A liquid drop connected to thin pliable object produces a deflection. If the volume of the liquid is sufficiently large, the deflection is modest and its shape is unique. Decreasing the volume from this state, however, leads to one of two possible minimal-volume outcomes, depending on the balance of rigidity and surface tension: The structure either returns to its original unstrained configuration or fully collapses to create a stable, highly stressed shape. Using a simple three-dimensional setup arising from self-assembly applications where the deflection is restricted to a single hinge, we characterize all the possible equilibrium shapes and show that the two possibilities arise as a consequence of a codimension-2 cusp bifurcation.

Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we investigate how the computational ability of reservoir recurrent neural networks (RNNs) scales with an increasing number of readout neurons. First, we demonstrate that the memory capacity of a reservoir RNN scales sublinearly with the number of readout neurons. To elucidate this observation, we develop a theoretical framework for analytically deriving memory capacity that incorporates the effect of neuronal correlations, which have been ignored in prior theoretical work for analytical simplicity. Our theory successfully relates the sublinear scaling of memory capacity to the strength of neuronal correlations. Furthermore, we show this principle holds across diverse types of RNNs, even those beyond the direct applicability of our theory. Next, we numerically investigate the scaling behavior of nonlinear computational ability, which, alongside memory capacity, is crucial for overall computational performance. Our numerical simulations reveal that as memory capacity growth becomes sublinear, increasing the number of readout neurons successively enables nonlinear processing at progressively higher polynomial orders. Our theoretical framework suggests that neuronal correlations govern not only memory capacity but also the sequential growth of nonlinear computational capabilities. Our findings establish a foundation for designing scalable and cost-effective reservoir computing, providing insights into the interplay among neuronal correlations, linear memory, and nonlinear processing.

Bipolaronic superconductivity is an exotic pairing mechanism proposed for materials like ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{BiO}}_3$ (BKBO); however, conclusive experimental evidence for a (bi)polaron metallic state in this material remains elusive. Here, we combine resonant inelastic x-ray and neutron total scattering techniques with advanced modeling to study the local lattice distortions, electronic structure, and electron-phonon $\left(e\text{−}\mathrm{ph}\right)$ coupling in BKBO as a function of doping. Data for the parent compound $(x=0)$ indicate that the electronic gap opens in predominantly oxygen-derived states strongly coupled to a long-range ordered breathing distortion of the oxygen sublattice. Upon doping, short-range breathing distortions and sizable $e$-ph coupling persist into the superconducting regime $(x=0.4)$. Comparisons with exact diagonalization and determinant quantum Monte Carlo calculations further support this conclusion. Our results provide compelling evidence that BKBO’s metallic phase hosts a liquid of small (bi)polarons derived from local breathing distortions of the lattice, with implications for understanding the low-temperature superconducting instability.

Understanding the electronic structure of actinide materials is crucial for both fundamental research and nuclear applications. The partially filled $5f$ shells exhibit complex behavior due to strong correlations and ligand hybridization, requiring advanced spectroscopic techniques. Here, we report on the development and application of high-resolution valence band resonant inelastic x-ray spectroscopy (VB-RIXS) experiments at the uranium $M_{4,5}$ edges (3551 and 3725 eV). We present data of ${\mathrm{UO}}_2$, a well-established model actinide compound. VB-RIXS is particularly well suited for probing the $5f$-shell electronic structure, as it probes, in contrast to core-to-core RIXS, excitations without leaving a high-energy core hole in the final state. In VB-RIXS, we achieve energy resolutions of 50 meV $\left(M_5\right)$ and 90 meV $\left(M_4\right)$, enabling the resolution of multiplet excitations and crystal-field effects, as well as charge-transfer and fluorescencelike features with unprecedented clarity. As such, high-resolution VB-RIXS offers direct insights into both low-energy, near-ground-state properties and high-energy hybridization and covalency effects. Our results demonstrate the power of VB-RIXS as a versatile and powerful tool for probing the strongly correlated electronic structure of actinide materials, providing essential input for quantitative modeling and the validation of theoretical concepts.

We study the emergence of complexity in deep random $N$-qubit $T$-gate-doped Clifford circuits, as reflected in their spectral properties and in magic generation, characterized by the stabilizer Rényi entropy distribution and the nonstabilizing power of the circuit. For pure (undoped) Clifford circuits, a unique periodic orbit structure in the space of Pauli strings implies peculiar spectral correlations and level statistics with large degeneracies. $T$-gate doping induces an exponentially fast transition to chaotic behavior, described by random matrix theory. We compare these complexity indicators with magic generation properties of the Clifford $+T$ ensemble, and determine the distribution of magic, as well as the average nonstabilizing power of the quantum circuit ensemble. In the dilute limit, $N_T\ll N$, magic generation is governed by single-qubit behavior. Magic is generated in approximate quanta, increases approximately linearly with the number of $T$ gates, $N_T$, and displays a discrete distribution for small $N_T$. At $N_T\approx N$, the distribution becomes quasicontinuous, and for $N_T\gg N$, it converges to that of Haar-random unitaries, and averages to a finite magic density, $m_2, {lim}_{N\to \infty }{\langle m_2\rangle }_{\text{Haar}}=1$. This is in contrast to the spectral transition, where $\mathcal{O}\left(1\right) T$ gates suffice to remove spectral degeneracies and to induce a transition to chaotic behavior in the thermodynamic limit. Magic is therefore a more sensitive indicator of complexity.

We formulate a theory for phase reduction analysis of traveling breathers in reaction-diffusion systems with spatial translational symmetry. In this formulation, the spatial and temporal phases represent the position and oscillation of a traveling breather, respectively. We perform phase reduction analysis on a pair of FitzHugh-Nagumo models exhibiting standing breathers and a pair of Gray-Scott models exhibiting traveling breathers. The derived phase equations for the spatial and temporal phases indicate nontrivial spatiotemporal dynamics, where both phases are mutually coupled. Using the phase equations, we obtain the time evolution of the phase differences, which is consistent with that obtained from direct numerical simulations.

Recognized as a potential resource for quantum technologies and a possible test bed for fundamental physics, the control and preparation of nonclassical states of mechanical oscillators have been explored extensively. Within optomechanics, quantum state synthesis can be realized by entangling photonic and phononic degrees of freedom followed by optical detection. Single-photon detection enables one of the most powerful forms of such heralded quantum state preparation, permitting the creation of single-phonon states when applied to conventional cavity optomechanical systems. As the complexity of optomechanical systems increases, single-photon detection may provide heralded access to a larger class of exotic quantum states. Here, we examine the quantum dynamics of optomechanical systems that permit forward Brillouin scattering, where a single-phonon mode mediates transitions between a collection of equally spaced optical resonances. Solving both the Schrodinger equation and the Lindblad master equation for this system, we find that initial states comprised of single photons or weak laser pulses evolve into complex quantum states where the frequency of single-photon states and the phonon occupation number are entangled. Physically, these interactions permit a single photon to scatter to lower frequencies, where phonon excitation occurs for each scattering event. Combining this result with frequency filtering, we show how single-photon detection can herald selected multiphonon Fock states, even in the presence of optical losses. We also present an approach for quantum tomography of the heralded phonon states, which in the form of a state swap from the phononic to photonic domain enables on-demand generation of multiphoton Fock states.

Recent generative machine learning models applied to protein multiple sequence alignment (MSA) datasets include simple and interpretable physics-based Potts covariation models and other machine learning models such as MSA Transformer (MSA-T). The best models accurately reproduce MSA statistics induced by the biophysical constraints within proteins, raising the question of which functional forms best model the underlying physics. The Potts model is usually specified by an effective potential including pairwise residue-residue interaction terms, but it has been suggested that MSA-T can capture the effects induced by effective potentials that include more than pairwise interactions and implicitly account for phylogenetic structure in the MSA. Here, we compare the ability of the Potts model and MSA-T to reconstruct higher-order sequence statistics reflecting complex biophysical sequence constraints. We show how the model performance depends greatly on the treatment of phylogenetic relationships between the sequences, which can induce nonbiophysical mutational covariation in MSAs. When using explicit corrections for phylogenetic dependencies, we find that the Potts model outperforms MSA-T in detecting epistatic interactions of biophysical origin. Furthermore, the sequences generated by the models we studied here are predicted to fold into nativelike structures, as indicated by AlphaFold predictions.

Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest from both a fundamental and a technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models: the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin-$S$ $\mathrm{U}\left(1\right)$ quantum link model. By tuning a confining parameter in these models, it is found that branch (manifold) DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.

We describe an approach to subsystem decoherence without the usual tracing out of the environment. The subsystem of focus is described entirely by a pure state evolving nonunitarily along a single classical trajectory of its environment. The approach is deduced from the exact factorization framework for arbitrary systems of electrons and nuclei. The nonunitarity of the electronic dynamics arises exclusively from nonadiabatic correlations between electrons and nuclei. We demonstrate that the approach correctly describes the coherence gain and the subsequent decoherence for the example of a nuclear trajectory passing through an avoided crossing, the prototypical case where single-trajectory Ehrenfest dynamics fails to produce decoherence.

We investigate numerically the joint distribution of magic (as described by the stabilizer 2-Rényi entropy $M_2$) and entanglement (as described by the von Neumann entropy $S$) in $N$-qubit Haar-random quantum states. The distribution $P_N(M_2,S)$ and the marginals become exponentially localized, and centered around the typical values, $\widetilde{M_2}\to N-2$ and $\tilde{S}\to N/2$ as $N\to \infty$. Magic and entanglement fluctuations are, however, found to become exponentially uncorrelated. While the set of stabilizer states grows exponentially with $N$, they nevertheless form a measure-zero subset of Haar-random states and thus occur with vanishing probability. Typical quantum states are characterized by large magic and entanglement entropy, and uncorrelated magic and entanglement fluctuations. The mutual information of the joint distribution vanishes exponentially as $N\to \infty$, implying that fluctuations of these two resources are not only uncorrelated but asymptotically independent.

Entanglement often increases quantum measurement schemes’ sensitivity. However, we find that in precision measurements with zero-mean Gaussian states, such as squeezed states, entanglement between different paths degrades measurement sensitivity. We prove an inverse relationship between entanglement entropy and sensitivity for measurements of single-mode phase shifts in multimode systems and for phase shifts on both modes in two-mode systems. In the two-mode case, which models devices such as interferometers, we find that entanglement strongly degrades differential phase sensitivity. Finally, we show that minimizing entanglement between paths maximizes the phase sensitivity of $N$-mode systems with zero-mean Gaussian state inputs.

We coarse-grain a model of closely packed ellipses that can vary their aspect ratio to derive continuum equations for materials comprising confluent deformable particles such as epithelial cell layers. We show that contractile nearest-neighbor interactions between ellipses can lead to their elongation and nematic ordering. Adding flows resulting from active hydrodynamic stresses produced by the particles also affects the aspect ratio and can result in active turbulence. Our results, which agree well with multiphase field simulations of deformable isotropic cells, provide a bridge between models that explicitly resolve cells and continuum theories of active matter.

Entanglement distillation is a key component of modular quantum computing and long-range quantum communications. However, this powerful tool to reduce noise in entangled states is difficult to realize in practice for two main reasons. First, operations used to carry out distillation inject noise they seek to remove. Second, the extent to which distillation can work under realistic device noise is less well studied. In this work, we both simulate distillation using a variety of device noise models and perform distillation experiments on fixed-frequency IBM devices. We find reasonable agreement between experimental data and simulation done using Pauli and non-Pauli noise models. In our data, we find broad improvement when the metric of success for distillation is to improve average Bell fidelity under effective global depolarizing noise, remove coherent errors, or improve the Bell fidelity of mildly degraded Bell pairs. We pave the way to obtain broad improvement from distillation under a stricter, but practically relevant, metric: distill (physically) nonlocal Bell pairs with higher fidelity than possible to obtain with other available methods. Our results also help understand metrics and requirements for quantum devices to use entanglement distillation as a primitive for modular computing.

Optical beamsplitters with similar properties for orthogonal, linear polarization modes are required for realizing polarization-based speed meter schemes to reduce backaction noise in gravitational-wave interferometers. In this paper, we investigate two beamsplitter coatings obtained from Laseroptik GmbH and Optoman on a best-effort basis that aim for a 50/50 power splitting ratio and equal overall phase shift for two orthogonal, linear polarization modes interacting with the optic. We show that while Laseroptik GmbH opted for coating stack with 22 alternating layers of ${\mathrm{Ta}}_2{\mathrm{O}}_5$ and ${\mathrm{SiO}}_2$, Optoman produced a much thinner coating made of five ${\mathrm{SiO}}_2$ and ${\mathrm{SiO}}_x$ ($0<x<2$) layers. With these strategies, the Laseroptik coating achieves an equal power reflectivity of $51\%$ at ${46}^{\circ }$ angle of incidence and zero phase shift between both polarizations at $44.{25}^{\circ }$ angle of incidence. The Optoman coating achieves power reflectivities of $49\%$ for $s$ polarization and $51\%$ for $p$ polarization with a differential phase shift around $5^{\circ }$ largely independent of the angle of incidence.

Efficient transmissive pure-phase resonances are highly desirable for optical modulation and wave front engineering. Here, we propose a principle to realize a pure-phase resonance in an extremely broad transmission band, as opposed to previous approaches restricted to operating in reflection mode or over a narrow spectral band. We show that a glide-symmetric bilayer metasurface mathematically mimicking a two-dimensional Dirac semimetal induces unidirectional guided-mode excitation and perfect leakage-radiation blazing at the transmission channel. These effects create a peculiar resonant-scattering configuration, similar to the classical reflective Gires-Tournois etalon, but in transmission, providing full 2π phase modulation with constant transmittance near 100%. Most importantly, this effect persists over an extremely wide band, associated with topological effects. Hence, our proposed approach produces a spectrally and parametrically robust pure-phase resonance effect in transmission, which is highly beneficial for practical applications.

The behavior of electromagnetic waves in a medium modulated in time and space, largely investigated decades ago, has recently attracted renewed interest. Here, we address an intriguing problem of this research: can light with an initial frequency ${\omega }_0$ be amplified solely pumped by a traveling wave with a much lower frequency ${\omega }_p\ll {\omega }_0$? Generally, the bandwidth of the modulation-induced optical frequency comb spectrum can be substantially broadened when the phase velocity of the traveling wave, $v_p$, approaches the phase velocity of light, $v_0$. However, in realistic photonic waveguides, the amplification effect remains small due to the unfeasible modulation and waveguide parameters required. In contrast, we demonstrate that modulating an optical resonator by a traveling wave having the frequency ${\omega }_p$ and phase velocity $v_p$ much smaller than the frequency ${\omega }_0$ and phase velocity $v_0$ of light can result in large light amplification accompanied by conversion to multiple comb lines within a relatively small frequency band.

Leakage errors are unwanted transfer of population outside of a defined computational subspace and they occur in almost every platform for quantum computing. While prevalent, leakage is often overlooked when measuring and reporting the fidelity of quantum gates with standard methods. In fact, when leakage is substantial it can cause a large overestimation of fidelity from the typical method used to measure fidelity, randomized benchmarking. We provide several methods for properly estimating fidelity in the presence of leakage errors that are applicable in different error regimes with carefully chosen sequence lengths. Then, we numerically demonstrate the methods for two-qubit randomized benchmarking, which often have the largest errors. Finally, we reanalyze previously shared data from Quantinuum systems with some of the methods provided.