In multicellular organisms, cells differentiate into multiple types as they divide. States of these cell types, as well as their numbers, are known to be robust to external perturbations, as conceptualized by Waddington’s epigenetic landscape where cells embed themselves in valleys corresponding to final cell types. How is such robustness achieved by developmental dynamics and evolution? To address this question, we consider a model of cells with gene expression dynamics and epigenetic feedback, governed by a gene regulation network. By evolving the network to achieve more cell types, we identified three major differentiation processes exhibiting different properties regarding their variance, attractors, stability, and robustness. The first of these, type A, exhibits chaos and long-lived oscillatory dynamics that slowly transition until reaching a steady state. The second, type B, follows a channeled annealing process where the epigenetic changes in combination with noise shift the cells toward varying final cell states that increase the stability. Finally, type C exhibits a quenching process where cell fate is quickly decided by falling into preexisting fixed points while cell trajectories are separated through periodic attractors or saddle points. We find types A and B to correspond well with Waddington’s landscape while being robust. Finally, the dynamics of type B demonstrate a differentiation process that uses a directed shifting of fixed points, visualized through the dimensional reduction of gene expression states. Correspondence with the experimental data of gene expression variance through differentiation is also discussed.

Cell migration is closely linked to cell shape, yet cell size is often assumed to remain constant. This assumption is challenged by recent experiments showing that cells undergo volume loss during spreading and swelling upon activation, with migration velocity correlated to cell size. In this work, we present a minimal theoretical framework for cellular size regulation and its influence on migration velocity. We connect cell size to membrane potential and active, actin-driven forces. Spatial inhomogeneities in these forces establish cell polarization and drive migration. Crucially, inhomogeneity is easier to establish over larger sizes, giving rise to a critical contact area, above which migration is possible. Our theory captures the coupled dynamics of cell volume, surface area, and motility and explains recent experiments on neutrophils.

From weather to neural networks, modeling is not only useful for understanding various phenomena but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their solutions are difficult to obtain. Based on the expectation of quantum transcendence, quantum algorithms for efficiently solving nonlinear differential equations continue to be developed. However, even the latest promising algorithm has been pointed out to have an evolution time limit. This limit is the theoretically predestined divergence of solutions. We propose algorithms of divergence-free simulation for nonlinear differential equations in quantum computers. For Hamiltonian simulations, a pivot state $\mathit{s}$ is introduced in the neighborhood of state $\mathit{x}$ to be solved. Divergence of the solutions is prevented by moving $\mathit{s}$ to a neighborhood of $\mathit{x}$ whenever $\mathit{x}$ leaves the neighborhood of $\mathit{s}$. Since updating $\mathit{s}$ is directly related to computational cost, to minimize the number of updates, the nonlinear differential equations are approximated by nonlinear polynomials around $\mathit{s}$, which are then Carleman linearized. Hamiltonian simulations of nonlinear differential equations based on several representative models are performed to show that the proposed methods break through the theoretical evolution time limit. Furthermore, we demonstrate that the proposed methods work well on an actual quantum computer. The solution of nonlinear differential equations free from evolution time constraints opens the door to practical applications of quantum computers.

We determine whether excitonic effects affect predictions of dark matter (DM)-electron scattering rates by calculating the energy- and momentum-dependent energy-loss function, including electron-hole interaction excitonic effects, for the DM scintillating detector materials GaAs and NaI. By comparing our results using the Bethe-Salpeter equation in the framework of many-body perturbation theory, which explicitly includes excitonic effects, with those using the quasiparticle random-phase approximation, which includes only electron-electron interaction and crystal local-field effects, we find that excitonic effects in NaI significantly increase the predicted scattering rate at low energy and as a result improve the cross-section sensitivity considering a realistic background. In contrast, the predicted scattering rate and the DM-electron scattering cross section for GaAs are minimally affected by excitonic effects.

Quantum devices comprised of elementary components with more than two stable levels—so-called qudits—enrich the accessible Hilbert space, enabling applications ranging from fault-tolerant quantum computing to simulating complex many-body models. While several quantum platforms are built from local elements that are equipped with a rich spectrum of stable energy levels, schemes for the efficient control and entanglement of qudits are scarce. Importantly, no experimental demonstration of multiqudit control has been achieved to date in neutral atom arrays. Here, we propose a general scheme for controlling and entangling qudits and perform a full analysis for the case of qutrits, encoded in ground and metastable states of alkaline earth atoms. We find an efficient implementation of single-qudit gates via the simultaneous driving of multiple transition frequencies. For entangling operations, we provide a concrete and intuitive recipe for the controlled-$\mathcal{Z}$ ($\mathrm{C}\mathcal{Z}$) gate for any local dimension $d$, realized through alternating single qudit and entangling pulses that simultaneously drive up to two Rydberg transitions. We further prove that two simultaneous Rydberg tones are, in general, the minimum necessary for implementing the $\mathrm{C}\mathcal{Z}$ gate with a global drive. The pulses we use are optimally controlled, smooth, and robust to realistic experimental imperfections, as we demonstrate using extensive noise simulations. This amounts to a minimal, resource-efficient, and practical protocol for realizing a universal set of gates. Our scheme for the native control of qudits in a neutral atom array provides a high-fidelity route toward qudit-based quantum computation, ready for implementation on near-term devices.

The nitrogen-vacancy (NV) center in diamond has become a widely used platform for quantum sensing. The four NV axes in monocrystalline diamond specifically allow for vector magnetometry, with magnetic-field sensitivities reaching down to $\mathrm{fT}/\sqrt{\mathrm{Hz}}$. The current literature primarily focuses on improving the precision of NV-based magnetometers. Here, we study the experimental accuracy of determining the magnetic field from measured spin-resonance frequencies via solving the NV Hamiltonian. We derive exact, analytical, and fast-to-compute formulas for calculating resonance frequencies from a known magnetic-field vector, and vice versa (formulas for calculating the magnetic-field vector from measured resonance frequencies). Additionally, the accuracy of often-used approximations is assessed. Finally, we promote using the Voigt profile as a fit model to determine the linewidth of measured resonances accurately. An open-source Python package accompanies our analysis.

Using computer simulations in two dimensions, we investigate the dynamics and structure of a passive polymeric tracer with different topologies immersed in a low-density active particle bath. One of the key observations is that polymers exhibit faster dynamics compared to passive colloidal particles at high activity, for the same particle density, in both linear and star polymer topologies. This enhanced motion is attributed to the accumulation of active particles, which induces prolonged and persistent movement of the polymer. Further analysis reveals that star polymers exhibit more complex and intriguing behavior than their linear counterparts. Notably, the accumulation of active particles promotes the pairing of arms in star polymers. For instance, a three-armed star polymer adopts a conformation similar to a linear polymer with two arms due to this pairing; as a result, at high activity, the dynamics of both the polymers converge. Finally, we explore the dynamics of a linear polymer with the same total number of beads as the star polymer. Interestingly, at high activity—where arm pairing in the star polymer is significant—the star polymer demonstrates faster dynamics than the linear polymer, despite having the identical number of beads. These findings contribute to a broader understanding of the interactions between active and passive components of varying topologies in dilute systems and highlight their potential for innovative applications ranging from materials science to biomedicine.

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing midcircuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and nonlinear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers’ equation. For a turbulence data set, we demonstrate potential advantages of the quantum-tensor scheme over its classical counterparts.

Calcium carbonate ($\mathrm{Ca}{\mathrm{CO}}_3$) is a widely occurring mineral that is crucial to many natural and synthetic processes. $\mathrm{Ca}{\mathrm{CO}}_3$ crystallizes in three anhydrous polymorphs and often serves as a model system to study nucleation and growth phenomena. In this article, we employ coherent diffraction imaging coupled with wide-angle x-ray diffraction (CXDI-WAXD) to investigate the three-dimensional (3D) morphology and crystal structure of $\mathrm{Ca}{\mathrm{CO}}_3$ microparticles crystallized under different reaction temperatures. We report particles containing both vaterite and aragonite, which we interpret as an intermediate growth stage between early vaterite and later aragonite formation. The results are based on the density variations observed in the 3D tomographic CXDI images, x-ray diffraction, and focussed ion beam-transmission electron microscopy study of the mixed vaterite-aragonite microparticles. A computational study based on Monte Carlo and molecular dynamics energy minimization was used to identify the small energetic variations between the different crystalline forms of $\mathrm{Ca}{\mathrm{CO}}_3$. The results presented in this article provide a better understanding of the morphology-structure correlation for $\mathrm{Ca}{\mathrm{CO}}_3$ polymorphs, depicting a transitional stage where both vaterite and aragonite coexist.

We present a detailed and self-contained theoretical study of polarons in two-dimensional (2D) polar materials, which extends the classical macroscopic theory of Fröhlich polarons to the 2D case. The theory is fully determined by experimentally accessible parameters, the static and optical 2D polarizabilities of a monolayer, the frequency of transverse optical phonons, and the effective mass of charge carriers. We define a single dimensionless parameter, which characterizes the coupling of electrons with longitudinal optical phonons, analyze both weak- and strong-coupling regimes, and adapt the Feynman variational path-integral approach for a high-quality interpolation between these limits. Our results provide insight into the ground-state energy and effective mass of polarons in modern 2D polar monolayers.

Synthetic materials that emulate tight-binding Hamiltonians have enabled a wide range of advances in topological and non-Hermitian physics. A crucial requirement in such systems is the engineering of nonreciprocal couplings and synthetic magnetic fields. More broadly, the development of these capabilities in a manner compatible with quantum-coherent degrees of freedom remains an outstanding challenge, particularly for superconducting circuits, which are highly sensitive to magnetic fields. Here, we demonstrate that pure gyration—a nonreciprocal coupling with exactly matched magnitude but nonreciprocal $\pi$ phase contrast—can be realized between degenerate states using only spatiotemporal modulation. We first show the existence of continuous exceptional surfaces in modulation parameter space where coupling with arbitrarily large magnitude contrast can be achieved, with robust volumes of $\pi$ phase contrast contained within. We then demonstrate that intersection of these volumes necessarily gives rise to continuous surfaces in parameter space where pure gyration is achieved. Our experiments are performed using microwave superconducting resonators that are modulated using dc superconducting quantum interference device arrays, and achieve isolation and pure gyration coupling with only superconducting circuit elements. However, our method is fully agnostic to physical implementation (classical or quantum) or frequency range and paves the way to realizing large-scale nonreciprocal metamaterials in any platform.

Molecular nanomagnets have garnered significant attention in recent years thanks to their unique potential in quantum information processing as molecular qudits and in high-density memory encoding as single-molecule magnets. However, fully unlocking the potential of these systems requires a comprehensive understanding of the interplay between the various mechanisms that govern their relaxation dynamics, which remains a noncompletely understood phenomenon. In this work, we employ a cost-effective semi-ab initio approach to model the magnetization relaxation dynamics in a testbed Dy-based single-molecule magnet and determine the effects of applied external pressure on the interplay between various mechanisms, such as coupling with molecular vibrations and quantum tunneling. Ab initio phonon calculations are validated by direct comparison with inelastic neutron scattering experiments, which are used for the first time to investigate pressure-induced modifications of phonons and vibrations in a molecular nanomagnet. The combination of our theoretical approach with different experimental techniques allows us to predict an overall acceleration of the relaxation dynamics under pressure, disentangling the role of different ingredients, such as crystal field axiality and phonons.

Information and free-energy maximization are physics principles that provide general rules for an agent to optimize actions in line with specific goals and policies. These principles can serve as building blocks for designing decision-making policies capable of efficient performance with only partial information. Notably, the information-maximization principle has shown remarkable success in the classical bandit problem and has recently been shown to yield optimal algorithms for Gaussian and sub-Gaussian reward distributions. This article explores a broad extension of physics-based approaches to more complex and structured bandit problems. To this end, we cover three distinct types of bandit problems, where information maximization is adapted and leads to strong performance for Gaussian and Bernoulli reward distributions. Since the main challenge of information maximization lies in avoiding overexploration, we highlight how information is tailored at various levels to mitigate this issue, paving the way for more efficient and robust decision-making strategies.

We present a theoretical framework that integrates Majorana's infinite-component relativistic equation within the algebraic structure of paraparticles through the minimal nontrivial ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie algebras and $R$-matrix quantization. By mapping angular momentum-dependent mass spectra of the Majorana Tower to graded sectors associated with generalized quantum statistics, we derive an equation describing Majorana quasiparticles of structured light carrying spin and orbital angular momentum. These quanta in the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded algebras and $R$-matrix formulations extend the previous results from superconducting qubits to photonic platforms and set up deterministic two-photon gates involving at least two qubits encoded in a single photon without nonlinear effects. This makes feasible the writing of general quantum computing pathways exploiting fractional statistics through Nelson's quantum mechanics and implementing a procedure for error correction in photonic platforms. Furthermore, this approach makes possible to set paraparticle-based quantum information processing, beyond fermions and bosons, using graded qudits.

Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use space-and-time-dependent PCA to detect transitions in nonequilibrium systems that are difficult to characterize with equilibrium methods. Here, we demonstrate that feature vectors incorporating the position and velocity information of driven skyrmions moving through random disorder permit PCA to resolve different types of disordered skyrmion motion as a function of driving force and the ratio of the Magnus force to the dissipation. Since the Magnus force creates gyroscopic motion and a finite Hall angle, skyrmions can exhibit a greater range of flow phases than what is observed in overdamped driven systems with quenched disorder. We show that in addition to identifying previously known skyrmion flow phases, PCA detects several additional phases, including different types of channel flow, moving fluids, and partially ordered states. Guided by the PCA analysis, we further characterize the disordered flow phases to elucidate the different microscopic dynamics and show that the changes in the PCA-derived order parameters can be connected to features in bulk transport measures, including the transverse and longitudinal velocity-force curves, differential conductivity, topological defect density, and changes in the skyrmion Hall angle as a function of drive. We discuss how asymmetric feature vectors can be used to improve the resolution of the PCA analysis, and how this technique can be extended to find disordered phases in other nonequilibrium systems with time-dependent dynamics.

High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error model is ideally calibrated using the same circuit as is used for the error correction experiment. Here, we present an experimental approach guided by an analytical formula to characterize the probability of independent errors using correlations in the syndrome data generated by executing the error correction circuit. Using the method on a distance-three surface code, we analyze error channels that flip an arbitrary number of syndrome elements, including Pauli $\widehat{Y}$ errors, hook errors, multiqubit errors, and leakage, in addition to standard Pauli $\widehat{X}$ and $\widehat{Z}$ errors. We use the method to find the optimal weights for a minimum-weight perfect matching decoder without relying on a theoretical error model. Additionally, we investigate whether improved knowledge of the Pauli $\widehat{Y}$ error channel, based on correlating the X- and Z-type error syndromes, can be exploited to enhance matching decoding. Furthermore, we find correlated errors that flip many syndrome elements over up to eight cycles, potentially caused by leakage of the data qubits out of the computational subspace. The presented method provides the tools for accurately calibrating a broad family of decoders, beyond the minimum-weight perfect matching decoder, without relying on prior knowledge of the error model.

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order.