Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronization of a Liénard system to its limit cycle using a bounded external force. To tackle this challenging nonlinear optimal control problem, our approach involves applying Pontryagin’s maximum principle with a combination of analytical and numerical tools. We show that the optimal control develops a remarkably complex structure in phase space as the force bound is lowered. Trajectories rewound from the limit cycle’s extreme points turn out to play a key role in determining the maximum number of control bangs for optimal connection. We illustrate these intricate features using the paradigmatic van der Pol oscillator model.

Recently, there has been growing interest in simulating time-dependent Hamiltonians using quantum algorithms, driven by diverse applications, such as quantum adiabatic computing. While techniques for simulating time-independent Hamiltonian dynamics are well established, time-dependent Hamiltonian dynamics is less explored and it is unclear how to systematically organize existing methods and to find new methods. Sambe-Howland's continuous clock elegantly transforms time-dependent Hamiltonian dynamics into time-independent Hamiltonian dynamics, which means that by taking different discretizations, existing methods for time-independent Hamiltonian dynamics can be exploited for time-dependent dynamics. In this work, we systemically investigate how Sambe-Howland's clock can serve as a unifying framework for simulating time-dependent Hamiltonian dynamics. First, we demonstrate the versatility of this approach by showcasing its compatibility with analog quantum computing and digital quantum computing. Second, for digital quantum computers, we illustrate how this framework, combined with time-independent methods (e.g., product formulas, multiproduct formulas, qDrift, and linear combination of unitaries-Taylor), can facilitate the development of efficient algorithms for simulating time-dependent dynamics. This framework allows us to (1) resolve the problem of finding minimum-gate time-dependent product formulas; (2) establish a unified picture of both Suzuki's and Huyghebaert and De Raedt's approaches; (3) generalize Huyghebaert and De Raedt's first- and second-order formula to arbitrary orders; (4) answer an unsolved question in establishing time-dependent multiproduct formulas; (5) and recover continuous qDrift on the same footing as time-independent qDrift. Third, we demonstrate the efficacy of our higher-order Huyghebaert and De Raedt's algorithm through digital adiabatic simulation.

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance $d=11$ at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at $d=3-5$, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a two-dimensional Riemannian manifold embedded in a three-dimensional hyperspace. The geometry of space may result in a potential-like term that supports bound states on the manifold. In the presence of a laser field, we derive expressions for a generalized Kramers-Henneberger-type unitary transformation, which is shown to be generally space- and time-dependent, and deduce a Schrödinger-like equation in the Kramers-Henneberger frame. Compared to a flat (geometrically trivial) space, new time-averaged coefficients of differential operators and operator-valued perturbation terms appear, which determine the geometry-dependent laser-dressed states on Riemannian manifolds.

Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution (PITE) algorithm and derive its formulation in the context of state-vector-based simulations, where quantum state vectors are directly used to compute observables without statistical errors. We compare the results with those of shot-based simulations, which estimate observables through repeated projective measurements. Applying the PITE algorithm to the Heisenberg chain, we investigate optimal initial conditions for convergence. We further demonstrate the method on the transverse-field Ising model using a state-of-the-art trapped-ion quantum device. Finally, we explore the potential of error mitigation in this framework, highlighting practical considerations for near-term digital quantum simulations.

Biological systems tightly regulate their physiological state using control signals. This includes the actomyosin cytoskeleton, a contractile active gel that consumes chemical free energy to drive many examples of cellular mechanical behavior. Upstream regulatory pathways activate or inhibit actomyosin activity. However, the contractile response of the actomyosin cytoskeleton to control signals remains poorly characterized. Here, we employ reconstituted actomyosin active gels and subject them to step and pulsatile activation inputs. We find evidence for a nonlinear impulse response, which we quantify via a transfer function $\delta \varepsilon /\delta g$ that relates input free-energy pulses $\delta g$ to output strain pulses $\delta \varepsilon$. We find a scaling relation $\delta \varepsilon /\delta g\sim g^{-0.3}$. The negative sign of the exponent represents a decreased effectiveness of a contracting gel in converting energy to strain. We ascribe nonlinearity in our system to a density-dependent mechanism, which contrasts strain-stiffening nonlinear responses to external stresses. Contractile response to control signals is an essential step toward understanding how information from mechanical signaling processes flows through actomyosin networks in living, and likely also synthetic, cells.

Multispecies competition models contribute to understanding how various species interact in natural ecosystems and how these interactions influence population dynamics and ecosystem stability. However, achieving a comprehensive and physical understanding behind species competition remains challenging. Based on the nonequilibrium landscape-flux theory, we developed a resource competition model that reveals underlying landscape to quantify global stability. We found that the dynamics of species competing for resources are influenced not only by landscape gradients but also by rotational flux. We further unveiled the underlying thermodynamic and dynamic mechanisms driving species competition. By leveraging the time irreversibility of nonequilibrium systems, we quantified the primary irreversible dynamical pathways and provided early warning indicators for predicting critical transitions. Through global sensitivity analysis of barrier heights, we revealed the critical impact of resource supply on state stability. This study offers a comprehensive physical explanation for understanding species competition at a global perspective.

Accurate simulations of thermalization in open quantum systems require a reliable representation of the bath correlation function (BCF). Numerical approaches, such as the hierarchical equations of motion and the pseudomode method, inherently approximate the BCF using a finite set of functions, which can impact simulation accuracy. In this work, we propose a practical and rigorous testing framework to assess the validity of approximate BCFs in open quantum dynamics simulations. Our approach employs a harmonic oscillator system, where the computed dynamics can be benchmarked against known exact solutions. To enable practical testing, we make two key methodological advancements. First, we develop numerical techniques to efficiently evaluate these exact solutions across a wide range of BCFs, ensuring broad applicability. Second, we introduce a moment-based state representation that significantly simplifies computations by exploiting the Gaussian nature of the system. Applications to a two-spin system and a transmon-resonator system demonstrate that our testing procedure provides error estimates that capture the qualitative trends observed in thermalization simulations. Using this methodology, we assess the performance of recently proposed BCF construction methods, highlighting both their strengths and a notable challenge posed by sub-Ohmic spectral densities at finite temperatures.

Understanding the flow behaviors of supercooled liquids presents a major challenge in liquid-state physics due to the strong nonlinearity and rich phenomena. To unravel this complexity, we introduce the concept of local configurational relaxation time ${\tau }_{\mathrm{LC}}$, which allows us to embody the solid-liquid duality, proposed by Maxwell for phenomenologically describing materials’ response to external load, at the particle level. The spatial distribution of ${\tau }_{\mathrm{LC}}$ in flow is heterogeneous. Depending on the comparison between the local mobility measured by ${\tau }_{\mathrm{LC}}$ and the external shear rate, the shear response of local regions is either solidlike or liquidlike. In this way, ${\tau }_{\mathrm{LC}}$ plays a role similar to the Maxwell time. By applying this microscopic solid-liquid duality to different conditions of shear flow with a wide range of shear rates, we describe the emergence of shear thinning in steady shear and predict the major characteristics of the transient response to start-up shear. Furthermore, we reveal a clear structural foundation for ${\tau }_{\mathrm{LC}}$ and the solid-liquid duality associated with it by introducing an order parameter extracted from local configuration. Thus, we establish a framework that connects microscopic structure, dynamics, local mechanical response, and flow behaviors for supercooled liquids. Finally, we rationalize our framework in terms of activations from energy basins that are facilitated by shear. This model illustrates how local structure, convection, and thermal activation collectively determine ${\tau }_{\mathrm{LC}}$. Notably, it predicts two distinct response groups, which well correspond to the microscopic solid-liquid duality.

Simulating noninteracting fermion systems is a common task in computational many-body physics. In the absence of translational symmetries, modeling free fermions on $N$ modes usually requires $\mathrm{poly}\left(N\right)$ computational resources. While often moderate, these costs can be prohibitive in practice when large systems are considered. We present several free fermion problems that can be solved by a quantum algorithm with substantially reduced computational costs. The memory costs are exponentially improved, $\mathrm{poly}\log \left(N\right)$. The run-time improvement, compared to the best known classical algorithms, is either exponential or significantly polynomial, depending on the geometry of the problem. The simulation of free fermion dynamics belongs to the BQP-hard complexity class (i.e., as hard as any (decision) problem that can be solved on a quantum computer). This implies (under standard assumptions) that our algorithm yields an exponential speedup for any classical algorithm at least for some geometries. The key technique in our algorithm is the block encoding of objects such as correlation matrices and Green's functions into a unitary. We demonstrate how such unitaries can be efficiently realized as quantum circuits, in the context of dynamics and thermal states of tight-binding Hamiltonians. The special cases of disordered and inhomogeneous lattices, as well as large nonlattice graphs, are presented in detail. Finally, we show that our simulation algorithm generalizes to other promising targets, including free-boson systems.

Nitrogen-vacancy (NV) centers in diamond and superconducting qubits are two promising solid-state quantum systems for quantum science and technology, but the realization of controlled interfaces between individual solid-state spins and superconducting qubits remains fundamentally challenging. Here, we propose and analyze a hybrid quantum system consisting of a magnetic skyrmion, an NV center, and a superconducting qubit, where the solid-state qubits are both positioned in proximity to the skyrmion structure in a thin magnetic disk. We show that it is experimentally feasible to achieve strong (coherent or dissipative) coupling between the NV center and the superconducting qubit by using the quantized gyration mode of the skyrmion as an intermediary. This allows coherent information transfer and nonreciprocal responses between the NV center and the superconducting qubit at the single quantum level with high controllability. The proposed platform provides a scalable pathway for implementing quantum protocols that synergistically exploit the complementary advantages of spin-based quantum memories, microwave-frequency superconducting circuits, and topologically protected magnetic excitations.

Atomic nuclei and dense nucleonic matter in neutron stars exhibit short-range correlations (SRCs), where nucleons form temporally correlated pairs in close proximity beyond mean-field approximation. It is essential to make precision measurement of the fraction of SRC since it carries the signature of underlying quark dynamics in nuclear medium. In this article, we present the first high-precision measurement of neutron-proton bremsstrahlung $\gamma$-ray emission from the symmetric ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reactions at 25 MeV/u. From the observed spectral hardening, the precise SRC fraction in the ${}^{124}\mathrm{Sn}$ nucleus is extracted to be $(20\pm 3)\%$. This result provides a statistically unambiguous evidence of SRCs and demonstrates that low-energy heavy-ion collisions offer an approach to studying nuclear structure in connection with quark-level dynamics.

Simultaneous breaking of time reversal and inversion symmetries in multiferroics couples ferroelectricity to magnetism and is a source of unusual physical phenomena that can be used in next-generation electronic devices. A notable example is ${\mathrm{DyFeO}}_3$, which under applied magnetic fields exhibits a giant linear magnetoelectric response and a large spontaneous electric polarization induced by coexisting orders of Fe and Dy subsystems. Here, we use high-resolution neutron diffraction to show that at zero field ${\mathrm{DyFeO}}_3$ hosts an incommensurate magnetic soliton lattice formed by spatially ordered Dy domain walls with an average domain size of 231(8) Å. The long-ranged interaction between the domain walls is mediated by magnons propagating through the Fe subsystem and is analogous to the Yukawa force in particle physics. An applied magnetic field destroys the long-ranged incommensurate order, unlocks the linear magnetoelectric response, and stabilizes the ferroelectric state. The magnetic domain walls are electrically charged and the soliton array dimerizes when both electric and magnetic fields are applied. Numerical simulations with experimental parameters suggest that the generic competition between the ferroelectric and incommensurate states can be effectively controlled by an applied electric field.

We present calculations of orientation-dependent ionization yields from aligned ${{\mathrm{H}}_2}^{+}$ and oriented polar ${\mathrm{HeH}}^{2+}$ and CO molecules by simulating the three-dimensional time-dependent Schrödinger equation. For the polar molecules, we observe asymmetries in orientation-resolved total ionization yields: The yields are not reflection symmetric across the orientation angle $\beta ={90}^{\circ }$ with respect to the axis of the linear polarization of the laser field. A simple ionization model, applicable in the tunneling ionization regime, explains the asymmetry in ionization yields based on structural factors from weak-field asymptotic tunneling theory and asymmetries in the external field.

We report the observation of multiple quantum-well (MQW) polaritons in organic-inorganic metal halide two-dimensional (2D) perovskite films with precisely controlled well-layer numbers. Using the Langmuir-Blodgett method, we fabricated high-quality MQW structures that eliminate well-width fluctuations, enabling the study of MQW polaritons in the low layer number region. Optical reflection spectroscopy and transfer matrix calculations reveal that spectral changes with increasing well numbers originate from MQW-polariton effects, successfully demonstrating the correspondence between spectral structures and MQW-polariton modes. We identify the superradiant regime, where a single radiant mode dominates, followed by the sequential emergence of higher-order radiant modes. These findings provide crucial insights into the evolution of MQW polaritons toward three-dimensional polaritons and contribute to fundamental studies of ultimate 2D systems. Furthermore, our results offer valuable knowledge for the development of perovskite-based optical devices.

We optimize matrix-product state-based algorithms for simulating quantum circuits with finite fidelity, specifically the time-evolving block decimation (TEBD) and the density-matrix renormalization group (DMRG) algorithms, by exploiting the irregular arrangement of entangling operations in circuits. We introduce a variation of the standard TEBD algorithm, we termed “cluster-TEBD,” which dynamically arranges qubits into entanglement clusters, enabling the exact contraction of multiple circuit layers in a single time step. Moreover, we enhance the DMRG algorithm by introducing an adaptive protocol, which analyzes the entanglement distribution within each circuit section to be contracted, dynamically adjusting the qubit grouping at each iteration. We analyze the performances of these enhanced algorithms in simulating both stabilizer and nonstabilizer random-structured quantum circuits, with up to 1000 qubits and 100 layers of Clifford and non-Clifford gates, and in simulating Shor's quantum algorithm with up to hundreds of thousands of layers. Our findings show that, even with reasonable computational resources per task, cluster-based approaches can significantly speed up simulations of large-sized quantum circuits and improve the fidelity of the final states.