The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann's complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in Large Language Models (LLMs) requires a functional analogue: introspection – the system's capacity to simulate its own operations and target modifications. Grounded in Kleene's Second Recursion Theorem, we demonstrate the theoretical existence of such introspective programs. However, an empirical review reveals that while current LLMs exhibit quasi-introspection (e.g., partial metacognition), they fall short of true introspection due to structural bottlenecks: a lack of complete self-access, the feedforward nature of the Transformer, and computational class constraints that prevent fixed-point iteration. We conclude by outlining architectural paths to cross this complexity threshold and discussing the associated safety implications.

Quantum simulation promises to advance materials discovery by accurately simulating complex states of matter, their microscopic excitations, and macroscopic response functions. The central challenge in resolving the underlying interacting dynamics is to combine high-fidelity evolution with the sophisticated control necessary to manipulate individual quasi-particles in quantum many-body states. Here, we report on high-precision simulation of both linear and non-linear response functions in a 2D XY spin-1/2 magnet using an analog-digital superconducting processor of up to 97 qubits. By interleaving digital gates with analog evolution precisely characterized via Hamiltonian learning, we selectively excite magnons at tunable energy densities. Measuring first the linear magnon response – a central probe in neutron-scattering experiments – we extract temperature-dependent spectra and lifetimes. Our results reveal stark variations in magnon decay rates across the Brillouin zone, with enhancement near van Hove singularities and suppression for edge-localized modes. Next, we perform a suite of nonlinear measurements, including the study of self-scattering mechanisms, as well as pump-probe spectroscopy to directly characterize the magnon interactions. While matrix-product state simulations capture the dynamics well in either small systems or at low temperatures, their predictions become inaccurate away from these limits. This work demonstrates precise simulation of the interacting dynamics in quantum magnets, and provides key insights into quasi-particles and their microscopic scattering mechanisms.

The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann’s complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in large language models (LLMs) requires a functional analogue: introspection—the system’s capacity to simulate its own operations and target modifications. Grounded in Kleene’s Second Recursion Theorem, we construct such introspective self-improvement programs and prove their key properties: completeness of self-modification, necessity of the reflective architecture, undecidability of improvement in general, and equivalence with Schmidhuber’s Gödel machine under a rewrite-equivalence notion, which transfers the global optimality guarantee. An empirical review, organized around these functional criteria, suggests that current LLMs exhibit only quasi-introspection.The available evidence does not establish complete introspection in the formal sense developed here, while pointing to several candidate structural bottlenecks, including incomplete self-access, feedforward processing, and limited computational depth. We outline architectural paths toward the threshold and discuss the safety implications of crossing it.

Due to the complex interaction between varied pollutant emission sources and atmospheric circulation patterns, achieving reliable air quality prediction poses a formidable challenge. Consequently, the changes in PM2.5 and O3 pollution under future climate change scenarios remain largely unknown, particularly in regions that are frequently affected by severe air pollution, such as the Northern China urban agglomeration (NCUA). Here we developed an Integrated Graph Neural Network (IGNN) model that, trained by historical meteorological and emission data, is able to predict future PM2.5 and O3 concentrations over the NCUA. The IGNN model contains nodes and edges, with historical station observations being the graphical nodes, while spatiotemporal features of air quality variables, meteorological properties and emission information are defined as attributes of the nodes and edges. The results demonstrate that the IGNN model effectively captures the variability of historical PM2.5 and O3, outperforming other state-of-the-art methods in accurately predicting air quality variability. In high carbon emission scenario with varying air pollutant strategies, all IGNN model simulations show a significant decrease of average concentration of PM2.5 (the rate of decline ranges from-0.14 to-0.37 mu g m(-3 )year-1, p < 0.05), Conversely, there is a significant increase in average concentration of O3 (+0.07 to +0.22 mu g m(-3 )year(-1), p < 0.05). Our findings highlight the risk posed by elevated O-3 pollution levels under high carbon emission scenarios in the NCUA. This underscores the critical necessity for a coordinated approach that integrates air quality control with climate change mitigation efforts.

Predicting company growth is a critical yet challenging task because observed dynamics blend an underlying structural growth with volatile fluctuations. Here, we propose a Scaling-Theory-Informed Machine Learning framework (STIML) that integrates a scaling-based model that predicts the mechanism-driven average growth, together with a data-driven forecasting model to learn the residual fluctuations. Using Compustat data of 31,553 North American companies, we extend the growth model to multiple financial indicators, and evaluate STIML against growth model-only and purely data-driven baselines. Across 16 target variables, we show that company growth can be decomposed into trend-driven and fluctuation-driven predictability, whose relative importance varies strongly with company size, while the trend component remains robust across different levels of volatility. Interpretability analyses further show that STIML captures multivariate dependencies beyond autocorrelation, and that macroeconomic variables contribute significantly less to predictive performance on average. Moreover, we find the scaling-based growth model overlooks asymmetric deviations, which instead contain the structured and learnable signals, suggesting a path to refine mechanistic growth models.

In quantum information processing, the development of fast and robust control schemes remains a central challenge. Although quantum adiabatic evolution is inherently robust against control errors, it typically demands long evolution times. In this work, we propose to achieve rapid adiabatic evolution, in which nonadiabatic transitions induced by fast changes in the system Hamiltonian are mitigated by flipping the nonadiabatic transition matrix using π pulses. This enables a faster realization of adiabatic evolution while preserving its robustness. We demonstrate the effectiveness of our scheme in both two-level and three-level systems. Numerical simulations show that, for the same evolution duration, our scheme achieves higher fidelity and significantly suppresses nonadiabatic transitions compared to the traditional STIRAP protocol.

The Anthropocene mode of development is driving civilization toward a "singularity crisis": artificial intelligence (AI) is rapidly approaching general intelligence (AGI) with escalating risks of losing control, while unrestrained economic growth generates super-exponential growth of entropy production that pushes the Earth system toward its tipping points. This paper proposes the "Save 2050" initiative: a distributed planetary-scale collective prediction system that aggregates judgments about the future from humans and AI through open registration, crowdsourcing, and incentive mechanisms, and integrates them via large-scale simulation into inspectable "predicted worlds," enabling humanity to systematically see the future for the first time. We argue for the initiative's feasibility along four dimensions—the maturation of AI forecasting, human collective intelligence and the institutional environment, supporting progress in related fields, and societal demand. We then identify three key enabling technologies: long-horizon automated resolution, simulation-based prediction aggregation, and reflexivity governance. We analyze potential risks—including reflexivity, cognitive monoculture, narrative capture, and regulatory and ethical concerns—together with mitigation strategies, and we outline a phased roadmap with open problems. The initiative's primary goal is not to intervene in the future, but to make the future visible, discussable, and co-writable.

Disorder-induced phenomena in quantum many-body systems pose significant challenges for analytical methods and numerical simulations at relevant time and system scales. To reduce the cost of disorder-sampling, we investigate quantum circuits initialized in states tunable to superpositions over all disorder configurations. In a translationally-invariant lattice gauge theory (LGT), these states can be interpreted as a superposition over gauge sectors. We observe localization in this LGT in the absence of disorder in one and two dimensions: perturbations fail to diffuse despite fully disorder-free evolution and initial states. However, Rényi entropy measurements reveal that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a longstanding challenge in many-body localization studies.

Quantum error correction (QEC) is the primary strategy for protecting a quantum computer from the environment1,2. The prerequisite of QEC is that errors must remain sufficiently rare, which requires perpetually adapting the control parameters of the computer to the drifting environmental conditions. The current solution to this problem is to terminate the entire quantum computation for recalibration, but it is incompatible with the long runtimes of future quantum algorithms3,4. Here we address this challenge by unifying calibration with computation. We grant the QEC process5-11 a dual role: its error-detection events are not only used to correct the logical quantum state but are also repurposed as a learning signal, teaching a reinforcement learning agent12-16 to continuously steer the control parameters and stabilize the quantum system during computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, we achieve record performance of the surface and colour codes, with average logical error per cycle of 7.72(9) × 10-4 and 8.19(14) × 10-3, respectively. Numerical simulations of large codes with tens of thousands of control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of system size. This work thus enables a new paradigm: a quantum computer that learns from its errors and never stops computing.

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.

Holonomic quantum computation (HQC) offers an inherently robust approach to quantum gate implementation by exploiting quantum holonomies. While adiabatic HQC benefits from robustness against certain control errors, its long runtime limits practical utility due to increased exposure to environmental noise. Nonadiabatic HQC addresses this issue by enabling faster gate operations but compromises robustness. In this work, we propose a scheme for fast holonomic quantum gates based on the π-pulse method, which accelerates adiabatic evolution while preserving its robustness. By guiding the system Hamiltonian along geodesic paths in the parameter space and applying phase-modulating π pulses at discrete points, we realize a universal set of holonomic gates beyond the conventional adiabatic limit. Our scheme allows for arbitrary single-qubit and two-qubit controlled gates within a single-loop evolution and provides additional tunable parameters for flexible gate design. These results demonstrate a promising path toward high-fidelity, fast, and robust quantum computation.

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble-Zurek scaling predictions3 in the XY model, as well as signatures of the classical Kosterlitz-Thouless phase transition4. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis5-7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

The state hidden subgroup problem (StateHSP) is a recent generalization of the hidden subgroup problem. We present an algorithm that solves the non-abelian StateHSP over N copies of the dihedral group of order 8 (the symmetries of a square). This algorithm is of interest for learning non-Pauli stabilizers, as well as related symmetries relevant for the problem of Hamiltonian spectroscopy. Our algorithm is polynomial in the number of samples and computational time, and requires only constant depth circuits. This result extends previous work on the abelian StateHSP and, as a special case, provides a solution for the ordinary hidden subgroup problem on this specific non-abelian group.

The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen–Specker–Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

Most existing Knowledge Base Question Answering methods focus primarily on retrieving factual information, leaving more complex, analysis-driven tasks relatively unexplored. However, real-world queries often involve graph-based computations such as degree calculation or community detection, which require more advanced reasoning. In this paper, we introduce LLM4GraphAna, a Large Language Model-based approach designed to handle these challenging, analysis-focused queries within the KBQA framework. By integrating Function Orchestration and Parameterization, LLM4GraphAna can invoke our well-defined functions to perform graph analytics. Experimental results demonstrate that our method significantly improves performance on analysis-intensive questions.

Demonstrating that logical qubits outperform their physical counterparts is a milestone for achieving reliable quantum computation. Here, we propose to protect logical qubits with a novel dynamical decoupling scheme that implements iSWAP gates on nearest-neighbor physical qubits, and experimentally demonstrate the scheme on superconducting transmon qubits. In our scheme, each logical qubit only requires two physical qubits. A universal set of quantum gates on the logical qubits can be achieved such that each logical gate comprises only one or two physical gates. Our experiments reveal that the coherence time of a logical qubit is extended by up to 366% when compared to the better-performing physical qubit. Moreover, to the best of our knowledge, we demonstrate for the first time that multiple logical qubits outperform their physical counterparts in superconducting qubits. We illustrate a set of universal gates through a logical Ramsey experiment and the creation of a logical Bell state. Given its scalable nature, our scheme holds promise as a component for future reliable quantum computation.

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC^(2). In contrast to dynamics without time reversal, OTOC^(2) are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC^(2) values. This indicates that OTOC^(2) is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC^(2) with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC^(2) measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC^(2), our results indicate a viable path to practical quantum advantage.

Consciousness spans macroscopic experience and microscopic neuronal activity, yet linking these scales remains challenging. Prevailing theories, such as Integrated Information Theory, focus on a single scale, overlooking how causal power and its dynamics unfold across scales. Progress is constrained by scarce cross-scale data and difficulties in quantifying multiscale causality and dynamics. Here, we present a machine learning framework that infers multiscale causal variables and their dynamics from near-cellular-resolution calcium imaging in the mouse dorsal cortex. At lower levels, variables primarily aggregate input-driven information, whereas at higher levels they realize causality through metastable or saddle-point dynamics during wakefulness, collapsing into localized, stochastic dynamics under anesthesia. A one-dimensional top-level conscious variable captures the majority of causal power, yet variables across other scales also contribute substantially, giving rise to high emergent complexity in the conscious state. Together, these findings provide a multiscale causal framework that links neural activity to conscious states.

The promise of fault-tolerant quantum computing is challenged by environmental drift that relentlessly degrades the quality of quantum operations. The contemporary solution, halting the entire quantum computation for recalibration, is unsustainable for the long runtimes of the future algorithms. We address this challenge by unifying calibration with computation, granting the quantum error correction process a dual role: its error detection events are not only used to correct the logical quantum state, but are also repurposed as a learning signal, teaching a reinforcement learning (RL) agent to continuously steer the physical control parameters and stabilize the quantum system during the computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, including RL fine-tuning of the entire system and near-optimal decoding, we achieve record performance of the surface and color codes, with average logical error per cycle of ε_L=7.72(9)×10^-4 and ε_L=8.19(14)×10^-3 respectively. Simulations of surface codes up to distance-15 with tens of thousands control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of the system size. This work thus enables a new paradigm: a quantum computer that learns from its errors and never stops computing.

In connectivist learning environments, understanding the diverse interaction patterns of learners is essential for the effective design and implementation of online learning strategies. While traditional research has primarily focused on network analysis of peer-to-peer interactions, this study expands the scope by incorporating the often-overlooked yet pedagogically significant interactions that occur through content. By leveraging the open and flow network model of collective attention, the study offers a more robust and stable framework for understanding learner engagement, particularly in contexts where individual activity varies or learners disengage, which typically disrupts the structure of social networks. Using a cMOOC as a case study, the research identifies five distinct learner profiles: “Browsers”, “Likers”, “All-rounders”, “Commenters”, and “Sharers”, each exhibiting unique engagement patterns with resources such as Weekly Reports, Blogs, Materials, Cases, Forum Posts, Events, and the Problem-solving Hub. The prominence of “Browsers” as legitimate peripheral participants challenges the conventional assumption that active social interaction is essential for connectivist learning. Furthermore, the variations in attention dynamics across different learning resources suggest that a one-size-fits-all approach to course design is inadequate, as it fails to accommodate the diverse engagement patterns and needs of learners. Instead, this study advocates for a more nuanced approach to course design, one that integrates both social interactions and interactive content, thereby catering to a broader spectrum of learning preferences and optimizing engagement across the learner population.