Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it to the canonical problem of fluid dynamics: three-dimensional homogeneous and isotropic turbulence. By doing numerical experiments we perform a systematic assessment of how well the technique reconstructs large- and small-scale features of the flow with respect to the quantity and the quality or type of data supplied to it. The types of data used are (i) field values on a fixed number of spatial locations (Eulerian nudging), (ii) Fourier coefficients of the fields on a fixed range of wave numbers (Fourier nudging), or (iii) field values along a set of moving probes inside the flow (Lagrangian nudging). We present state-of-the-art quantitative measurements of the scale-by-scale transition to synchronization and a detailed discussion of the probability distribution function of the reconstruction error, by comparing the nudged field and the truth point by point. Furthermore, we show that for more complex flow configurations, like the case of anisotropic rotating turbulence, the presence of cyclonic and anticyclonic structures leads to unexpectedly better performances of the algorithm. We discuss potential further applications of nudging to a series of applied flow configurations, including the problem of field reconstruction in thermal Rayleigh-Bénard convection and in magnetohydrodynamics, and to the determination of optimal parametrization for small-scale turbulent modeling. Our study fixes the standard requirements for future applications of nudging to complex turbulent flows.

In this work we introduce two code families, which we call the heavy-hexagon code and the heavy-square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low-degree graphs. Such a layout is particularly suitable for superconducting qubit architectures to minimize frequency collisions and cross talk. In some cases, frequency collisions can be reduced by several orders of magnitude. The heavy-hexagon code is a hybrid surface and Bacon-Shor code mapped onto a (heavy-) hexagonal lattice, whereas the heavy-square code is the surface code mapped onto a (heavy-) square lattice. In both cases, the lattice includes all the ancilla qubits required for fault-tolerant error correction. Naively, the limited qubit connectivity might be thought to limit the error-correcting capability of the code to less than its full distance. Therefore, essential to our construction is the use of flag qubits. We modify minimum-weight perfect-matching decoding to efficiently and scalably incorporate information from measurements of the flag qubits and correct up to the full code distance while respecting the limited connectivity. Simulations show that high threshold values for both codes can be obtained using our decoding protocol. Further, our decoding scheme can be adapted to other topological code families.

Fluorescence time traces are used to report on dynamical properties of molecules. The basic unit of information in these traces is the arrival time of individual photons, which carry instantaneous information from the molecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus, it is theoretically possible to monitor molecular dynamics at such timescales from traces containing only a sufficient number of photon arrivals. In practice, however, traces are stochastic and in order to deduce dynamical information through traditional means—such as fluorescence correlation spectroscopy (FCS) and related techniques—they are collected and temporally autocorrelated over several minutes. So far, it has been impossible to analyze dynamical properties of molecules on timescales approaching data acquisition without collecting long traces under the strong assumption of stationarity of the process under observation or assumptions required for the analytic derivation of a correlation function. To avoid these assumptions, we would otherwise need to estimate the instantaneous number of molecules emitting photons and their positions within the confocal volume. As the number of molecules in a typical experiment is unknown, this problem demands that we abandon the conventional analysis paradigm. Here, we exploit Bayesian nonparametrics that allow us to obtain, in a principled fashion, estimates of the same quantities as FCS but from the direct analysis of traces of photon arrivals that are significantly smaller in size, or total duration, than those required by FCS.

Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here, we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data. This determination is accomplished by extracting the one-particle irreducible (1PI) correlation functions from which one can construct all physical observables. To match the capabilities of experimental techniques, our approach employs a formulation of quantum field theory based on equal-time correlation functions only. We illustrate the theoretical foundations of our procedure by applying it to the sine-Gordon model in thermal equilibrium and then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract all 1PI correlation functions up to the 1PI four-point function (interaction vertex) and their variation with momentum, encoding the “running” of the couplings. The measured 1PI correlation functions are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing complex many-body questions emerging in a large variety of settings from fundamental science to practical quantum technology.

Heat conduction in dielectric crystals originates from the dynamics of atomic vibrations, whose evolution is well described by the linearized Boltzmann transport equation for the phonon populations. Recently, it was shown that thermal conductivity can be resolved exactly and in a closed form as a sum over relaxons, i.e., collective phonon excitations that are the eigenvectors of Boltzmann equation’s scattering matrix [A. Cepellotti and N. Marzari, Phys. Rev. X 6, 041013 (2016)]. Relaxons have a well-defined parity, and only odd relaxons contribute to the thermal conductivity. Here, we show that the complementary set of even relaxons determines another quantity—the thermal viscosity—that enters into the description of heat transport, and is especially relevant in the hydrodynamic regime, where dissipation of crystal momentum by umklapp scattering phases out. We also show how the thermal conductivity and viscosity parametrize two novel viscous heat equations—two coupled equations for the temperature and drift-velocity fields—which represent the thermal counterpart of the Navier-Stokes equations of hydrodynamics in the linear, laminar regime. These viscous heat equations are derived from a coarse graining of the linearized Boltzmann transport equation for phonons, and encompass both the limit of Fourier’s law and that of second sound, taking place, respectively, in the regime of strong or weak momentum dissipation. Last, we introduce the Fourier deviation number as a descriptor that captures the deviations from Fourier’s law due to hydrodynamic effects. We showcase these findings in a test case of a complex-shaped device made of graphite, obtaining a remarkable agreement with the recent experimental demonstration of hydrodynamic transport in this material, and also suggesting that hydrodynamic behavior can appear at room temperature in micrometer-sized diamond crystals. The present formulation rigorously generalizes Fourier’s heat equation, extending the reach of physical and computational models for heat conduction also to the hydrodynamic regime.

Quantum probes are atomic sized devices mapping information of their environment to quantum-mechanical states. By improving measurements and at the same time minimizing perturbation of the environment, they form a central asset for quantum technologies. We realize spin-based quantum probes by immersing individual Cs atoms into an ultracold Rb bath. Controlling inelastic spin-exchange processes between the probe and bath allows us to map motional and thermal information onto quantum-spin states. We show that the steady-state spin population is well suited for absolute thermometry, reducing temperature measurements to detection of quantum-spin distributions. Moreover, we find that the information gain per inelastic collision can be maximized by accessing the nonequilibrium spin dynamic. Keeping the motional degree of freedom thermalized, individual spin-exchange collisions yield information about the gas quantum by quantum. We find that the sensitivity of this nonequilibrium quantum probing effectively beats the steady-state Cramér-Rao limit by almost an order of magnitude, while reducing the perturbation of the bath to only three quanta of angular momentum. Our work paves the way for local probing of quantum systems at the Heisenberg limit, and moreover, for optimizing measurement strategies via control of nonequilibrium dynamics.

We address the long-standing problem of the structure of the low-energy eigenstates and long-time coherent dynamics in quantum spin-glass models. Below the spin-glass freezing transition, the energy landscape of the spin system is characterized by a proliferation of local minima where classical dynamics gets trapped. A theoretical description of quantum dynamics in this regime is challenging due to the complex nature of the distribution of the tunneling matrix elements between the local minima of the energy landscape. We study the transverse-field-induced quantum dynamics of the following “impurity band” (IB) spin model: zero energy of all spin configurations except for a small fraction of spin configurations (“marked states”) that form a narrow band at a large negative energy. At a zero transverse field, the IB model demonstrates the freezing transition at inverse temperature ${\beta }_f\sim 1$ characterized by a nonzero value of the Edwards-Anderson order parameter. At a finite transverse field, the low-energy dynamics can be described by the effective down-folded Hamiltonian that acts in the Hilbert subspace involving only the marked states. We obtain in an explicit form the heavy-tailed probability distribution of the off-diagonal matrix elements of the down-folded Hamiltonian. This Hamiltonian is dense and belongs to the class of preferred basis Levy matrices. Analytically solving nonlinear cavity equations for the ensemble of down-folded Hamiltonians allows us to describe the statistical properties of the eigenstates. In a broad interval of transverse fields, they are nonergodic, albeit extended. It means that the band of marked states splits into a set of narrow minibands. Accordingly, the quantum evolution that starts from a particular marked state leads to a linear combination of the states belonging to a particular miniband. An analytical description of this qualitatively new type of quantum dynamics is a key result of our paper. Based on our analysis, we propose the population transfer (PT) algorithm: The quantum evolution under constant transverse field $B_{\perp }$ starts at a low-energy spin configuration and ends up in a superposition of $\mathrm{\Omega }$ spin configurations inside a narrow energy window. This algorithm crucially relies on the nonergodic nature of delocalized low-energy eigenstates. In the considered model, the run-time of the best classical algorithm (exhaustive search) is $t_{\mathrm{cl}}=2^n/\mathrm{\Omega }$. For $\sqrt{n}\gg B_{\perp }\gg 1$, the typical run-time of the quantum PT algorithm $\sqrt{t_{\mathrm{cl}}}{e}^{n/(2B_{\perp }^2)}$ scales with $n$ and $\mathrm{\Omega }$ as that of Grover’s quantum search, except for the small correction to the exponent. Unlike the Hamiltonians proposed for analog quantum unstructured search algorithms, the model we consider is nonintegrable and the transverse field delocalizes the marked states. As a result, our PT protocol does not require fine-tuning of the transverse field and may be initialized in a computational basis state. We find that the run-times of the PT algorithm are distributed according to the alpha-stable Levy law with tail index 1. We argue that our approach can be applied to study the PT protocol in other transverse-field spin-glass models, with a potential quantum advantage over classical algorithms.

Key to collective cell migration is the ability of cells to rearrange their position with respect to their neighbors. Recent theory and experiments demonstrate that cellular rearrangements are facilitated by cell shape, with cells having more elongated shapes and greater perimeters more easily sliding past their neighbors within the cell layer. Though it is thought that cell perimeter is controlled primarily by cortical tension and adhesion at each cell’s periphery, experimental testing of this hypothesis has produced conflicting results. Here we study collective migration in an epithelial monolayer by measuring forces, cell perimeters, and motion, and find all three to decrease with either increased cell density or inhibition of cell contraction. In contrast to previous understanding, the data suggest that cell shape and rearrangements are controlled not by cortical tension or adhesion at the cell periphery but rather by the stress fibers that produce tractions at the cell-substrate interface. This finding is confirmed by an experiment showing that increasing tractions reverses the effect of density on cell shape and rearrangements. Our study therefore reduces the focus on the cell periphery by establishing cell-substrate traction as a major physical factor controlling shape and motion in collective cell migration.

Evaluating the nonlinear dynamics of human descending thoracic aortas is essential for building the next generation of vascular prostheses. This study characterizes the nonlinear dynamics, viscoelastic material properties, and fluid-structure interaction of 11 ex-vivo human descending thoracic aortas the full range of physiological heart rates. The aortic segments are harvested from heart-beating donors screened for transplants. A mock circulatory loop is developed to reproduce physiological pulsatile pressure and flow. The results show cyclic axisymmetric diameter changes, which are satisfactorily compared to in-vivo measurements at a resting pulse rate of 60 bpm, with an additional bending vibration. An increase of the dynamic stiffness (i.e., storage modulus) with age is also observed. This increase is accompanied by a strong reduction with age of the cyclic diameter change during the heart pulsation at 60 bpm and by a significant reduction of the loss factor (i.e., damping). Large dissipation is observed at higher pulse rates due to the combined effects of fluid-structure interaction and viscoelasticity of the aortic wall. This study presents data necessary for developing innovative grafts that better mimic the dynamics of the aorta.

We report the first measurement of ground-state diamagnetism of isolated neutral atoms in an atomic beam. We realize this measurement using magnetic deflection of fringes in a long-baseline matter-wave interferometer. The observed diamagnetic susceptibilities of $-5.8\pm 0.2\pm 0.4\times {10}^{-9}{\mathrm{m}}^3/\mathrm{kg}$ for barium and $-7.0\pm 0.3\pm 0.7\times {10}^{-9}{\mathrm{m}}^3/\mathrm{kg}$ for strontium are in good agreement with the theoretical values and correspond to a measured force on the order of ${10}^{-26}\mathrm{N}$. The high force sensitivity also allows us to observe the isotope dependence of the interference visibility due to the nuclear permanent magnetic moment, thereby demonstrating a new method for neutral isotope selection. The universality of the technique allows the magnetism of a wide range of atoms and molecules to be studied in the gas phase.

Traditional origami structures can be continuously deformed back to a flat sheet of paper, while traditional kirigami requires glue or seams in order to maintain its rigidity. In the former, nontrivial geometry can be created through overfolding paper, while in the latter, the paper topology is modified. Here we propose a hybrid approach that relies on overlapped flaps that create in-plane compression resulting in the formation of polyhedra composed of freely supported plates. Not only are these structures self-locking, but they have colossal load-to-weight ratios of order $10^4$.

Here, we report the investigation of the anomalous Hall effect in the magnetically doped topological insulator $(\mathrm{V},\mathrm{Bi},\mathrm{Sb}{)}_2{\mathrm{Te}}_3$. We find it contains two contributions of opposite sign. Both components are found to depend differently on carrier density, leading to a sign inversion of the total anomalous Hall effect as a function of applied gate voltage. The two contributions are found to have different magnetization reversal fields, which in combination with a temperature dependent study points towards the coexistence of two ferromagnetic orders in the system. Moreover, we find that the sign of total anomalous Hall response of the system depends on the thickness and magnetic doping density of the magnetic layer. The thickness dependence suggests that the two ferromagnetic components originate from the surface and bulk of the magnetic topological insulator film. We believe that our observations provide insight into the magnetic behavior, and thus will contribute to an eventual understanding of the origin of magnetism in this material class. In addition, our data bear a striking resemblance to anomalous Hall signals often associated with skyrmion contributions. Our analysis provides a straightforward explanation for both the magnetic field dependence of the Hall signal and the observed change in sign without needing to invoke skyrmions, and thus suggest that caution is needed when making claims of effects from skyrmion phases.

Spontaneous parametric down-conversion (SPDC) has been a key enabling technology in exploring quantum phenomena and their applications for decades. For instance, traditional SPDC, which splits a high-energy pump photon into two lower-energy photons, is a common way to produce entangled photon pairs. Since the early realizations of SPDC, researchers have thought to generalize it to higher order, e.g., to produce entangled photon triplets. However, directly generating photon triplets through a single SPDC process has remained elusive. Here, using a flux-pumped superconducting parametric cavity, we demonstrate direct three-photon SPDC, with photon triplets generated in a single cavity mode or split between multiple modes. With strong pumping, the states can be quite bright, with flux densities exceeding 60 photons per second per hertz. The observed states are strongly non-Gaussian, which has important implications for potential applications. In the single-mode case, we observe a triangular star-shaped distribution of quadrature voltages, indicative of the long-predicted “star state.” The observed state shows strong third-order correlations, as expected for a state generated by a cubic Hamiltonian. By pumping at the sum frequency of multiple modes, we observe strong three-body correlations between multiple modes, strikingly, in the absence of second-order correlations. We further analyze the third-order correlations under mode transformations by the symplectic symmetry group, showing that the observed transformation properties serve to “fingerprint” the specific cubic Hamiltonian that generates them. The observed non-Gaussian, third-order correlations represent an important step forward in quantum optics and may have a strong impact on quantum communication with microwave fields as well as continuous-variable quantum computation.

A microscopic-level understanding of the high-pressure states achieved under shock compression, including comparisons with static compression, is a long-standing and important scientific challenge. Unlike hydrostatic compression, uniaxial strains inherent to shock compression result in plastic deformation and abundant lattice defects. At high pressures ($>50\mathrm{GPa}$), the role of shock-induced deformation and defects remains an open question. Because of the nanosecond time scales in shock experiments, real-time in situ observations of shock-induced lattice defects have been challenging. Here, we present synchrotron x-ray diffraction measurements on laser-shock-compressed gold that provide the first unambiguous in situ measurements of stacking faults (SFs), likely formed by partial dislocations, during shock compression. SF abundance increases monotonically with shock compression up to 150 GPa, where SFs comprise almost every 6th atomic layer. Our results show that SFs play an important role in the plastic deformation of face-centered-cubic metals shocked to high stresses, providing a quantitative benchmark for future theoretical developments.

Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on a novel structure, a “conformal quasicrystal,” that provides a discrete model of conformal geometry. We introduce and construct a class of one-dimensional conformal quasicrystals and discuss a higher-dimensional example (related to the Penrose tiling). Our construction permits discretizations of conformal field theories that preserve an infinite discrete subgroup of the global conformal group at the cost of lattice periodicity.

Few-mode models are a cornerstone of the theoretical work in quantum optics, with the famous single-mode Jaynes-Cummings model being only the most prominent example. In this work, we develop an ab initio few-mode theory, a framework connecting few-mode system-bath models to ab initio methods. We first present a method to derive exact few-mode Hamiltonians for noninteracting quantum potential scattering problems and demonstrate how to rigorously reconstruct the scattering matrix from such few-mode Hamiltonians. We show that, upon inclusion of a background scattering contribution, an ab initio version of the well-known input-output formalism is equivalent to standard scattering theory. On the basis of these exact results for noninteracting systems, we construct an effective few-mode expansion scheme for interacting theories, which allows us to extract the relevant degrees of freedom from a continuum in an open quantum system. As a whole, our results demonstrate that few-mode as well as input-output models can be extended to a general class of problems and open up the associated toolbox to be applied to various platforms and extreme regimes. We outline differences of the ab initio results to standard model assumptions, which may lead to qualitatively different effects in certain regimes. The formalism is exemplified in various simple physical scenarios. In the process, we provide a proof of concept of the method, demonstrate important properties of the expansion scheme, and exemplify new features in extreme regimes.

We show that frustrated quasidoublets without time-reversal symmetry can host highly unconventional magnetic structures with continuously distributed order parameters even in a single-phase crystal. Our study comprises a comprehensive thermodynamic and neutron diffraction investigation on the single crystal of ${\mathrm{TmMgGaO}}_4$, which entails non-Kramers ${\mathrm{Tm}}^{3+}$ ions arranged on a geometrically perfect triangular lattice. The crystal electric field randomness caused by the site-mixing disorder of the nonmagnetic ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Ga}}^{3+}$ ions merges two lowest-lying crystal electric field singlets of ${\mathrm{Tm}}^{3+}$ into a ground-state quasidoublet. Well below $T_c\sim 0.7\mathrm{K}$, a small fraction of the antiferromagnetically coupled ${\mathrm{Tm}}^{3+}$ Ising quasidoublets with small inner gaps condense into two-dimensional up-up-down magnetic structures with continuously distributed order parameters, and give rise to the columnar magnetic neutron reflections below ${\mu }_0{H}_c\sim 2.6\mathrm{T}$, with highly anisotropic correlation lengths, ${\xi }_{ab}\ge 250a$ in the triangular plane and ${\xi }_c<c/12$ between the planes. The remaining fraction of the ${\mathrm{Tm}}^{3+}$ ions remain nonmagnetic at 0 T and become uniformly polarized by the applied longitudinal field at low temperatures. We argue that the similar model can be generally applied to other compounds of non-Kramers rare-earth ions with correlated ground-state quasidoublets.

At its core, quantum mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases. Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature. Neural networks have recently emerged as a powerful tool that can extract nontrivial correlations in vast datasets. These networks routinely outperform state-of-the-art techniques in language translation, medical diagnosis, and image recognition. It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory. Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence, and continuous measurement from physical observations only. The network extracts the system Hamiltonian, measurement operators, and physical parameters. It is also able to perform tomography of an unknown initial state without any prior calibration. This method has the potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback, and optimization of quantum control.

We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified as those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead, their maximum matchings have a monomer density of $81-50\phi \approx 0.098$ in the thermodynamic limit, with $\phi =(1+\sqrt{5})/2$ the golden ratio. Maximum matchings divide the tiling into a fractal of nested closed regions bounded by loops that cannot be crossed by monomers. These loops connect second-nearest-neighbor even-valence vertices, each of which lies on such a loop. Assigning a charge to each monomer with a sign fixed by its bipartite sublattice, we find that each bounded region has an excess of one charge, and a corresponding set of monomers, with adjacent regions having opposite net charge. The infinite tiling is charge neutral. We devise a simple algorithm for generating maximum matchings and demonstrate that maximum matchings form a connected manifold under local monomer-dimer rearrangements. We show that dart-kite Penrose tilings feature an imbalance of charge between bipartite sublattices, leading to a minimum monomer density of $(7-4\phi )/5\approx 0.106$ all of one charge.

Proposals for experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation allows one to treat more difficult problems using fewer qubits and lower gate depths than would otherwise be possible. However, while this approximation captures many important qualitative features, it may leave the results wanting in terms of absolute accuracy (basis error) of the representation. In traditional approaches, increasing this accuracy requires increasing the number of qubits and an appropriate increase in circuit depth as well. Here we explore two techniques requiring no additional qubits or circuit depth that are able to remove much of this approximation in favor of additional measurements. The techniques are constructed and analyzed theoretically, and some numerical proof-of-concept calculations are shown. As an example, we show how to achieve the accuracy of a 20-qubit representation using only four qubits and a modest number of additional measurements for a hydrogen molecule. We close with an outlook on the impact such techniques may have on both near-term and fault-tolerant quantum simulations.