For simple two-component mixtures phase-separated states are global free energy minima. However, local free energy minima, i.e., metastable states, are known to play a dominant role in complex systems with many components. For example, Hopfield neural networks can retrieve stored information from partial cues via relaxation to metastable states. Under what conditions can phase separated states be metastable, and what are the implications for information retrieval in multicomponent liquids? In this work we develop the general thermodynamic formalism of metastable phase separation. We then apply this formalism to an illustrative toy example inspired by recent experiments, binary mixtures with high-order interactions. Finally, as core application of the formalism, we study metastability in Hopfield liquids, a class of multicomponent mixtures capable of storing information on the composition of phases. We show that these phases can be nucleated from partial cues via metastable phase separation. Spatial simulations of liquids with a large number of components match our analytical solution. Our work suggests that complex biological mixtures can retrieve information through metastable phase separation.

Molecular hydrogen (${\mathrm{H}}_2$) is the simplest neutral molecule, and its ionization and dissociation energies are key benchmarks for testing first-principles calculations of nonadiabatic, relativistic, quantum-electrodynamic, and finite-nuclear-size effects in molecules. To obtain improved ${\mathrm{H}}_2$ ionization and dissociation energies, we performed precision measurements of 15 transition frequencies in para-${\mathrm{H}}_2$. They connect the X ${}^1{\mathrm{\Sigma }}_g^{+}(v=0,N=0)$ ground state, the long-lived ${\mathrm{EF}}^1{\mathrm{\Sigma }}_g^{+}(v=0,N=0)$ excited state, and several high members of the $np$ and $nd$ Rydberg series with principal quantum number $n$ in the range between 48 and 70. These data lead to a 5 times more accurate value of the ionization energy of the ground state of para-${\mathrm{H}}_2$, equivalent to a relative frequency accuracy of $5\times {10}^{-11}$. Combined with a global network analysis of 45 energy intervals in para- and ortho-${\mathrm{H}}_2$ that have been measured in the past three decades, we obtain statistically robust values for the ionization energy [$E_{\mathrm{I}}(0,0)/(hc)=124417.4911573(58){\mathrm{cm}}^{-1}$] and the dissociation energy [$D_0^{N=0}=36118.0696646(58){\mathrm{cm}}^{-1}$] of ${\mathrm{H}}_2$. These values have an unprecedented accuracy equivalent to 175 kHz. The network analysis also leads to improved term values and dissociation energies of the excited states involved in the analysis. By comparing the results with first-principles calculations of the level structures of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}$, a significantly reduced upper bound of 540 kHz is derived for putative beyond-the-standard-model contributions to the energy difference between para- and ortho-${\mathrm{H}}_2$.

Establishing the nature of a quantum phase transition in finite-size simulations—whether continuous, first order, or weakly first order—is a fundamental challenge in quantum many-body computation. The weakly first-order transition is particularly elusive: its anomalously large correlation length invariably mimics a continuous critical point at accessible system sizes, and no unified finite-size scaling theory has existed to distinguish these scenarios under realistic computational constraints. In this work, we address this problem by introducing a finite-size scaling framework based on the Rényi thermal entropy (RTE) and its derivative (DRTE). We derive the finite-size scaling forms for the RTE and DRTE at continuous, first-order, and weakly first-order quantum phase transitions and show that the DRTE isolates the universal contribution of the free energy and strengthens the characteristics of various phase transitions in finite sizes. Using quantum Monte Carlo simulations, we demonstrate accurate data collapse and extraction of critical exponents at ($2+1$)-dimensional $\mathrm{O}(N)$ critical points. Most importantly, the DRTE provides a definitive signature of weakly first-order transitions at visitable sizes—a zero crossing and a double-peak structure—which we observe in the debated deconfined quantum criticality candidates such as the $J\text{−}Q$ and SU(8) $J_1\text{−}{J}_2$ models. Our approach offers a general, order-parameter-agnostic, and numerically efficient diagnostic tool, resolving long-standing ambiguities between continuous and weakly first-order scenarios in the finite-size simulations.

Incoherent imaging, including fluorescence and absorption microscopy, is often hindered by weak signals and resolution limits—notoriously, Rayleigh’s curse. We introduce a framework for incoherent quantum imaging in the perturbative (weak-signal) regime that leverages spatially structured quantum probes and multiplexed quantum readout to overcome these limitations. We propose a novel twin-beam echo protocol that maps absorption and fluorescence onto distinct idler and signal modes that carry thermal-like signatures characteristic of passive imaging. This yields an explicit architecture for simultaneous absorption and fluorescence imaging at the quantum limit and allows passive-imaging methods to be directly repurposed for active quantum imaging. As a corollary, we show that subdiffraction absorption imaging with quantum probes evades Rayleigh’s curse, whereas classical probes remain provably afflicted. Remarkably, the same protocol supports displacement-field reconstruction of multiple quadratures (e.g., oscillators’ positions) and pertains to both conventional and subdiffraction imaging. We further identify Fock states in a structured spatial mode basis as a non-Gaussian alternative with comparable performance. Though primarily developed for optical imaging, our framework suggests broad applications to phononic and acoustic imaging, and to reconstructing forces, fields, or charge distributions with an array of mechanical oscillators.

We design a lattice model of a “mixed” U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations. In this mixed construction, dynamical magnetic monopole events are suppressed in the temporal-continuum limit. For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics (${\mathrm{QED}}_3$) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, which corresponds to a Zeeman field perturbing the Dirac spin liquid, we find a “chiral flux” phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. We use field-theory arguments to argue that in this state a ${\mathrm{U}(1)}_m$ magnetic symmetry is spontaneously broken, leading to a gapless photon mode. Because of spin-flux attachment this mode would contribute to the low-energy longitudinal spin response. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.

Antiferromagnetic topological insulators provide a fertile platform where symmetry-breaking magnetic order is intertwined with topological electronic states. In particular, magnetic domain walls have attracted much attention, as they can be easily controlled by external fields as in general magnets, and moreover, host nontrivial electronic states distinct from those in bulks and sample surfaces. Here, we report a new antiferromagnetic topological insulator candidate DyPtBi, which hosts conductive magnetic domain walls controllable by uniaxial stress and magnetic field. We find that the resistivity exhibits abrupt increase upon the magnetic and structural phase transition. Concomitantly, the transverse ultrasonic mode shows remarkable softening of 6%, indicating that the Dy $4f$ ferroquadrupolar order plays a vital role in the phase transition. Furthermore, we reveal by neutron experiments that applying compressive uniaxial stress aligns the magnetic domain state, leading to the strong resistivity enhancement of 14% while eliminating the conductive magnetic domain walls. These findings demonstrate that DyPtBi exhibits topological electronic states entangled with multipolar degrees of freedom, providing a promising route for in situ control of topological properties.

Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly desirable but challenging. In this work, we introduce a highly general certification framework based on a physical phenomenon that we call localizable quantumness: for generic many-body states, essential quantum properties are robustly preserved within the projected ensembles on small subsystems after performing local projective measurements on the rest of the system. Leveraging this insight, we develop protocols to certify global properties—including multipartite entanglement, circuit complexity, and quantum magic—by witnessing them on a small, accessible subsystem. Remarkably, randomizing the local measurement bases extends this capability to certify state fidelity. Relying solely on local Pauli measurements, these protocols achieve constant sample complexity and robustness for almost all quantum states, including a wide range of physically relevant states. For certifying the fidelity of $n$-qubit states, this $\mathcal{O}(1)$ scaling dramatically improves upon state-of-the-art protocols requiring $\mathcal{O}(n^4)$ samples. Our unified framework provides both a practical toolkit for large-scale quantum certification and a novel lens into complex many-body systems.

Living systems operate out of equilibrium, continuously consuming energy to sustain organized, functional states. Their emergent behavior usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes that keep some species at fixed concentrations. Hence, uncovering the principles governing the functioning of these CRNs is crucial to understand how living systems generate and regulate complexity. While kinetics plays a key role in shaping detailed dynamical phenomena, the range of operations of a CRN is fundamentally constrained by thermodynamics. Here, we introduce and analytically derive the “thermodynamic space” of a CRN, i.e., the range of accessible stationary concentrations that can be realized under a given energetic budget. We establish analogous bounds for reaction affinities, shedding light on how global thermodynamic properties, such as the total nonequilibrium driving, can limit local nonequilibrium quantities, and further showing that these bounds can be used to test candidate network topologies and expose hidden multimolecular pathways. We illustrate our results in various paradigmatic examples, demonstrating how the onset of complex behaviors is intimately tangled with the presence of nonequilibrium conditions. By providing a general tool for analyzing CRNs, the presented framework constitutes a stepping stone to deepen our ability to predict complex out-of-equilibrium phenomena and design artificial chemical systems, starting from the sole knowledge of the underlying thermodynamic properties.

Modern precision experiments often probe unknown classical fields with bosonic sensors in quantum-noise-limited regimes where vacuum fluctuations limit conventional readout. We introduce quantum signal learning, a sensing framework that extends metrology to a broader property-learning setting, and propose a quantum-enhanced protocol that simultaneously estimates many properties of a classical signal with shot noise suppressed below the vacuum level. Our scheme requires only two-mode squeezing, passive optics, and static homodyne measurements, and enables post hoc classical estimation of many properties from the same experimental dataset. We prove that our protocol enables a quantum speedup for common classical sensing tasks, including measuring electromagnetic correlations, real-time feedback control of interferometric cavities, and Fourier-domain matched filtering. To establish these separations, we introduce an optimal-transport conditioning method and show both worst-case exponential separations from all entanglement-free strategies and practical speedups over homodyne and heterodyne baselines. We further show that when squeezing is treated as a resource, a protocol with squeezed light can sense a structured classical background exponentially faster than any coherent classical probe.

The past decade has witnessed significant progress in topological materials investigation. Symmetry-indicator theory and topological quantum chemistry provide an efficient scheme to diagnose topological phases from only partial information of wave functions without full knowledge of topological invariants, which has resulted in a recent comprehensive materials search. However, not all topological phases can be captured by this framework, and topological invariants are needed for a more refined diagnosis of topological phases. In this study, we present a systematic framework to construct topological invariants for a large part of symmetry classes, which should be contrasted with the existing invariants discovered through one-by-one approaches. Our method is based on the recently developed Atiyah-Hirzebruch spectral sequence in momentum space. As a demonstration, we construct topological invariants for time-reversal-symmetric spinful superconductors with conventional pairing symmetries of all space groups, for which symmetry indicators are silent. We also validate that the obtained quantities work as topological invariants by computing them for randomly generated symmetric Hamiltonians. Remarkably, the constructed topological invariants completely characterize $K$ groups in 159 space groups. Our topological invariants for normal conducting phases are defined under some gauge conditions. To facilitate efficient numerical simulations, we discuss how to derive gauge-independent topological invariants from the gauge-fixed topological invariants through some examples. Combined with first-principles calculations, our results will help us discover topological materials that could be used in next-generation devices and pave the way for a more comprehensive topological materials database.

We search for gravitational-wave background signals produced by various early Universe processes in the Advanced LIGO O4a dataset, combined with the data from the earlier O1, O2, and O3 (LIGO-Virgo) runs. The absence of detectable signals enables powerful constraints on fundamental physics. We derive gravitational-wave background energy density upper limits from the O1–O4a data to constrain parameters associated with various possible processes in the early Universe: first-order phase transitions, cosmic strings, domain walls, stiff equation of state, axion inflation, second-order scalar perturbations, primordial black hole binaries, and parity violation. In our analyses, the presence of an astrophysical background produced by compact (black hole and neutron star) binary coalescences throughout the Universe is also considered. We address the implications for various cosmological and high-energy physics models based on the obtained parameter constraints. We conclude that LIGO-Virgo data already yield significant constraints on numerous early Universe scenarios.

The interplay of superconductivity, band topology, and spontaneous time-reversal-symmetry breaking (TRSB) is expected to enable topological superconducting boundary states. Intriguingly, the iron-chalcogenide superconductor ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ exhibits spontaneous magnetization in the superconducting state, motivating its use as a single-material platform in which three ingredients coexist. Here, we report evidence for a nontrivial, boundary-mediated superconducting transport response in exfoliated Fe(Te,Se) devices, exhibiting long-range nonlocality and strongly suppressed thermal broadening. Polar Kerr measurements establish that TRSB emerges below $T_{\text{Kerr}}<T_c$ and coexists with superconductivity across multiple Fe(Te,Se) compositions studied here, providing an independent symmetry-breaking scale that can be directly compared with transport. To reliably access boundary transport, we engineer crystallographically sharp, continuous edges and implement side-surface-dominant contacts, as validated by contact-size analysis and cross-sectional imaging. Under these conditions, topological ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ exhibits an anomalous conductance plateau that is absent in topologically trivial ${\mathrm{FeTe}}_{0.40}{\mathrm{Se}}_{0.60}$ and ${\mathrm{Fe}}_{1.02}{\mathrm{Te}}_{0.55}{\mathrm{Se}}_{0.45}$ under comparable measurements. This plateau requires both the source and drain to be attached to uninterrupted sharp edges, persists over micrometer-scale separations far exceeding the bulk coherence length, has markedly reduced thermal decoherence, and collapses when the drain is moved to the top surface. Its temperature evolution is governed by TRSB: The plateau shows minimal thermal broadening below $T_{\text{Kerr}}^{*}$ and disappears near $T_{\text{Kerr}}$ rather than $T_c$. Collectively, the doping selectivity, TRSB correlation, edge-geometry requirement, and long-range nonlocal nature establish experimentally grounded criteria for identifying boundary-mediated superconducting transport in ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ and motivate further phase-sensitive and theoretical work to determine its microscopic origin.

We study quantum and classical many-body Hamiltonian systems that combine integrable contact interactions with generic long-range two-body potentials. Starting from an ansatz for the state at time $t$, which we call the correlated fluid-cell ensemble, we show that the dynamics of local observables at macroscopic times and length scales can be cast into a generalized Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy formulated in terms of the quasiparticle densities of the underlying integrable model and their correlations. We derive this hierarchy and validate these predictions against microscopic molecular-dynamics simulations, finding perfect agreement. At late times, the one-particle distribution relaxes via a Boltzmann-type scattering integral encoding the interplay between integrable contact processes and long-range collisions, whereas higher-point correlations remain strongly nonthermal on thermalization timescales, indicative of a form of incomplete or generalized thermalization. Focusing on long-range dipolar quantum gases, where the relevant matrix elements can be obtained explicitly, we show that our collision integral reduces exactly to the Fermi golden rule result and provide a complete theoretical account of the experimental observations of Tang et al. [Phys. Rev. X 8, 021030 (2018)]. More broadly, our framework extends the BBGKY program to regimes with strong local interactions and applies to a wide class of experimentally relevant systems, from one-dimensional dipolar cold-atom gases to Lennard-Jones molecular fluids.

Quantum systems coupled to (non-) Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional nonequilibrium phases beyond the Mermin-Wagner limit or dissipative state preparation demand a systematic analysis of quantum many-body phases out of equilibrium. Akin to the equilibrium case, this requires the computation of the low-lying eigenstates of Lindbladians, a problem challenging conventional approaches for simulating quantum many-body systems. Here, we undertake a first step to overcome this limitation and introduce a tensor-network-based framework to systematically compute not only steady states, but also low-lying excited states for large, driven quantum many-body systems. Our framework is based on recent advances utilizing complex-time Krylov spaces, and we leverage these ideas to create a toolbox tailored to solve the challenging non-Hermitian eigenvalue problem ubiquitous in open quantum systems. With an example of the interacting Bose-Hubbard model driven by dissipation-assisted hopping, we demonstrate the high efficiency and accuracy. From a reliable finite-size-scaling analysis of the spectral gap, we find strong evidence for nonlinear hydrodynamic behavior consistent with Kardar-Parisi-Zhang-type superdiffusive relaxation and establish the existence of exponentially accelerated, anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems suitable also for non-Markovian environments.