We present a general framework for extracting conformal data from critical two-dimensional classical lattice models using finite-size tensor-network flow. The central idea is to identify, from transfer-matrix spectra, a self-consistent finite-size window together with a crossover scale that separates the finite-size-scaling regime from the finite-entanglement-scaling regime induced by bond-dimension truncation. Within this window, the central charge, scaling dimensions, and conformal spins can be estimated without requiring a unique critical fixed-point tensor or detailed prior knowledge of the underlying conformal field theory. We benchmark the framework using three tensor-network renormalization schemes for the critical two-dimensional Ising and three-state clock models. Across schemes, we find robust universal behavior below the crossover scale, enabling accurate extraction of conformal data up to relatively high conformal levels. The analysis also yields a natural operational definition of entanglement scaling for classical tensor-network calculations and, in turn, a complementary estimator of the central charge.

We propose and implement a quantum-informed reduction algorithm for the maximum independent set problem that integrates classical kernelization techniques with information extracted from quantum devices. Our larger framework consists of dedicated application, algorithm, and hardware layers, and easily generalizes to the maximum weight independent set problem. In this hybrid quantum-classical framework, which we call qReduMIS, the quantum computer is used as a coprocessor to inform classical reduction logic about frozen vertices that are likely (or unlikely) to be in large independent sets, thereby opening up the reduction space after removal of targeted subgraphs. We systematically assess the performance of qReduMIS based on experiments with up to 231 qubits run on Rydberg quantum hardware available through Amazon Braket. Our experiments show that qReduMIS can help address fundamental performance limitations faced by a broad set of (quantum) solvers including Rydberg quantum devices. We outline implementations of qReduMIS with alternative platforms, such as superconducting qubits or trapped ions, and we discuss potential future extensions.

Recent advances in time-resolved cathodoluminescence have enabled ultrafast studies of single emitters in quantum materials with femtosecond temporal resolution. Here, we develop a quantum theory modeling the dynamics of free electrons interacting with quantum emitters in arbitrary initial states. Our analysis reveals that a free electron can induce transient coherent oscillations in the populations when the system is initially prepared in a coherent superposition of its states. Moreover, the electron energy spectrum exhibits a clear signature of the quantum coherence and sensitivity to the transition frequency of the emitter. These coherence effects manifest themselves as oscillations in the zero-loss peak of the spectral energy loss probability. Our findings pave the way for characterization of quantum-coherent dynamics of individual quantum emitters by electron probes.

We report time-resolved x-ray diffraction measurements of lead (Pb) subjected to laser-driven shock compression up to the melt on nanosecond timescales. Along its Hugoniot, Pb exhibits a sequence of structural transitions markedly different from those observed under static compression. The conventional fcc-to-hcp transition is suppressed. Instead, the stacking fault probability in the fcc phase increases with compression up to $\sim 20\mathrm{GPa}$, and the high-pressure bcc phase appears at 27 GPa, i.e., $\sim 60\mathrm{GPa}$ below the static hcp-bcc boundary at the same temperature. At 45.4 ($\pm 2.1$) GPa and a calculated temperature of 2695 K, partial melting is evidenced by diffuse scattering, in excellent agreement with previous diamond anvil cell (DAC) melting data. Our results demonstrate that the dynamical response of Pb involves a distinct solid-state pathway, likely associated with stacking faults probability increase. These findings highlight the need to revisit phase diagrams under shock compression, particularly when coupled with time-resolved in situ microscopic diagnostics.

To date, the laser cooling of rubidium atoms has inevitably relied on 780 nm cooling light corresponding to the first excited state $5{\mathrm{P}}_{3/2}$. Here, we demonstrate diffuse laser cooling of ${}^{87}\mathrm{Rb}$ atoms using the 420 nm $5{\mathrm{S}}_{1/2}\to 6{\mathrm{P}}_{3/2}$ transition without a preceding 780 nm cooling stage. A high-power $420\mathrm{nm}$ laser is used as the cooling light to produce cold atoms in a 1-m-long diffuse-cooling cell. Absorption spectroscopy yields a cold-atom density of approximately $1.4\times {10}^{11}{\mathrm{m}}^{-3}$. We compare the cooling performance of the 420 nm and conventional 780 nm diffuse-cooling schemes and verify the feasibility of using the high-excited-state transition as an independent cooling channel in this large-volume diffuse-cooling system. This approach provides an alternative cooling/pumping pathway for continuous cold-atom active optical clocks, where compatibility with the clock-lasing process and reduced cooling-light-induced perturbations are important. It is also expected to open up research directions and application prospects in frontier fields such as Rydberg atoms, quantum information, and so on.

The Lieb-Robinson correlation function can be used to characterize the propagation of quantum information in Ising chains. Considerable work has been done to establish bounds on this correlation function in various circumstances. To actually calculate the value of the correlation function directly typically requires a state space that grows exponentially with system size, and so is intractable for all but relatively small systems. We employ a recently developed method that enables direct calculation of the Lieb-Robinson correlation function and that scales linearly with system size. This enables the computation for systems with more than a thousand qubits, revealing the propagation of quantum information down the chain. We extend this technique to the problem of Ising chains with randomly disordered coupling strengths. Increasing disorder causes localization of the quantum correlations and halts propagation of quantum information down the chain. We see light-cone isocontours therefore becoming vertical. The decay of correlations down the chain is characterized by a correlation length that in the paramagnetic phase increases quadratically with mean coupling strength and inverse quadratically with disorder level. The correlation length peaks at the phase transition. We map our general expression for the correlation function in the Ising system onto the probability density in the single-particle tight-binding Su-Schrieffer-Heeger model for a specific initial condition.

For the BCS theory of superconductivity, the electron-phonon interaction is transformed to an attractive electron-electron interaction in the vicinity of the Fermi energy only. At the same time, its formal derivation using a unitary transformation reveals that the electrons attract one another whenever their energies do not differ by more than the phonon energy ${\omega }_{\mathrm{D}}$, independent of closeness to the Fermi energy. Consequently, the order parameter becomes finite even away from the Fermi level. Yet, for small interactions, its magnitude is usually small and can be safely ignored, justifying the BCS approximation. Intriguingly, we find that an accumulation of density of states at an energy ${\varepsilon }_{\mathrm{peak}}$ in proximity to the Fermi energy induces a significant order parameter magnitude around ${\varepsilon }_{\mathrm{peak}}$, which exceeds the one at $E_{\mathrm{F}}$ for moderate coupling strengths. This strong enhancement is heralded by the softening of an additional collective mode, which resembles a second phase transition. We predict measurable signatures in the thermodynamic and spectroscopic responses to this unexpected phenomenon, guiding future experimental searches for it. Finally, we demonstrate that these signatures remain robust upon including a phenomenological Coulomb repulsion, indicating that the enhancement is not an artifact of the idealized model.

Resolving the ultrafast decay of metastable electronic states into channels associated with spin-orbit-split ionization thresholds is a long-standing goal of attosecond photoelectron spectroscopy. Here, we use a variant of the rainbow reconstruction of attosecond beating by interference of two-photon transitions technique to study, experimentally and theoretically, the ultrafast dynamics, resolved in photoelectron energy and emission angle, of the autoionizing states comprised in the narrow 177 meV energy gap between the $3p^{-1} {}^{2}P_{3/2}^o$ and ${}^{2}P_{1/2}^o$ thresholds in argon. The scheme employs three pulses: an XUV attosecond pulse train (pump), generated as odd harmonics of a fundamental IR frequency $\omega$; a weak replica of the IR field (driver) that copropagates phase-locked with the pump; and a second IR pulse (probe) with controllable delay $\tau$ with respect to the pump. Two harmonics excite bound states below the ${}^{2}P_{3/2}^o$ threshold and the continuum above the ${}^{2}P_{1/2}^o$ threshold, and their overlapping sideband populates even-parity resonant states between the two thresholds, giving rise to resonant signals beating at both $\omega$ and $2\omega$. From the photoemission cross section and the ${\beta }_2$ and ${\beta }_4$ asymmetry parameters, we resolve both the $nf$ and the $np$ resonant series. In both theory and experiment, the relative weight of the $\omega$ and $2\omega$ beatings changes significantly across the interthreshold gap, an evolution that we trace back to higher-order probe-photon processes. The resonant photoelectron emission is found to be strongly localized in small spots within the $({\beta }_2,{\beta }_4)$ region admissible for two-photon transitions.

We propose a method to measure the interaction between an ultracold gas of neutral atoms and a surface. This solution combines an optical dipole trap reflected by the surface, a magnetic trap formed by current carrying wires embedded below the surface, and a rotation of the surface itself. It allows to adiabatically transport a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate from few micrometers to few hundred nanometers of the surface. At such distances, atom-surface interaction strongly affects the trapping potential, causing an increase of the tunneling rate toward the surface. In this paper, we show that the measurement of the lifetime of the cloud and its comparison to a tunneling model will allow to extract the Casimir-Polder force coefficient in the retarded regime ($c_4$). Our model includes noise-induced heating, calibration biases of experimentally controlled parameters, and accuracy of the atom lifetime measurement. Using typical trapping parameters and experimental uncertainties, we numerically estimate the relative uncertainty of $c_4$ to be 10%. This method can be implemented with any atomic species that can be magnetically and optically trapped.

Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here, we establish a link between mixed unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions 3 and 4, and show how the method can detect non-mixed-unitary behavior based on incomplete channel tomography.

Data assimilation (DA) optimally fuses observational data with mathematical models, serving as a core computational framework for forecasting complex dynamical systems like the weather. Because manipulating large-scale high-rank error covariances is classically intractable, conventional DA is forced into severe structural compromises such as artificial localization or static parametrizations that destroy genuine cross-variable correlations. Future fault-tolerant quantum computing (FTQC) could offer transformative advantages to overcome these classical computational limits. While quantum linear system solvers theoretically provide exponential speedups for matrix inversion, the practical mapping of large-scale, uncompromised DA onto quantum architectures remains largely unexplored. Our framework builds upon two emerging technologies: FTQC hardware and efficient block-encoded oracles of the error covariance and observation operators, which we envision being supplied by future artificial intelligence surrogate models. Under this premise, we identify a potential bottleneck in the quantum implementation. We show that a direct mapping of the DA equations leads to a quadratic increase in the subnormalization factor ($\alpha$) associated with block encoding when typical nonlocal observations are utilized. To mitigate this algorithmic overhead, we propose a quantum-ready, combined state-observation space formulation. By reconfiguring the DA problem into an expanded saddle-point block-matrix system, our approach avoids the explicit multiplication of nonlocal observation operators. This maintains a linear scaling of $\alpha$ and confines the conditioning of the quantum solver to that of the observation error covariance, decoupled from the severely ill-conditioned prior. Numerical verification using the chaotic Lorenz-96 model demonstrates that our formulation achieves perfect fidelity with the uncompromised DA solution. Although reading out the full analysis state reduces the exponential speedup to a polynomial one, the framework retains a substantial advantage over the classical matrix inversion. This work bridges computational geosciences and quantum information science, providing the essential algorithmic foundation for large-scale DA to become a compelling application for FTQC.

Levitated nanoparticles are being investigated as ultrasensitive quantum sensors of forces and accelerations, with applications ranging from fundamental physics phenomena such as dark matter or quantum gravity to real-world applications. Attention is now turning to multiparticle regimes, and an important question is whether collective effects offer advantages for sensing. We investigate here the spectral characteristics of collective motion of $N$ trapped nanoparticles interacting via the optical mode of a cavity. We find that the collective motion typically exhibits two generic spectral features: a broad spectral feature, the collective bright mode (CBM), which has been previously studied, and a structure of sharp peaks, the mechanical mode comb (MMC). We can describe all the detailed spectral features of the system, with a simple closed-form expression, by reducing the motion to a one-dimensional generic collective mode, which is non-Hermitian. We show that the MMC is more advantageous than the usual CBM for increased sensitivity in force sensing. We find that the mechanical comb can autonomously repair loss of “teeth” due to particle loss, a feature that may offer robustness in sensing.

Molecules containing short-lived isotopes, namely, radioactive molecules, are among the most promising candidates for probing new physics beyond the standard model, although their production and spectroscopic measurements remain technically challenging. Here, we demonstrate an integrated methodology that combines the formation of molecular ion beams in a radio-frequency quadrupole cooler-buncher with collinear laser spectroscopy. As a proof-of-principle experiment, we successfully produce molecular ions ${\mathrm{BaF}}^{+}$ and ${\mathrm{YbF}}^{+}$ via in-trap ion-molecule reactions and perform high-resolution laser spectroscopy of the target molecule ${}^{138}\mathrm{BaF}$. Vibrational and rotational structures of ${}^{138}\mathrm{BaF}$ molecules across different electronic states are obtained using resonance-enhanced multiphoton ionization schemes, confirming the feasibility of the proposed methodology. This work establishes a practical route for future formation and spectroscopic studies of short-lived radioactive molecules, such as those containing ${}^{225}\mathrm{Ra}$, at radioactive ion beam facilities.

We characterize spectroscopic and coherence properties of the 1451.37 nm excited-state zero-phonon line (ZPL) between the ${}^3\mathrm{F}_4$ and the ${}^3\mathrm{H}_4$ manifolds of a thulium-doped yttrium aluminum perovskite (${\mathrm{Tm}}^{3+}:{\mathrm{YAlO}}_3$) crystal at temperatures around 1.5 K. We measure the absorption spectrum between ${}^3\mathrm{H}_6\text{−}{}^3\mathrm{F}_4$ and ${}^3\mathrm{F}_4\text{−}{}^3\mathrm{H}_4$ manifolds, the inhomogeneous broadening of the ${}^3\mathrm{F}_4\text{−}{}^3\mathrm{H}_4$ (excited-state) ZPL, and the lifetimes of the higher-lying and lower-lying excited states. We also investigate level shifts caused by the quadratic Zeeman interaction as well as spectral hole-burning spectra with varying magnetic fields, providing insights into hyperfine interactions. Using spectral holes again but also optical free induction decays, we assess optical coherence times, finding a maximum of $4.75\pm 0.07 \mu \mathrm{s}$ at $B$ = 2 T and low ion concentration in the ${}^3\mathrm{F}_4$ level. Our results—the first to demonstrate coherence of an excited-state transition in a rare-earth crystal—suggest the possibility of exploiting such transitions for quantum technology.

We experimentally demonstrate a nonlinear dependence of the spin-noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin-noise spectroscopy (SNS) near the ${\mathit{D}}_2$ transition of rubidium, a quadratic spin-noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in noninteracting ensembles. This nonlinear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross correlations due to resonant dipole-dipole interaction (ddi) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin-noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.

Block encoding of sparse matrices underpins quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear system solvers, yet its efficient gate-level realization remains challenging, with index-mapping oracles constituting one important source of overhead. We introduce a block-encoding framework that focuses on the index-mapping component, where coherent permutation is used as the central mechanism to optimize shift, delete, and insert operations. This provides a unified treatment of index mapping and reduces local multicontrolled X control complexity through structured compression. We further connect coherent amplitude permutation to combinatorial optimization, enabling systematic assignment of control states under hardware connectivity constraints. The resulting construction supports entrywise block encoding for general sparse matrices, with efficiency gains in structured cases. We demonstrate the approach on representative examples and provide resource analysis using IBM superconducting backends, showing significant reductions in circuit depth.

Nanoscale engineered spin systems, ranging from spins on surfaces to nanographenes, provide flexible platforms to realize entangled quantum magnets from a bottom-up approach. However, assessing the quantum many-body Hamiltonian realized in a specific experiment remains an exceptional open challenge, due to the difficulty of disentangling competing terms accounting for the many-body excitations. Here, we demonstrate a machine learning strategy to learn a quantum many-body spin Hamiltonian from scanning spectroscopy measurements of spin excitations. Our methodology leverages the spatially resolved reconstruction of the many-body excitations induced by depositing quantum impurities next to the quantum magnet. We demonstrate that our algorithm allows us to predict long-range Heisenberg exchange interactions, anisotropic exchange, and antisymmetric Dzyaloshinskii-Moriya interaction, including in the presence of sizable noise. Our methodology establishes defect-induced spatially resolved dynamical excitations in quantum magnets as a powerful strategy to understand the nature of quantum spin many-body models.