Quantum sensors based on individual spins provide unprecedented access to local magnetic fields in condensed matter, chemistry, and biology, with solid-state defect spins emerging as the leading platform. However, their molecular-sensing capabilities are limited by confinement to a host lattice, which prevents placement in close proximity to a target molecule. Molecular spins offer an alternative, enabling chemical tunability and flexible positioning relative to the target system. Here we present a nanoscale sensing platform that combines molecular electron spins, ultrasensitive mechanical readout, and Hamiltonian engineering. Using a modified XYXY dipolar decoupling sequence, we suppress electron-electron dipolar interactions across a broad distribution of control fields, extending coherence times to $\sim 400\mathrm{\mu }\mathrm{s}$ in an attoliter-scale droplet containing $\sim 100$ trityl-OX063 radicals. Leveraging this sequence, we demonstrate frequency-selective detection of nanotesla-scale ac fields and perform sensing and spectroscopy of small, local nuclear-spin ensembles. Collectively, these results establish spin-based quantum integrated nanomechanical transduction as a framework for quantum sensing that affords molecular-level control over sensor properties and enables direct integration into complex molecular targets.

Heavy polar molecules are sensitive probes of physics beyond the standard model. However, uncontrolled external electromagnetic fields pose challenges to achieving precise and accurate measurements. Minimizing susceptibility to these fields is therefore critical and has played an important role in all precision experiments of this type. Here we devise and demonstrate clock transitions engineered to realize robust symmetry violation searches in the polyatomic molecule YbOH. Sensitivities to external fields can be suppressed by orders of magnitude while preserving high sensitivity to the electron electric dipole moment. We perform Ramsey measurements on these clock transitions and observe suppression of electric and magnetic sensitivities by at least factors of 700 and 200, respectively, and demonstrate the robustness of their spin coherence against large electromagnetic-field fluctuations. We further identify and employ selected quantum states to make sensitive measurements of external magnetic and electric fields, another critical feature for highly accurate measurements. This approach of molecular engineering is broadly applicable to diverse molecular species and states, including those with complex nuclei and those that are compatible with state-of-the-art cooling and trapping techniques, thereby offering the potential to significantly improve experimental sensitivity to a wide range of new physics while expanding the chemical design space for molecular quantum science.

Remote entanglement between widely separated qubits is a fundamental quantum phenomenon and a critical resource for quantum information applications. Generating entanglement between independent qubits separated by arbitrary, potentially large distances requires propagating quantum states and is typically achieved using pulsed protocols combining distinct steps of local entanglement generation followed by distribution. This necessity raises an intriguing question: Can remote entanglement be stabilized indefinitely, instead of periodically regenerated and redistributed only after decay? Here, we demonstrate that this is indeed possible, reporting autonomous stabilization of entanglement between two separate superconducting-qubit devices. Combining nonreciprocal waveguide coupling and local driving, we experimentally realize a symmetry-based coherent quantum-absorber scheme in a cascaded network. We quantify the degree of entanglement through quantum state tomography, finding that the protocol’s entangling power is severely limited by imperfections that break the required symmetry. We show, however, that a modified protocol based on an alternate symmetry is far more robust, enabling us to achieve a concurrence approaching 0.5, a limit set by only local loss in the network. Our results enable on-demand delivery of high-fidelity entanglement in modular quantum processors and networks and pave the way for autonomously protecting distributed quantum information.

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

The tin-vacancy center in diamond (SnV) has emerged as a compelling building block for realizing next-generation quantum networks thanks to its excellent optical and spin properties. Coupling to photonic crystal cavities (PCCs) promises to further enhance the SnV light-matter interface and unlock a diverse range of entanglement generation protocols. Recent pioneering experiments showing Purcell enhancement of SnV centers in PCCs underscore this potential. However, optical coupling that is coherent—the key ingredient for use in quantum protocols—has so far remained elusive. Here, we demonstrate above-unity coherent cooperativity of SnV centers embedded in photonic crystal cavities. We fabricate free-standing PCCs using a quasi-isotropic undercut. Across two samples, we conduct room-temperature characterizations, measuring resonances for 327 cavities, with an average quality factor exceeding $Q=1.1(4)\times {10}^4$. Two cavity-coupled emitters are examined in detail, exhibiting quality factors up to $Q=25.4(4)\times {10}^3$ and Purcell-reduced lifetimes corresponding to cooperativities up to $C=20.3(11)$. Furthermore, the single SnVs are observed to strongly modulate the cavity transmission with an extinction contrast up to 98.8(4)%% on resonance. Finally, SnV linewidth measurements reveal above-unity coherent cooperativities in both devices, with the highest value being $C_{\mathrm{coh}}=8.3(12)$. These results open the door to using cavity-coupled SnV centers as efficient, coherent light-matter interfaces for future quantum networks.

The paradigm of considering open quantum systems—i.e., focusing only on the system of interest, and treating the rest of the world as an effective environment—has proven to be a highly effective way to understand a range of quantum systems, across areas of study such as quantum optics, cold atoms, superconducting qubits, and impurities in solid-state systems. A common approach in many of these contexts has been to consider simplified approaches based on the Born and Markov approximations. While these approximations are indeed often appropriate in contexts such as quantum optics, the widespread application of these approximations has been driven more by simplicity than by accuracy. In particular, these Markovian treatments will fail in many cases, such as when coupling to the environment is not weak, when the environment is structured and has resonances, when the system couples to low-frequency modes of the environment, or when the questions of interest involve the propagation of information through the environment. Despite the fact that many real problems are non-Markovian, the Markov approximation is still widely used, as it is often assumed that a fully non-Markovian treatment is too complex to be practical. In this Perspective we discuss a recently developed set of techniques that address this challenge. Centering our discussion around the notion of the process tensor, we demonstrate that the generality of the process tensor concept, coupled with efficient tensor-network methods, opens the door to the description of a wide range of observable non-Markovian processes in a wide range of open quantum systems.

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of ${10}^{19}$ and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide between entanglement breaking and not; for sets of measurements, the divide between compatible and incompatible; for assemblages, the divide between unsteerable and steerable. However, these choices have not been motivated by any unified notion of what it means to be classically explainable. One well-motivated notion of classical explainability is the one based on generalized noncontextuality: A set of circuits is classically explainable if a generalized-noncontextual ontological model can realize the statistics they generate. In this work, we show that this notion can be leveraged to define a classical-nonclassical divide for individual quantum processes of arbitrary type. A set of measurements, for example, is judged to be classical if and only if a particular set of circuits—the one obtained by contracting these measurements with every possible quantum state—is classically explainable in the sense just articulated. We begin the task of characterizing where the classical-nonclassical divide lies according to this proposal for a variety of different types of processes. In particular, we show that all of the following are judged to be nonclassical: every entangled state, every set of incompatible measurements, every non-entanglement-breaking channel, and every steerable assemblage. Our proposal differs from the received wisdom, however, insofar as it also judges certain subsets of the complementary classes to be nonclassical, including certain separable states, compatible sets of measurements, entanglement-breaking channels, and unsteerable assemblages. Finally, we prove structure theorems characterizing the classical-nonclassical divide based on whether a process admits of a specific type of frame representation.

Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.

An attractive approach for stabilizing entangled many-body spin states is to employ engineered dissipation. Most existing proposals either target relatively simple collective spin states or require numerous independent and complex dissipative processes. Here, we show a surprisingly versatile scheme for many-body reservoir engineering that relies solely on fully collective single-excitation decay, augmented with local Hamiltonian terms. Crucially, all these ingredients are readily available in cavity QED setups. Our method is based on splitting the spin system into groups of subensembles and provides an easily tunable setup for stabilizing a broad family of pure, highly entangled states with closed-form analytic descriptions. Our results have immediate application to multiensemble quantum metrology, enabling Heisenberg-limited sensing of field gradients and curvatures. Notably, our approach solves an important challenge in differential quantum sensing by providing an example of Heisenberg-limited differential sensing immune to common-mode noise and accessible with only simple one-body measurements. The same setup also allows the stabilization of an entire family of entangled states in a one-dimensional chain of spin ensembles with symmetry-protected topological order and has a direct connection to the outputs of sequential unitary circuits. A special case of our protocol efficiently stabilizes the celebrated Affleck-Kennedy-Lieb-Tasaki state.

Physical qubits in a quantum computer are often represented by superposition states of single particles or excitations. Decay of the excitation itself is a fundamental error channel that is difficult to overcome via external drive or control techniques. Quantum error correcting codes, which encode information in superpositions involving multiple excitations, provide a path to preserve information beyond the capacity of individual excitations, but typically require exquisite active operations on the system. Here, we demonstrate a steady-state driven-dissipative quantum system, composed of a superconducting cavity and a transmon ancilla, that preserves a logical qubit beyond the photon-lifetime limit by about 5% using a binomial encoding. This realization of continuous quantum error correction at the breakeven point highlights the quantitative competitiveness of passive correction strategies, while circumventing some demanding hardware requirements of its active counterparts.

Among the thriving quantum computation and quantum simulation platforms based on arrays of Rydberg atoms, those using circular Rydberg atoms are particularly promising. These atoms uniquely combine the strong dipole-dipole interactions typical of Rydberg states with long lifetimes. However, low-angular-momentum ($\ell$) laser-accessible Rydberg levels have been so far mostly used, because circular Rydberg atoms have no optical transitions, hindering their individual detection and manipulation. We remove this limitation with a hybrid platform, combining an array of data laser-trapped circular Rydberg atoms of rubidium with an auxiliary array of Rb ancilla atoms transiently excited to a low-$\ell$ Rydberg level. We perform a quantum nondemolition detection of the data qubit with the ancilla, through the blockade of the ancilla optical excitation induced by a Förster resonance. Conversely, we locally manipulate the data qubit through the excitation of the ancilla. This dual-Rydberg platform is highly promising for quantum computation and simulation. It adds to the circular-atom toolbox the midcircuit measurements, essential for error correction. More strikingly, it gives access to time correlations in long-term quantum simulations, uniquely accessible to circular Rydberg atoms.

Advanced quantum technologies rely on non-Gaussian states of light, essential for universal quantum computation, fault-tolerant error correction, and quantum sensing. Their practical realization, however, faces hurdles: Simulating large multimode generators is computationally demanding, and benchmarks such as the stellar rank do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the non-Gaussian control parameters $(s_0,{\delta }_0)$, a continuous and operational measure that goes beyond stellar rank. Leveraging these parameters, we develop a universal optimization method that reduces photon-number requirements and greatly enhances success probabilities while preserving state quality. Applied to the Gottesman-Kitaev-Preskill state generation, for example, our method cuts the required photon detections by a factor of 3 and raises the preparation probability by nearly ${10}^8$. Demonstrations across cat states, cubic phase states, Gottesman-Kitaev-Preskill states, and even random states confirm broad gains in experimental feasibility. Our results provide a unifying principle for resource-efficient non-Gaussian state generation, charting a practical route toward scalable optical quantum technologies and fault-tolerant quantum computation.

Quantum information is typically fragile under measurements and environmental coupling. Remarkably, we find that its lifetime can scale exponentially with system size when the environment is continuously monitored via midcircuit measurements—regardless of bath size. Starting from a maximally entangled state with a reference, we analytically prove this exponential scaling for typical Haar-random unitaries and confirm it through numerical simulations in both random unitary circuits and chaotic Hamiltonian systems. In the absence of bath monitoring, the lifetime exhibits a markedly different scaling: It grows at most linearly—or remains constant—with system size and decays inversely with the bath size. We further extend our findings numerically to a broad class of initial states. In the intermediate regime of partial monitoring, we identify and prove a two-scale transition, where the quantum mutual information decays logarithmically at microscopic timescales but linearly at macroscopic timescales. We discuss implications for monitored quantum circuits in the weak-measurement limit, quantum algorithms such as quantum diffusion models and quantum reservoir computing, and quantum communication. Finally, we experimentally verify the gap of persisted information on IBM Quantum hardware.

The thermodynamic limit is foundational to statistical mechanics, underlying our understanding of many-body phases. It assumes that, as the system size grows infinitely at fixed density of particles, unambiguous macroscopic phases emerge that are independent of the system’s boundary shape. We present explicit quantum spin and dimer Hamiltonians whose ground states violate this principle. Our construction relies on the previous mathematical work on classical dimers on the Aztec diamond and the square-octagon fortress, where geometry-dependent phase behaviors are observed in the infinite-size limit. We reverse engineer quantum spin Hamiltonians on the square and the square-octagon lattices whose ground states at the Rokhsar-Kivelson points are described by classical dimer coverings. On diamond-shaped domains, we find macroscopic boundary regions exhibiting distinct quantum phases from those on square-shaped domains. We study the nature of these phases by calculating the dimer-dimer and vison correlators and adapt Kasteleyn matrix based analytical and numerical methods for computing the vison correlator, which are significantly more efficient than standard Monte Carlo techniques. Our results show that the square-octagon lattice supports a single gapped short-range entangled phase, with exponentially decaying dimer correlators and a constant vison correlator. When the same model is considered on a diamond-shaped domain, two additional macroscopic regions emerge, with one near the corners and exhibiting staggered dimer order, and another exhibiting critical correlations.

One of the premier utilities of present-day noisy quantum computers is simulation of many-body quantum systems. We study how long in time is such a discrete-time simulation representative of a continuous time Hamiltonian evolution; namely, a finite time step introduces so-called Trotterization errors. We demonstrate that the truncated operator propagator (Ruelle-Pollicott resonances) is a powerful tool to that end, as well as to study prethermalization and discrete-time crystals, including finding those phenomena at large gate duration. We show that the effective energy is more stable than suggested by Trotter errors—a manifestation of prethermalization—while all other observables are not. Even the most stable observable though deteriorates in the thermodynamic limit. Different than in classical systems with the strongest chaos, where the faithfulness time (the shadowing time) can be infinite, in quantum many-body chaotic systems it is finite. A corollary of our results is also that, opposite of previous claims, there is no Trotterization transition in nonintegrable many-body quantum systems. We demonstrate our results on a one-dimensional (1D) kicked Ising model, as well as on a 1D kicked XX model and a 2D kicked Ising model. The truncated propagator is also used to calculate the energy diffusion constant in the tilted-field Ising model with high accuracy.

Model order reduction encompasses mathematical techniques aimed at reducing the complexity of mathematical models in simulations while retaining the essential characteristics and behaviors of the original model. This is particularly useful in the context of large-scale dynamical systems, which can be computationally expensive to analyze and simulate. Here, we present a model order reduction technique to reduce the time complexity of open quantum systems, grounded in the principle of measurement-adapted coarse graining. This method, governed by a coarse-graining timescale $\tau$ and the spectral band center ${\omega }_0$ of the measurement channel, organizes corrections to the lowest-order model which aligns with the rotating-wave approximation Hamiltonian in certain limits and rigorously justifies the resulting effective quantum master equation (EQME). The focus on calculating to a high degree of accuracy what can only be resolved by the measurement introduces a principled regularization procedure to address singularities and generates low-stiffness models suitable for efficient long-time integration. The closed-form EQME parameters greatly enhance interpretability, while the predicted EQME structure provides a foundation for deriving stochastic master equations under continuous measurement and for constructing efficient gray-box models for system identification and control. As a demonstration, we derive the fourth-order EQME for a challenging problem related to the dynamics of a superconducting qubit under high-power dispersive readout in the presence of a continuum of dissipative waveguide modes. This derivation shows that the lowest-order terms align with previous results, while higher-order corrections suggest new phenomena.

The preparation of high-fidelity non-Clifford (magic) states is an essential subroutine for universal quantum computation but imposes substantial space-time overhead. Magic-state factories based on high-rate and -distance quantum low-density parity-check (LDPC) codes equipped with transversal non-Clifford gates can potentially reduce these overheads significantly, by circumventing the need for multiple rounds of distillation and by producing a large number of magic states in a single code block. As a step toward realizing efficient, fault-tolerant magic-state production, we introduce a class of finite block-length quantum LDPC codes which we name tricycle codes, generalizing the well-known bicycle codes to three homological dimensions. These codes can support constant-depth physical circuits that implement logical $CCZ$ gates between three code blocks. To construct these constant-depth $CCZ$ circuits, we develop analytical and numerical techniques that apply to a broad class of three-dimensional homological and balanced-product codes. We further show that tricycle codes enable single-shot state preparation and error correction, leading to a highly efficient magic-state generation protocol. Numerical simulations of specific codes confirm robust performance under circuit-level noise, demonstrating a high circuit-noise threshold of $>0.5\%$. With modest postselection, certain tricycle codes of block lengths of only approximately 50–100 qubits are shown to produce $|\overline{CCZ}⟩$ magic states with logical error rates ranging from $2\times {10}^{-8}$ to below $3\times {10}^{-11}$. Finally, we construct optimal depth syndrome extraction circuits for tricycle codes and present a protocol for implementing them efficiently on a reconfigurable neutral-atom platform.

Nonlinear phenomena underpin a broad array of technologies, from electronic frequency mixers and harmonic generation to parametric amplification and optical frequency doubling. Conventional schemes for generating microwave frequency combs are constrained by intrinsic material or junction properties that require high driving powers. Here, we overcome these limitations via phase-transition physics. We show that a hybrid quantum system—composed of a solid-state spin ensemble and a nonlinear oscillator—exhibits a distinct bistable phase transition point (BP) where system response becomes both highly enhanced and nonlinear. The nonlinearity around the BP is higher order than other phase transitions, such as exceptional points, critically producing high-order frequency response which enhances nonlinear processes. Approaching the BP, we demonstrate a frequency comb with a record number of teeth at unprecedentedly low driving powers, surpassing previous results using magnonic systems and traditional diode-based approaches. These findings highlight the potential of hybrid quantum systems in advancing high-performance frequency manipulation.