Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schrödinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type reformulation of isothermal compressible Navier-Stokes (NS) flow in Schrödinger-type amplitude variables. To our knowledge, this gives the first exact Cole-Hopf-type Schrödinger-variable reformulation of compressible NS flow. In two dimensions, a Helmholtz decomposition separates the velocity into compressive and vortical potentials, whose logarithmic transforms yield two scalar imaginary-time Schrödinger-type equations with nonlinear self-consistent potentials. We show that the mixed density-compressive amplitude ${\mathrm{\Psi }}_{\alpha }={\rho }^{\alpha }{\mathrm{\Theta }}^{1-2\alpha }$, where $\rho$ is the density, $\mathrm{\Theta }$ is the compressive amplitude, and $\alpha \ne 0,1/2$, satisfies a nonlinear Schrödinger-type equation with a vector-potential-coupled Laplacian. The transformed system is exactly equivalent to compressible NS and is nonlocal only through Helmholtz and Poisson projections. In three dimensions, the density-carrying equation retains the same vector-potential-coupled structure, while the solenoidal sector admits a compressible analog of Ohkitani’s [Phys. Rev. E 92, 033010 (2015)] incompressible NS Cole-Hopf formulation. Unlike unitary hydrodynamic Schrödinger-flow representations, the present equations are imaginary-time heat or drift-diffusion equations with self-consistent potentials, but they remain an exact change of variables for compressible NS. A two-dimensional Kelvin-Helmholtz shear-layer calculation verifies the transformed equations against a direct compressible NS simulation. The formulation exposes operator structures that may be useful for reduced flow descriptions, quantum algorithms for operator evolution, and quantum partial differential equation solvers.

Material defects give rise to parasitic two-level systems (TLS) that present a major source of decoherence in superconducting qubits. Here, we study a strongly coupled TLS that resides in the tunnel barrier of transmon qubit. We use multiphoton spectroscopy and TLS strain tuning to explore the rich spectrum of the interacting three-partite system consisting of TLS, qubit, and its readout resonator. This reveals a strong effective resonant coupling between the TLS and the qubit's readout resonator, which dresses the resonator states and results in a resonance frequency shift that spoils the readout signal. Our finding presents yet another way how material defects can interfere with qubit operation and hinder the realization of solid-state quantum processors.

Drawing inspiration from swarm intelligence, we show that short-range attractive interactions between thermally driven Brownian quasiparticles enable energy-efficient optimization. As quasiparticles can be generated directly within a material, the swarm size can be adjusted with minimal energy overhead. Using an optimization task defined by a spatially varying temperature landscape, we quantitatively show that interacting swarms reliably identify global optima and significantly outperform noninteracting searchers within a well-defined regime of interaction strength and swarm size. This improvement arises from emergent cooperative behavior, where local interactions guide the swarm toward high-quality solutions without central coordination. To link our physical model to experimental realizations, we coarse grain the quasiparticle dynamics onto a sensor lattice and generate trajectories emulating particle-tracking measurements. We further show that the interacting swarm adapts robustly to landscapes that evolve over time. These findings establish interacting Brownian quasiparticles as a physical platform for scalable and energy-efficient unconventional computing.

Code switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the $\left[\right[8,3,2\left]\right]$ code. One version supports weakly fault-tolerant single-qubit Clifford gates, while the other supports a logical $\overline{\mathrm{CCZ}}$ gate via transversal $T/T^{†}$ together with logical $\overline{\mathrm{CZ}}$, $\overline{\mathrm{CNOT}}$, and $\overline{\mathrm{SWAP}}$ gates. Because both codes have distance 2, the protocol operates in a postselected, error-detecting regime: Single faults lead to detectable outcomes, and accepted runs exhibit quadratic suppression of logical error rates. This yields a universal scheme for postselected fault-tolerant computation. We validate the protocol numerically through simulations of state preparation, interblock logical teleportation, code switching, and a three-logical-qubit implementation of Grover's search.

Quantum resource theories identify the features of quantum computers that provide their computational advantage over classical systems. We investigate the resources driving the complexity of classical simulation in the standard model of continuous-variable quantum computing, and their interplay enabling computational universality. Specifically, we uncover a new property in continuous-variable circuits, analogous to coherence in discrete-variable systems, termed symplectic coherence, defined as the ability of Gaussian gates to mix position and momentum operators. Using quadrature propagation across multiple computational paths, we develop an efficient classical simulation algorithm for continuous-variable computations with symplectic coherence constant in the size of the circuit. This establishes symplectic coherence as a necessary resource for universality in continuous-variable quantum computing, alongside non-Gaussianity and entanglement. Via the Gottesman-Kitaev-Preskill encoding, we show that the interplay of these three continuous-variable quantum resources mirrors the discrete-variable relationship between coherence, magic, and entanglement.

Feedback-based quantum algorithms (FQAs) operate by iteratively growing a quantum circuit to optimize a given task. At each step, feedback from qubit measurements is used to inform the next quantum circuit update. In practice, the sampling cost associated with these measurements can be significant. Here, we ask whether FQA parameter sequences can be predicted using classical machine learning, obviating the need for qubit measurements altogether. To this end, we train a teacher-student model to map problem instances to associated FQA parameter curves in a single classical inference step. We first study weighted MaxCut problem instances, where numerical experiments show that this machine learning model can accurately predict FQA parameter curves across a range of problem sizes, including sizes not seen during model training. We then extend the analysis to transverse-field Ising models on graphs and analyze how this learning strategy performs and generalizes beyond the original MaxCut setting. To evaluate performance, we compare the predicted parameter curves in simulation against FQA reference curves and linear quantum annealing schedules. We observe similar results to the former and performance improvements over the latter. These results suggest that machine learning can offer a heuristic, practical path to reducing sampling costs and resource overheads in quantum algorithms.

The Ti $L_{2,3}\text{−}\mathrm{edge}$ x-ray absorption spectra of various titanium oxides, including perovskite $\mathrm{SrTi}{\mathrm{O}}_3$, rutile and anatase $\mathrm{Ti}{\mathrm{O}}_2$, and ilmenite $\mathrm{CoTi}{\mathrm{O}}_3$, are analyzed with particular attention to the energy range beyond the near-edge/charge-transfer region and up to the oxygen $K$ edge. We found that the spectral structure varies among materials and can be described using density functional theory without including the multielectron effects indispensable for describing near-edge and charge-transfer structures. We term the structures in this energy range the middle-range-energy structure and show that the distinct features are determined by the local atomic geometry around the target Ti atoms and, essentially, by the partial density of states of those atoms. Here, we demonstrate how to extract information from middle-range-energy structures by comparing them with ab initio calculations, and we propose this energy-range analysis as a new method for studying local atomic geometry, free of parameters describing multielectron effects.

The increasing number of control lines connecting quantum processors to external electronics constitutes a major bottleneck in the realization of large-scale quantum computers. Frequency-division multiplexing is expected to enable control of multiple qubits through a single microwave cable; however, interference from off-resonant microwave tones hinders precise qubit control. Here, we propose an active interference suppression method for frequency-division-multiplexed simultaneous gates on microwave-controlled qubits. We demonstrate that the deliberate incorporation of off-resonant microwave tones improves single-qubit gate fidelity. In particular, the gate infidelity scales inversely with the square of the number of microwave tones when off-resonant orthogonal or quasi-orthogonal tones are incorporated. Furthermore, we show that fast oscillations, neglected under the rotating wave approximation, degrade the gate fidelity, and that this degradation can be mitigated through optimized frequency allocation. The proposed approach is simple and effective for improving the performance of frequency-division-multiplexed quantum gates.

We study the electronic structure and dynamical correlations in antiferromagnetic ${\mathrm{BiFeO}}_3$, a prototypical room-temperature multiferroic, using a variety of static and dynamical first-principles methods. Conventional static Hubbard corrections ($\mathrm{DFT}+U, \mathrm{DFT}+U+V$) incorrectly predict a deep-valence Fe $3d$ peak (around $-7\text{eV}$) in antiferromagnetic ${\mathrm{BiFeO}}_3$, in contradiction with hard x-ray photoemission. We resolve this failure by using a recent generalization of $\mathrm{DFT}+U$ to include a frequency-dependent screening—$\mathrm{DFT}+U\left(\omega \right)$—or using a dynamical Hubbard functional. The screened Coulomb interaction $U\left(\omega \right)$, computed with spin-polarized random-phase approximation and projected onto maximally localized Fe $3d$ Wannier orbitals, is expressed as a sum over poles, yielding a self-energy that augments the Kohn-Sham Hamiltonian. This $\mathrm{DFT}+U\left(\omega \right)$ approach predicts a fundamental band gap of $1.53\text{eV}$, consistent with experiments, and completely eliminates the unphysical deep-valence peak. The resulting simulated hard x-ray photoelectron spectroscopy spectrum reproduces the experimental line shape with an accuracy comparable to state-of-the-art approaches. Our work highlights the critical nature of dynamical screening in complex oxides and of $\mathrm{DFT}+U\left(\omega \right)$ as a predictive and computationally efficient approach to address the electronic structure of correlated materials.

Receptor-mediated ligand endocytosis underlies essential homeostatic functions and in signaling contexts it is often regarded as a mechanism for signal attenuation. Here, we show that ligand removal can paradoxically enhance directional information in autonomous cell-cell attraction. Many cell systems migrate toward one another in the absence of externally imposed gradients, implying that secretion, diffusion, and uptake must themselves generate usable directional cues. We develop a surface-resolved theory of a finite-sized detector exposed to a nearby source and derive analytical expressions for the steady-state ligand field. The resulting concentration profiles are governed by a single dimensionless Damköhler number that compares receptor-mediated endocytosis to diffusive ligand transport. Increasing ligand removal lowers extracellular ligand concentrations and reduces absolute concentration differences across the detector surface, but preferentially enhances relative surface anisotropy. Thus, destroying the signal can increase the usable information encoded in relative gradients. Incorporating nonlinear downstream processing reveals a trade-off between contrast enhancement and signal depletion, with the directional response greatest within a joint regime of endocytosis and downstream sensing that overlaps the measured range of receptor internalization rates. These results recast receptor-mediated endocytosis as an extracellular information-processing mechanism that reshapes the surrounding ligand gradient to enhance directional information.

We use spin dynamics simulations to determine the origin of the unusual correlated diffuse scattering, characterized by half-moon shapes bridging the magnetic Bragg peaks, observed in the polarized elastic neutron scattering from manganese tungstate, ${\mathrm{MnWO}}_4$. We first fit a Heisenberg Hamiltonian with 12 nearest-neighbor exchange interactions and single-ion anisotropy to the experimental ground-state magnon dispersion. We then show via spin dynamics simulations that our model Hamiltonian both reproduces the experimentally observed half-moon features and captures their persistence into the paramagnetic regime. Moreover, we identify the three-dimensional, competing antiferromagnetic interactions driving this behavior. Our work complements earlier studies of half-moon-shaped signatures in pyrochlore and triangular structures, by providing insight into their origin and showing that the half moons in ${\mathrm{MnWO}}_4$ result from three-dimensional competing exchange interactions, in the absence of the spin-liquid behavior with which they are usually associated.

Characterizing the temperature of materials in high-energy-density (HED) experiments is a major gap in the benchmarking of HED matter, such as matter in the deep interiors of planets and low-mass stars. Extended x-ray absorption fine structure (EXAFS) spectroscopy is one of the few techniques capable of determining temperature at HED conditions, but the inferred EXAFS temperature depends upon the atomic potential, which itself is not measured. This work compares simultaneous EXAFS and self-emission temperature measurements [S. Boccato et al., J. Geophys. Res.: Solid Earth, 122, 9921 (2017)], to quantify the impact of atomic potentials implicit in the EXAFS temperature analysis. Traditional EXAFS analysis employing a harmonic potential produces systematically lower temperatures than from self-emission ($\sim 35\%$ at 100 GPa and 3000 K), while a sixth-order distortion to the pair potential recovers agreement between the two measurements. These results highlight and quantify the need and complexity of distortions or anharmonic corrections to atomic potentials at HED conditions.

Multipartite quantum entanglement plays a crucial role in the emergence of quantum phases and their transitions in quantum many-body systems. It is of general interest to know what sort of analysis on quantum entanglement can bring us a profound insight to understand the rich dynamics of quantum many-body systems. In this work, we study the characteristics of quantum entanglement in relation to ${\mathbb{Z}}_n$-ordered phases emerging under a varied strength of one-dimensional Rydberg interaction via numerical investigation. We propose an approach based on the structure of pairwise entanglement across the Rydberg chain using two-qubit concurrence as an entanglement measure. We define an entanglement-structure factor via Fourier analysis of total concurrence at each site and address ${\mathbb{Z}}_n$ phase transitions in comparison with the conventional order parameter based on local density, i.e., magnetization. We also discuss how the required two-qubit concurrence can be measured in analog Rydberg atom arrays using site-selective erasure and parametrized laser pulses. Our numerical investigation suggests that an entanglement-structure-based approach can provide a powerful tool in analyzing symmetry breaking in quantum phase transitions.

We obtain an exact solution for the spectral function for one-dimensional Bose-Bose and Fermi-Fermi mixtures with strong repulsive interactions, valid in arbitrary confining potentials and at all frequency scales. For the case of harmonic confinement, we show that, on top of the ladder structure of the density excitations imposed by the external confinement, spin excitations emerge as sideband peaks, with dispersion related to the one of ferromagnetic or antiferromagnetic spin chains and a width fundamentally larger for fermionic mixtures than for bosonic ones, as determined by the different symmetry of spin-excited states. The observation of spin excitation branches can provide a univocal probe of interaction-induced magnetism in ultracold atoms.

We investigate proton acceleration in the relativistic transparency regime using ultrathin foils irradiated by petawatt-class laser pulses, achieving proton energies exceeding $80\mathrm{MeV}$. Shot-resolved analysis of transmitted spectra reveals that temporal gating at the onset of relativistically induced transparency shapes the pulse, producing either smooth or modulated spectra. A spectral smoothness metric, benchmarked against particle-in-cell simulations and a semianalytical gating model, demonstrates that different transmission levels correspond to distinct transparency onset times. We find that maximum proton energies are consistent with transparency occurring near the laser pulse peak, while later or absent onset can also drive efficient acceleration. These spectral diagnostics establish a powerful probe of acceleration cascades and a route to understanding and controlling shot-to-shot fluctuations in laser-ion interactions.

This article is part of a Physical Review Collection on the Physics of Changing Climate.

Tipping elements are large-scale components of the Earth system that may undergo abrupt and potentially irreversible transitions once critical thresholds are crossed. How these elements interact and coevolve under anthropogenic forcing remains poorly understood. Here, we introduce a Bayesian framework to quantify interdependence among tipping element regions based on lagged correlations, yielding a probabilistic measure of their connectivity that rigorously accounts for observational and sampling uncertainty. Using the preindustrial period as a baseline, we show that connectivity patterns among tipping elements are substantially weakened under high anthropogenic forcing, whereas the loss of coherence remains comparatively limited under low-forcing scenarios. This decorrelation is particularly pronounced in the Northern Hemisphere. We further identify the Atlantic meridional overturning circulation as a key contributor to the observed loss of connectivity, in line with recent evidence that it may be approaching a tipping point. In addition, we propose a simple toy model where tipping elements are seen as an adaptive dynamical system, losing coherence as a reaction to external perturbations. The results are robust across past decades and across different climate models, with deviations from the baseline strengthening into the future, especially under high-emission pathways.

We report the observation of the magnetic-field-induced $\left(5d^{10}6s^2\right){}^1\mathrm{S}_0\text{−}\left(5d^{10}6s6p\right){}^3\mathrm{P}_0$ transition in a bosonic isotope of mercury, ${}^{198}\mathrm{Hg}$, realized in an optical lattice clock. We characterize this ${}^{198}\mathrm{Hg}$ clock transition at 265.6 nm, determining key features such as the quadratic Zeeman shift, the probe light shift, and the magic frequency. We also report a comparison between the ${}^{198}\mathrm{Hg}$ optical lattice clock and ${}^{87}\mathrm{Sr}$. In this comparison, the ${}^{198}\mathrm{Hg}$ clock has a relative frequency stability of $6\times {10}^{-16}/\sqrt{\tau /\text{s}}$ and a total relative systematic uncertainty of $6.9\times {10}^{-16}$. This comparison yields the first direct determination of the ${}^{198}\mathrm{Hg}/{}^{87}\mathrm{Sr}$ optical frequency ratio: ${}^{198}\mathrm{Hg}/{}^{87}\mathrm{Sr}=2.6293157346841181$, with the same relative uncertainty.

In this article, we propose a squeezing-enhanced protocol for the efficient readout of bosonic qubits, whose encoding states can be first mapped onto a multilevel atom and then read out via dispersive coupling. We demonstrate that by simultaneously applying intracavity and external squeezing for the readout of this multilevel atom, the measurement signal-to-noise ratio between adjacent energy levels can be exponentially enhanced. We begin by examining this enhancement in a three-level system and subsequently extend the framework to multilevel systems, proving that the signal-to-noise ratio between any adjacent energy levels can achieve a similar exponential improvement. This dual-squeezing approach leads to an exponential enhancement in both the dispersive coupling strength and the signal-to-noise ratio. As a result, the single-shot readout time is exponentially shortened and the single-shot measurement error is exponentially reduced, ultimately improving the single-shot readout fidelity of bosonic qubits by more than an order of magnitude. This method provides an effective pathway for high-fidelity readout based on bosonic encoding.

Laser wakefield accelerators (LWFAs) provide extremely large accelerating gradients for compact electron accelerators and photon sources but are limited by dephasing, where trapped electrons outrun the accelerating phase of the wakefield. Flying-focus pulses can eliminate dephasing by driving a wake at the vacuum speed of light, but these pulses involve trade-offs, such as varying spot size, long duration, or large plasma volume. Here, we show that a spatiotemporally structured laser pulse propagating in a plasma waveguide can drive a wakefield at the vacuum speed of light while maintaining a constant spot size and ultrashort duration. The pulse is formed by superposing plasma-waveguide modes with appropriately selected frequencies. Compared with flying-focus approaches, the waveguide substantially reduces the required plasma volume. Scaling laws and quasi-three-dimensional particle-in-cell simulations show that the single-stage energy gain increases linearly with the number of modes used to construct the pulse, enabling larger energy gains or shorter stages than standard LWFA.

Long-range interactions can fundamentally reshape the low-energy properties of low-dimensional quantum matter, altering both continuous-symmetry breaking (CSB) and topological phenomena. However, their impact on the quantum criticality separating these regimes remains poorly understood. We determine the ground-state phase diagram and critical properties of the spin-one Heisenberg chain with single-ion anisotropy and staggered antiferromagnetic power-law interactions, using matrix-product state calculations complemented by high-order series expansions (perturbative continuous unitary transformations + Monte Carlo). Such long-range, nonfrustrated interactions circumvent the Hohenberg-Mermin-Wagner theorem, thereby stabilizing CSB phases in direct competition with the Haldane phase. We map out the resulting phase diagram and analyze the entanglement entropy scaling behavior in the U(1) and SU(2) CSB phases, finding logarithmic corrections beyond the short-range, universal contributions expected from linearly dispersed Goldstone modes. We further characterize all critical boundaries through finite-size scaling of either the entanglement entropy or the staggered magnetization. In particular, the large-$D$-to-U(1)-CSB transition exhibits unconventional, continuously varying critical exponents as a function of the long-range decay exponent with a strong dependence on the imposed boundary conditions leading to distinct finite-size scalings for sufficiently long-range potentials. Remarkably, the Haldane-to-U(1)-CSB transition likewise displays unconventional quantum criticality with distinct continuously varying critical exponents. Our work positions this model as a target for near-term atomic platforms with tunable long-range couplings and exhibiting natural single-ion anisotropy, offering a minimal playground for exploring the interplay between long-range interactions, continuous symmetry breaking, and topology.