Stability achieved by large angular momentum is ubiquitous in nature, with examples ranging from classical mechanics, over optics and chemistry, to nuclear physics. In atoms, angular momentum can protect excited electronic orbitals from decay due to selection rules. This manifests spectacularly in highly excited Rydberg states. Low angular momentum Rydberg states are at the heart of recent breakthroughs in quantum computing, simulation and sensing with neutral atoms. For these applications the lifetime of the Rydberg levels sets fundamental limits for gate fidelities, coherence times, or spectroscopic precision. The quest for longer Rydberg state lifetimes has motivated the generation, coherent control and trapping of circular Rydberg atoms, which are characterized by the maximally allowed electron orbital momentum and were key to Nobel prize-winning experiments with single atoms and photons. Here, we report the observation of individually trapped circular Rydberg atoms with lifetimes of more than 10 milliseconds, two orders of magnitude longer-lived than the established low angular momentum orbitals. This is achieved via Purcell suppression of blackbody modes at room temperature. We coherently control individual circular Rydberg levels at so far elusive principal quantum numbers of up to $n=103$, and observe tweezer trapping of the Rydberg atoms on the few hundred millisecond scale. Our results pave the way for quantum information processing and sensing utilizing the combination of extreme lifetimes and giant Rydberg blockade.

This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the Lindblad equation, its unraveling in terms of pure-state trajectories, the structure of steady states with emphasis on the role of symmetry and conservation laws, and a sampling of the novel physical phenomena that arise from nonunitary dynamics (dissipation and measurements). This is far from a comprehensive summary of the field. Rather, the objective is to provide a conceptual foundation and physically illuminating examples that are useful to graduate students and researchers entering this subject. There are exercise problems and references for further reading throughout the notes.

Large language models are now integrated into many scientific workflows, accelerating data analysis, hypothesis generation, and design space exploration. In parallel with this growth, there is a growing need to carefully evaluate whether models accurately capture domain-specific knowledge and notation, since general-purpose benchmarks rarely reflect these requirements. This gap is especially clear in quantum science, which features non-intuitive phenomena and requires advanced mathematics. In this study, we introduce QuantumBench, a benchmark for the quantum domain that systematically examine how well LLMs understand and can be applied to this non-intuitive field. Using publicly available materials, we compiled approximately 800 questions with their answers spanning nine areas related to quantum science and organized them into an eight-option multiple-choice dataset. With this benchmark, we evaluate several existing LLMs and analyze their performance in the quantum domain, including sensitivity to changes in question format. QuantumBench is the first LLM evaluation dataset built for the quantum domain, and it is intended to guide the effective use of LLMs in quantum research.

Environmentally induced decoherence poses a fundamental challenge to quantum energy storage systems, causing irreversible energy dissipation and performance aging of quantum batteries (QBs). To address this issue, we propose a QB protocol utilizing the nonlocal coupling properties of giant atoms (GAs). In this architecture, both the QB and its charger are implemented as superconducting GAs with multiple nonlocal coupling points to a shared microwave waveguide. By engineering these atoms in a braided configuration, where their coupling paths are spatially interleaved, we show the emergence of decoherence-immune interaction dynamics. This unique geometry enables destructive interference between decoherence channels while preserving coherent energy transfer between the charger and the QB, thereby effectively suppressing the aging effects induced by waveguide-mediated dissipation. The charging properties of separated and nested coupled configurations are investigated. The results show that these two configurations underperform the braided configuration. Additionally, we propose a long-range chiral charging scheme that facilitates unidirectional energy transfer between the charger and the battery, with the capability to reverse the flow direction by modulating the applied magnetic flux. Our result provides guidelines for implementing a decoherence-resistant charging protocol and remote chiral QBs in circuits with GAs engineering.

Quantum computing is advancing rapidly, yet substantial gaps separate today's noisy intermediate-scale quantum (NISQ) devices from tomorrow's fault-tolerant application-scale quantum (FASQ) machines. We identify four related hurdles along the road ahead: (i) from error mitigation to active error detection and correction, (ii) from rudimentary error correction to scalable fault tolerance, (iii) from early heuristics to mature, verifiable algorithms, and (iv) from exploratory simulators to credible advantage in quantum simulation. Targeting these transitions will accelerate progress toward broadly useful quantum computing.

The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of financial derivatives-traditionally addressed through Monte Carlo integration techniques. In this work, we introduce two hybrid classical-quantum methods to address the option pricing problem. These approaches rely on reconstructing Fourier series representations of statistical distributions from the outputs of Quantum Machine Learning (QML) models based on Parametrized Quantum Circuits (PQCs). We analyze the impact of data size and PQC dimensionality on performance. Quantum Accelerated Monte Carlo (QAMC) is employed as a benchmark to quantitatively assess the proposed models in terms of computational cost and accuracy in the extraction of Fourier coefficients. Through the numerical experiments, we show that the proposed methods achieve remarkable accuracy, becoming a competitive quantum alternative for derivatives valuation.

A spin-polarized muon implanted into a fluoride forms a coupled F--$\mu$--F complex in which the muon spin and neighbouring fluorine nuclear spins become entangled. Here we apply radio-frequency (RF) excitation to this coupled system and use the three-dimensional distribution of emitted positrons to reconstruct the time-dependent evolution of the muon spin polarization. This three-dimensional readout, using single spin detection, is not possible in a single NMR experiment and demonstrates significant advantages that are achieved by using RF muon techniques. We demonstrate the application of this vector-readout method to the experimental observation of a muon spin echo signal that is controlled by the dipolar coupling to fluorine, as well as to a double resonance experiment, in which we use pulses tuned to separate frequencies to address both the muon and fluorine spins. This targeted approach, in which selective RF pulses can control the muon spin and other spins to which it is coupled, provides a novel route for probing systems of entangled spins.

We rebut a recent paper that claims that classical gravity can entangle two massive superpositions by local means. We refute the misconceptions appearing in this paper and confirm that the quantum features are necessary in the gravitational field if it can lead to entanglement by local propagation between distant masses.

As quantum computers scale toward millions of physical qubits, it becomes essential to robustly encode individual logical qubits to ensure fault tolerance under realistic noise. A high-quality foundational encoding allows future compilation techniques and heuristics to build on optimal or near-optimal layouts, improving scalability and error resilience. In this work, we synthesize a one-dimensional shuttling bus architecture for the rotated surface code, leveraging coherent spin-qubit shuttling. We formulate a mixed-integer optimization model that yields optimal solutions with relatively low execution time for small code distances, and propose a scalable heuristic that matches optimal results while maintaining linear computational complexity. We evaluate the synthesized architecture using architectural metrics, such as shuttling distance and cycle time, and full quantum simulations under realistic noise models, showing that the proposed design can sustain logical error rates as low as $2\cdot 10^{-10}$ per round at code distance 21, showcasing its feasibility for scalable quantum error correction in spin-based quantum processors.

$W$ states are quantum correlated states possessing both bipartite and multipartite entanglement, which makes them useful for several quantum algorithms. We propose a protocol to generate these states by exploiting {\it topological ring frustration}, and implement it on a programmable Rydberg atom array up to 11 qubits, successfully generating many-body $W$ states of Rubidium atoms. Numerical simulations show promising scaling of the algorithm to tens of qubits with near-term achievable updates on the quantum machines. To validate our state preparation protocol and probe quantum entanglement, we devise a fidelity estimator that requires only two sets of measurements. To implement it, we develop a novel and efficient Bayesian state-tomography approach that takes advantage of accurate classical numerical simulations to overcome limitations in the experimental setup. Hence, a lower bound fidelity of around $77\%$ is certified for the experimentally prepared state of 11 qubits. This work provides a state-of-the-art procedure to generate high-quality quantum entangled $W$ states, demonstrating once more how principles of physics can overcome traditional barriers of computation, and be exploited for quantum advantage.

We introduce local information flows as a diagnostic tool for characterizing out-of-equilibrium quantum dynamics in lattice gauge theories. We employ the information lattice framework, a local decomposition of total information into spatial- and scale-resolved contributions, to characterize the propagation and buildup of quantum correlations in real-time processes. Focusing on the Schwinger model, a canonical $(1+1)$-dimensional U(1) lattice gauge theory, we apply this framework to two scenarios. First, in the near-threshold scattering of two vector mesons, we demonstrate that the emergence of correlations at a longer length scale in the information lattice marks the production of heavier scalar mesons. Second, in the dynamics of electric field strings, we clearly distinguish between the confining regime, which evolves towards a steady state with a static correlation profile, and the string-breaking sector. The latter is characterized by dynamic correlation patterns that reflect the sequential formation and annihilation of strings. This information-centric approach provides a direct, quantitative, and interpretable visualization of complex many-body phenomena, offering a promising tool for analyzing dynamics in higher-dimensional gauge theories and experiments on quantum hardware.

Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that defines the phases. In this work we adopt unsupervised learning, where the algorithm has no access to any priorly labeled states, as a tool for determining quantum phase diagrams of many-body systems. The algorithm directly works with quantum states: given the ground-state configurations for different values of the Hamiltonian parameters, the process uncovers the most significant way of grouping them based on a similarity criterion that refers to the fidelity between quantum states, that can be easily estimated, even experimentally. We benchmark our method with two specific spin-$\frac{1}{2}$ chains, with states determined via tensor network techniques. We find that unsupervised learning algorithms based on spectral clustering, combined with ``silhouette'' and ``elbow'' methods for determining the optimal number of phases, can accurately reproduce the phase diagrams. Our results show how unsupervised learning can autonomously recognize and possibly unveil novel phases of quantum matter.

We study the collective emission of a disordered array of $N$ excited two-level atoms into a one-dimensional photonic waveguide. In the perfectly ordered case, where atoms are spaced by exact integer multiples of the wavelength, the system exhibits the characteristic superradiant burst with a peak emission rate scaling as $N^2$. Using large-scale semiclassical simulations, we find that this key signature of superradiance remains asymptotically robust under strong spatial and spectral disorder, but also exhibits subtle finite-size scaling toward this limit. To explain our observations, we provide an analytical variational estimate for the maximal decay rate, which tightly bounds the numerical results and reveals how disorder shapes the collective decay. Specifically, we find that even in the presence of strong disorder, the spins tend to self-organize spontaneously according to their locations, which overall optimizes constructive interference effects and explains the emergence of mirror-asymmetric correlations in superradiant decay. These findings resolve important open questions regarding the existence and nature of superradiance in strongly disordered arrays and offer valuable insights for understanding collective quantum optical phenomena in realistic systems.