Recently, strong evidence for a gravitational-wave background has been reported by collaborations of pulsar timing arrays (PTAs). In the framework of scalar-induced gravitational waves, we concurrently investigate the second- and third-order gravitational waves by jointly analyzing PTA data alongside big-bang nucleosynthesis and cosmic microwave background datasets. We determine the primordial curvature spectral amplitude as $0.021<A_{\zeta }<0.085$ and the spectral peak frequency as ${10}^{-7.3}\mathrm{Hz}<f_{*}<{10}^{-6.3}\mathrm{Hz}$ at a 95% confidence interval, pointing towards a mass range for primordial black holes of ${10}^{-4.5}{M}_{\odot }<m_{\mathrm{PBH}}<{10}^{-2.5}{M}_{\odot }$. Our findings suggest that third-order gravitational waves contribute more significantly to the integrated energy density than the second-order ones when $A_{\zeta }\gtrsim 0.06$. Furthermore, we expect future PTA projects to validate these findings and provide robust means to investigate the genesis and evolution of the universe, especially inflation.

Understanding thermodynamics in liquids at the atomic level is challenging because of strong atomic interactions and lack of spatial symmetry. Recent prior theoretical works have focused on describing heat capacity of liquids in terms of phonon-like excitations but often rely on fitting factors and ad hoc assumptions. In this work, we propose characterizing various phases in terms of instantaneous normal modes (INMs) of structural snapshots from molecular dynamics simulations of single-element systems over wide ranges of temperature and pressure. We use the INMs to build a mode-level microscopic description of heat capacity and demonstrate that heat capacity of liquids can be described by a combination of both solidlike and gaslike degrees of freedom, leading to a more unified framework to fundamentally describe heat capacity of all three phases of matter: solid, liquid, and gas.

The variational quantum eigensolver (VQE) stands as a prominent quantum-classical hybrid algorithm for near-term quantum computers to obtain the ground states of molecular Hamiltonians in quantum chemistry. However, due to the noncommutativity of the Pauli operators in the Hamiltonian, the number of measurements required on quantum computers increases significantly as the system size grows, which may hinder practical applications of VQE. In this work, we present a protocol termed joint Bell measurement VQE (JBM-VQE) to reduce the number of measurements and speed up the VQE algorithm. Our method employs joint Bell measurements, enabling the simultaneous measurement of the absolute values of all expectation values of Pauli operators present in the Hamiltonian. In the course of the optimization, JBM-VQE estimates the absolute values of the expectation values of the Pauli operators for each iteration by the joint Bell measurement, while the signs of them are measured less frequently by the conventional method to measure the expectation values. Our approach is based on the empirical observation that the signs do not often change during optimization. We illustrate the speed-up of JBM-VQE compared to conventional VQE by numerical simulations for finding the ground states of molecular Hamiltonians of small molecules, and the speed-up of JBM-VQE at the early stage of the optimization becomes increasingly pronounced in larger systems. Our approach based on the joint Bell measurement is not limited to VQE and can be utilized in various quantum algorithms whose cost functions are expectation values of many Pauli operators.

Controlling the quantum interface between two bosonic modes is essential in countless implementations of quantum information processing. However, full controllability is rarely achieved in most platforms due to specific physical limitations. In this work, we completely characterize the linear two-mode interfaces under the most pessimistic restriction that only single-mode operation is available. When arbitrary Gaussian single-mode operations can be applied to both modes, we find that every interface can be characterized by an invariant transmission strength. Moreover, in the practical situation that squeezing is restricted in one of the modes, we discover two additional quantities, irreducible squeezing and irreducible shearing, that are invariant under the allowable controls. By using this characterization, we develop systematic strategies to engineer an arbitrary linear interface through cascading multiple fixed component interfaces. Without squeezing restriction, our protocol is optimal and requires at most three component interfaces. Under the squeezing constraint, our protocol can be extended to engineer also the additional invariants by using no more than two more rounds of cascade. We also propose the remote squeezing scheme to tackle the squeezing restriction through interfacing with an active auxiliary mode.

Dynamically encircling exceptional points (EEPs) in non-Hermitian systems have been utilized to realize robust on-chip mode conversions by taking the advantage that the output states are usually fixed and independent of the input states. This highly protects one of the specific eigenstates, but restricts their practical applications requiring superposition states. Here, we realize an on-chip robust eigenstate generator using a depth-varying 3D waveguide to overpass the EEP system. It not only preserves the robustness of the EEP system to generate one determinate eigenstate, but also generates another two-level eigenstate and arbitrary superposition states. Furthermore, by ingeniously combining two identical generators with a symmetric Y combiner, both the all-optical XOR and OR logic operations insensitive to the variations in the input light are realized by the destructive or constructive interference between the two generators' near-neighboring output signals. This paper paves the way for applications of EEP systems to highly robust state manipulations and information processing in integrated photonic and quantum devices.

Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in table-top experiments. However, several challenges remain, such as implementing dynamical fermions in higher spatial dimensions and magnetic field terms. Here, we map U(1) Abelian lattice gauge theories in arbitrary spatial dimensions onto qudit systems with local interactions. We propose a variational quantum simulation scheme for the qudit system with a local Hamiltonian, that can be implemented on a universal qudit quantum device as the one developed in [Nat. Phys. 18, 1053 (2022)]. We describe how to implement the variational imaginary-time evolution protocol for ground-state preparation as well as the variational real-time evolution protocol to simulate nonequilibrium physics on universal qudit quantum computers, supplemented with numerical simulations. Our proposal can serve as a way of simulating lattice gauge theories, particularly in higher spatial dimensions, with minimal resources, regarding both system sizes and gate count.

We investigate the persistent orientation of asymmetric-top molecules induced by time-delayed THz pulses that are either collinearly or cross polarized. Our theoretical and numerical results demonstrate that the orthogonal configuration outperforms the collinear one, and a significant degree of persistent orientation—approximately 10% at 5 K and nearly 3% at room temperature—may be achieved through parameter optimization. The dependence of the persistent orientation factor on temperature and field parameters is studied in detail. The proposed application of two orthogonally polarized THz pulses is both practical and efficient. Its applicability under standard laboratory conditions lays a solid foundation for future experimental realization of THz-induced persistent molecular orientation.

Investigating the cosmological implication of the fact that neutrino has finite mass is of importance for fundamental physics. In particular, massive neutrino affects the formation of the large-scale structure (LSS) of the universe, and, conversely, observations of the LSS can give constraints on the neutrino mass. Numerical simulations of the LSS formation including massive neutrino along with conventional cold dark matter is thus an important task. For this, calculating the neutrino distribution in the phase space by solving the Vlasov equation is a suitable approach, but it requires solving the PDE in the $(6+1)$-dimensional space and is thus computationally demanding: Configuring $n_{\mathrm{gr}}$ grid points in each coordinate and $n_t$ time grid points leads to $O\left(n_{\mathrm{gr}}^6\right)$ memory space and $O\left(n_t{n}_{\mathrm{gr}}^6\right)$ queries to the coefficients in the discretized PDE. We propose a quantum algorithm for this task. Linearizing the Vlasov equation by neglecting the relatively weak self-gravity of the neutrino, we perform the Hamiltonian simulation to produce quantum states that encode the phase-space distribution of neutrino. We also propose a way to extract the power spectrum of the neutrino density perturbations as classical data from the quantum state by quantum amplitude estimation with accuracy $\epsilon$ and query complexity of order $\tilde{O}[(n_{\mathrm{gr}}+n_t)/\epsilon ]$. Our method also reduces the space complexity to $O\left[\mathrm{polylog}(n_{\mathrm{gr}}/\epsilon )\right]$ in terms of the qubit number, while using quantum random access memories with $O\left(n_{\mathrm{gr}}^3\right)$ entries. As far as we know, this is the first quantum algorithm for the LSS simulation that outputs the quantity of practical interest with guaranteed accuracy.

The quantum gravity-induced entanglement of masses (QGEM) protocol for testing quantum gravity using entanglement witnessing utilizes the creation of spatial quantum superpositions of two neutral, massive matter-wave interferometers kept adjacent to each other, separated by a distance $d$. The mass and the spatial superposition should be such that the two quantum systems can entangle solely via the quantum nature of gravity. Despite being charge-neutral, many electromagnetic backgrounds can also entangle the systems such as the dipole-dipole and Casimir-Polder interactions. To minimize electromagnetic-induced interactions between the masses, it is pertinent to isolate the two superpositions by a conducting plate. However, the conducting plate will also exert forces on the masses and hence the trajectories of the two superpositions would be affected. To minimize this effect, we propose to trap the two interferometers such that the trapping potential dominates over the attraction between the conducting plate and the matter-wave interferometers. The superpositions can still be created via the Stern-Gerlach effect in the direction parallel to the plate, where the trapping potential is negligible. The combination of trapping and shielding provides a better parameter space for the parallel configuration of the experiment, where the requirement on the size of the spatial superposition, to witness the entanglement between the two masses purely due to their quantum nature of gravity, decreases by at least two orders of magnitude as compared to the original protocol paper.

The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a promising platform to realize, manipulate, and understand such systems with a high degree of controllability. Recently, an atomic $\nu =1/2$ Laughlin state has been realized experimentally for a small system of two particles on $4\times 4$ sites [Léonard et al., Nature (London) 619, 495 (2023)]. The next challenge concerns the preparation of Laughlin states in extended systems, ultimately giving access to anyonic braiding statistics or gapless chiral edge-states in systems with open boundaries. Here, we propose and analyze an experimentally feasible scheme to grow larger Laughlin states by connecting multiple copies of the already-existing $4\times 4$ system. First, we present a minimal setting obtained by coupling two of such patches, producing an extended $8\times 4$ system with four particles. Then, we analyze different preparation schemes, setting the focus on two shapes for the extended system, and discuss their respective advantages: While growing striplike lattices could give experimental access to the central charge, squarelike geometries are advantageous for creating quasihole excitations in view of braiding protocols. We highlight the robust quantization of the fractional quasihole charge upon using our preparation protocol. We benchmark the performance of our patchwork preparation scheme by comparing it to a protocol based on coupling one-dimensional chains. We find that the patchwork approach consistently gives higher target-state fidelities, especially for elongated systems. The results presented here pave the way towards near-term implementations of extended Laughlin states in quantum gas microscopes and the subsequent exploration of exotic properties of topologically ordered systems in experiments.

A plane-Couette flow (PCF) is considered in a stably stratified three-dimensional (3D) Yukawa liquid, perturbed initially with a finite amplitude 3D perturbation. Stable stratification in density is achieved by subjecting the medium to external gravity. We demonstrate turbulent spot formation in a stably stratified PCF. The dynamics of the system is shown to depend upon the value of $\kappa$, which is associated with the range of interaction. We have performed “first principles” classical 3D molecular dynamics (MD) simulations for “hypergravity” ($1.3g_0$, $g_0$ is Earth's gravitational force for unit mass in our normalized unit) and “milligravity” $(9\times {10}^{-3}{g}_0)$ cases for $\kappa$, 1.0 and 4.0, respectively. We extract relevant fluid quantities from MD data. For the hypergravity case, when the system is evolved in time under stable stratification, the kinetic energy is observed to deposit in the lower wave vectors $(K_x$, $K_z)$, leading to “inverse cascade” in the plane perpendicular to the direction of stratification. As a result, we observe large-scale structure formation in velocity and streamwise vorticity fields. Nucleation of velocity streak is observed for the first time in the stably stratified case in our simulation. The coherent structures in the velocity and streamwise vorticity fields are found to sustain for longer period of time for the stably stratified cases as compared to the unstratified case. For the milligravity case, the large-scale dynamics is observed to enhance. Unlike unstratified PCF, a background flow in Y-averaged streamwise fluid velocity field is observed for the stably stratified case. We believe that our results using “first principles” classical MD simulations on subcritical turbulence in stably stratified Yukawa liquid, may have ramifications to wider class turbulence problems.

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian, and spatiotemporal nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.

Numerous measurements of the dielectric constant $\varepsilon$ of the recently discovered ferroelectric nematic (${\mathrm{N}}_{\mathrm{F}}$) liquid crystal (LC) phase report extraordinarily large values of $\varepsilon$′ (up to ∼30 000) in the ${\mathrm{N}}_{\mathrm{F}}$ phase. We show that what is in fact being measured in such experiments is the high capacitance of the nonferroelectric, interfacial, insulating layers of nanoscale thickness that bound the ${\mathrm{N}}_{\mathrm{F}}$ material in typical cells. Polarization reorientation as a linear response to AC electric field drive renders the ${\mathrm{N}}_{\mathrm{F}}$ layer effectively electrically conductive, exhibiting low resistance that enables the charging of the interfacial capacitors. We analyze the commonly employed parallel-plate cell filled with ${\mathrm{N}}_{\mathrm{F}}$ material of high polarization P, oriented parallel to the plates at zero applied voltage. Minimization of the dominant electrostatic energy renders P spatially uniform and orients the polarization to make the electric field in the ${\mathrm{N}}_{\mathrm{F}}$ as small as possible, a condition under which the voltage applied to the cell appears almost entirely across the high-capacity interfacial layers. This coupling of orientation and charge creates a combined polarization-external capacitance (PCG) Goldstone reorientation mode requiring applied voltages orders of magnitude smaller than that of the ${\mathrm{N}}_{\mathrm{F}}$ layer alone to effectively transport charge across the ${\mathrm{N}}_{\mathrm{F}}$ layer. The ${\mathrm{N}}_{\mathrm{F}}$ layer acts as a low-value resistor, and the interfacial capacitors act as reversible energy storage reservoirs, lowering the restoring force (mass) of the PCG mode and producing strong reactive dielectric behavior. Analysis of data from a variety of experiments on ferroelectric LCs (chiral smectics C, bent-core smectics, and the ${\mathrm{N}}_{\mathrm{F}}$ phase) supports the PCG model, showing that deriving dielectric constants from electrical impedance measurements of high-polarization ferroelectric LCs, without properly accounting for the self-screening effects of polarization charge and the capacitive contributions of interfacial layers, can result in overestimation of the $\varepsilon$′ values of the LC by many orders of magnitude.

Cascade failures in power grids occur when the failure of one component or subsystem causes a chain reaction of failures in other components or subsystems, ultimately leading to a widespread blackout or outage. Controlling cascade failures on power grids is important for many reasons like economic impact, national security, public safety and even rippled effects like troubling transportation systems. Monitoring the networks on node level has been suggested by many, either controlling all nodes of a network or by subsets. This study identifies sensitive graph elements of the weighted European power-grids (from 2016 and 2022) by two different methods. Bridges are determined between communities and “weak” nodes are selected by the lowest local synchronization of the swing equation. In the latter case we add bypasses of the same number as the bridges at weak nodes, and we compare the synchronization, cascade failure behavior by the dynamical improvement with the purely topological changes. The results are also compared if bridges are removed from networks, which results in a case similar to islanding, and with the addition of links at randomly selected places. Bypassing was found to improve synchronization the best, while the average cascade sizes are the lowest with bridge additions. However, for very large or small global couplings these network changes do not help, they seem to be useful near the synchronization transition region, where self-organization drives the power grid. Thus, we provide a demonstration for the Braess' Paradox on continent-sized power-grid simulations and uncover the limitations of this phenomenon. We also determine the cascade size distributions and justify the power-law tails near the transition point on these grids.

We consider a smooth interface between a topological nodal-line semimetal and a topologically trivial insulator (e.g., the vacuum) or another semimetal with a nodal ring of different radius. Using a low-energy effective Hamiltonian including only the two crossing bands, we show that these junctions accommodate a two-dimensional zero-energy level and a set of two-dimensional dispersive bands, corresponding to states localized at the interface. We characterize the spectrum, identifying the parameter ranges in which these states are present, and highlight the role of the nodal radius and the smoothness of the interface. We also suggest material-independent ways to detect and identify these states, using optical conductivity and infrared absorption spectroscopy in magnetic field.