Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard data sets including the Bars and Stripes random binary patterns and the MNIST handwritten digits to illustrate the abilities, features, and drawbacks of our model over popular generative models such as the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.

We present a fundamentally new approach to laboratory acoustic and seismic wave experimentation that enables full immersion of a physical wave propagation experiment within a virtual numerical environment. Using a recent theory of immersive boundary conditions that relies on measurements made on an inner closed surface of sensors, the output of numerous closely spaced sources around the physical domain is continuously varied in time and space. This allows waves to seamlessly propagate back and forth between both domains, without being affected by reflections at the boundaries between both domains, which enables us to virtually expand the size of the physical laboratory and operate at much lower frequencies than previously possible (sonic frequencies as low as 1 kHz). While immersive boundary conditions have been rigorously tested numerically, here we present the first proof of concept for their physical implementation with experimental results from a one-dimensional sound wave tube. These experiments demonstrate the performance and capabilities of immersive boundary conditions in canceling boundary reflections and accounting for long-range interactions with a virtual domain outside the physical experiment. Moreover, we introduce a unique high-performance acquisition, computation, and control system that will enable the real-time implementation of immersive boundary conditions in three dimensions. The system is capable of extrapolating wave fields recorded on 800 simultaneous inputs to 800 simultaneous outputs, through arbitrarily complex virtual background media with an extremely low total system latency of $200\mu \mathrm{s}$. The laboratory allows studying a variety of long-standing problems and poorly understood aspects of wave physics and imaging. Moreover, such real-time immersive experimentation opens up exciting possibilities for the future of laboratory acoustic and seismic experiments and for fields such as active acoustic cloaking and holography.

We observe collective quantum spin states of an ensemble of atoms in a one-dimensional light-atom interface. Strings of hundreds of cesium atoms trapped in the evanescent field of a tapered nanofiber are prepared in a coherent spin state, a superposition of the two clock states. A weak quantum nondemolition measurement of one projection of the collective spin is performed using a detuned probe dispersively coupled to the collective atomic observable, followed by a strong destructive measurement of the same spin projection. For the coherent spin state we achieve the value of the quantum projection noise 40 dB above the detection noise without atoms, well above the 3 dB required for reconstruction of the negative Wigner function of nonclassical states. We analyze the effects of strong spatial inhomogeneity inherent to atoms trapped and probed by the evanescent waves. We furthermore study temporal dynamics of quantum fluctuations relevant for measurement-induced spin squeezing and assess the impact of thermal atomic motion. This work paves the road towards observation of spin-squeezed and entangled states and many-body interactions in 1D spin ensembles.

A remarkable feature of typical ground states of strongly correlated many-body systems is that the entanglement entropy is not an extensive quantity. In one dimension, there exists a proof that a finite correlation length sets a constant upper bound on the entanglement entropy, called the area law. However, the known bound exists only in a hypothetical limit, rendering its physical relevance highly questionable. In this paper, we give a simple proof of the area law for entanglement entropy in one dimension under the condition of exponentially decaying correlations. Our proof dramatically reduces the previously known bound on the entanglement entropy, bringing it into a realistic regime for the first time. The proof is composed of several simple and straightforward steps based on elementary quantum information tools. We discuss the underlying physical picture, based on a renormalization-like construction underpinning the proof, which transforms the entanglement entropy of a continuous region into a sum of mutual information in different length scales and the entanglement entropy at the boundary.

We consider a scenario where we wish to bring a closed system of known Hilbert space dimension $d_S$ (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time $t_0$. The target is out of our control: This means that we ignore both its free Hamiltonian and how the system interacts with other quantum systems we may use to influence it. Under these conditions, we prove that there exist protocols within the framework of nonrelativistic quantum physics that reset the target system to its exact quantum state at $t_0$. Each “resetting protocol” is successful with nonzero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure. When the target is a qubit and the interaction is sampled from the Haar measure, the simplest resetting circuits have a significant average probability of success and their implementation is within reach of current quantum technologies. Finally, we find that, in case the resetting protocol fails, it is possible to run a further protocol that, if successful, undoes both the natural evolution of the target and the effects of the failed protocol over the latter. By chaining in this fashion several such protocols, one can substantially increase the overall probability of a successful resetting.

Connecting nanoscale mechanical resonators to microwave quantum circuits opens new avenues for storing, processing, and transmitting quantum information. In this work, we couple a phononic crystal cavity to a tunable superconducting quantum circuit. By fabricating a one-dimensional periodic pattern in a thin film of lithium niobate and introducing a defect in this artificial lattice, we localize a 6-GHz acoustic resonance to a wavelength-scale volume of less than 1 cubic micron. The strong piezoelectricity of lithium niobate efficiently couples the localized vibrations to the electric field of a widely tunable high-impedance Josephson junction array resonator. We measure a direct phonon-photon coupling rate $g/2\pi \approx 1.6\mathrm{MHz}$ and a mechanical quality factor $Q_m\approx 3\times {10}^4$, leading to a cooperativity $C\sim 4$ when the two modes are tuned into resonance. Our work has direct application to engineering hybrid quantum systems for microwave-to-optical conversion as well as emerging architectures for quantum information processing.

Recent theories predict that discontinuous shear thickening (DST) involves an instability, the nature of which remains elusive. Here, we explore unsteady dynamics in a dense cornstarch suspension by coupling long rheological measurements under constant shear stresses to ultrasound imaging. We demonstrate that unsteadiness in DST results from localized bands that travel along the vorticity direction with a specific signature on the global shear rate response. These propagating events coexist with quiescent phases for stresses slightly above DST onset, resulting in intermittent, turbulentlike dynamics. Deeper into DST, events proliferate, leading to simpler, Gaussian dynamics. We interpret our results in terms of unstable vorticity bands as inferred from recent model and numerical simulations.

In this work (multipartite) entanglement, discord, and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, local operations, and classical communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows us to consider a reduced setting as well, namely, the one with only the wire connected to a single quantum system, which leads to discordlike resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound—and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement.

The description of the dynamics of an electron in an external electromagnetic field of arbitrary intensity is one of the most fundamental outstanding problems in electrodynamics. Remarkably, to date, there is no unanimously accepted theoretical solution for ultrahigh intensities and little or no experimental data. The basic challenge is the inclusion of the self-interaction of the electron with the field emitted by the electron itself—the so-called radiation reaction force. We report here on the experimental evidence of strong radiation reaction, in an all-optical experiment, during the propagation of highly relativistic electrons (maximum energy exceeding 2 GeV) through the field of an ultraintense laser (peak intensity of $4\times {10}^{20}\mathrm{W}/{\mathrm{cm}}^2$). In their own rest frame, the highest-energy electrons experience an electric field as high as one quarter of the critical field of quantum electrodynamics and are seen to lose up to 30% of their kinetic energy during the propagation through the laser field. The experimental data show signatures of quantum effects in the electron dynamics in the external laser field, potentially showing departures from the constant cross field approximation.

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination require classifying the manifolds in a manner that is insensitive to variability within a manifold. How neuronal systems give rise to invariant object classification and recognition is a fundamental problem in brain theory as well as in machine learning. Here, we study the ability of a readout network to classify objects from their perceptual manifold representations. We develop a statistical mechanical theory for the linear classification of manifolds with arbitrary geometry, revealing a remarkable relation to the mathematics of conic decomposition. We show how special anchor points on the manifolds can be used to define novel geometrical measures of radius and dimension, which can explain the classification capacity for manifolds of various geometries. The general theory is demonstrated on a number of representative manifolds, including ${\ell }_2$ ellipsoids prototypical of strictly convex manifolds, ${\ell }_1$ balls representing polytopes with finite samples, and ring manifolds exhibiting nonconvex continuous structures that arise from modulating a continuous degree of freedom. The effects of label sparsity on the classification capacity of general manifolds are elucidated, displaying a universal scaling relation between label sparsity and the manifold radius. Theoretical predictions are corroborated by numerical simulations using recently developed algorithms to compute maximum margin solutions for manifold dichotomies. Our theory and its extensions provide a powerful and rich framework for applying statistical mechanics of linear classification to data arising from perceptual neuronal responses as well as to artificial deep networks trained for object recognition tasks.

In the Dirac-Weyl semimetal, the chiral anomaly appears as an “axial” current arising from charge pumping between the lowest (chiral) Landau levels of the Weyl nodes, when an electric field is applied parallel to a magnetic field $\mathbf{B}$. Evidence for the chiral anomaly was obtained from the longitudinal magnetoresistance (LMR) in ${\mathrm{Na}}_3\mathrm{Bi}$ and GdPtBi. However, current-jetting effects (focusing of the current density $\mathbf{J}$) have raised general concerns about LMR experiments. Here, we implement a litmus test that allows the intrinsic LMR in ${\mathrm{Na}}_3\mathrm{Bi}$ and GdPtBi to be sharply distinguished from pure current-jetting effects (in pure Bi). Current jetting enhances $J$ along the mid-line (spine) of the sample while decreasing it at the edge. We measure the distortion by comparing the local voltage drop at the spine (expressed as the resistance $R_{\text{spine}}$) with that at the edge ($R_{\text{edge}}$). In Bi, $R_{\text{spine}}$ sharply increases with $B$, but $R_{\text{edge}}$ decreases (jetting effects are dominant). However, in ${\mathrm{Na}}_3\mathrm{Bi}$ and GdPtBi, both $R_{\text{spine}}$ and $R_{\text{edge}}$ decrease (jetting effects are subdominant). A numerical simulation allows the jetting distortions to be removed entirely. We find that the intrinsic longitudinal resistivity ${\rho }_{xx}(B)$ in ${\mathrm{Na}}_3\mathrm{Bi}$ decreases by a factor of 10.9 between $B=0$ and 10 T. A second litmus test is obtained from the parametric plot of the planar angular magnetoresistance. These results considerably strengthen the evidence for the intrinsic nature of the chiral-anomaly-induced LMR. We briefly discuss how the squeeze test may be extended to test ${\mathrm{ZrTe}}_5$.

The spin-$1/2$ triangular lattice antiferromagnet ${\mathrm{YbMgGaO}}_4$ has attracted attention recently as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field-polarized state of ${\mathrm{YbMgGaO}}_4$ to obtain better insight of its exchange interactions. Terahertz spectroscopy in this fashion functions as a high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4 T, informed by the analysis of the terahertz spectroscopy linewidths, yields constraints on the disorder-averaged $g$ factors and exchange interactions. Our results paint ${\mathrm{YbMgGaO}}_4$ as an easy-plane $XXZ$ antiferromagnet with the combined and necessary presence of subleading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained $g$ factors are substantially different from previous reports. This work establishes the hierarchy of exchange interactions in ${\mathrm{YbMgGaO}}_4$ from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology.

Photonic time-bin qubits are well suited to transmission via optical fibers and waveguide circuits. The states take the form $\frac{1}{\sqrt{(2)}}(\alpha |0⟩+e^{i\varphi }\beta |1⟩)$, with $|0⟩$ and $|1⟩$ referring to the early and late time bin, respectively. By controlling the phase of a laser driving a spin-flip Raman transition in a single-hole-charged InAs quantum dot, we demonstrate complete control over the phase, $\varphi$. We show that this photon generation process can be performed deterministically, with only a moderate loss in coherence. Finally, we encode different qubits in different energies of the Raman scattered light, paving the way for wavelength-division multiplexing at the single-photon level.

The generation of abnormal excitations in pathological regions of the heart is a main trigger for lethal cardiac arrhythmias. Such abnormal excitations, also called ectopic activity, often arise from areas with local tissue heterogeneity or damage accompanied by localized depolarization. Finding the conditions that lead to ectopy is important to understand the basic biophysical principles underlying arrhythmia initiation and might further refine clinical procedures. In this study, we are the first to address the question of how geometry of the abnormal region affects the onset of ectopy using a combination of experimental, in silico, and theoretical approaches. We paradoxically find that, for any studied geometry of the depolarized region in optogenetically modified monolayers of cardiac cells, primary ectopic excitation originates at areas of maximal curvature of the boundary, where the stimulating electrotonic currents are minimal. It contradicts the standard critical nucleation theory applied to nonlinear waves in reaction-diffusion systems, where a higher stimulus is expected to produce excitation more easily. Our in silico studies reveal that the nonconventional ectopic activity is caused by an oscillatory instability at the boundary of the damaged region, the occurrence of which depends on the curvature of that boundary. The onset of this instability is confirmed using the Schrödinger equation methodology proposed by Rinzel and Keener [SIAM J. Appl. Math. 43, 907 (1983)]. Overall, we show distinctively novel insight into how the geometry of a heterogeneous cardiac region determines ectopic activity, which can be used in the future to predict the conditions that can trigger cardiac arrhythmias.

The interaction between water protons and suitable quadrupolar nuclei (QN) can lead to quadrupole relaxation enhancement (QRE) of proton spins, provided the resonance condition between both spin transitions is fulfilled. This effect could be utilized as a frequency selective mechanism in novel, responsive $T_1$ shortening contrast agents (CAs) for magnetic resonance imaging (MRI). In particular, the proposed contrast mechanism depends on the applied external flux density—a property that can be exploited by special field-cycling MRI scanners. For the design of efficient CA molecules, exhibiting narrow and pronounced peaks in the proton $T_1$ relaxation dispersion, the nuclear quadrupole resonance (NQR) properties, as well as the spin dynamics of the system $\mathrm{QN}\text{−}{}^1\mathrm{H}$, have to be well understood and characterized for the compounds in question. In particular, the energy-level structure of the QN is a central determinant for the static flux densities at which the contrast enhancement appears. The energy levels depend both on the QN and the electronic environment, i.e., the chemical bonding structure in the CA molecule. In this work, the NQR properties of a family of promising organometallic compounds containing ${}^{209}\mathrm{Bi}$ as QN have been characterized. Important factors like temperature, chemical structure, and chemical environment have been considered by NQR spectroscopy and ab initio quantum chemistry calculations. The investigated Bi-aryl compounds turned out to fulfill several crucial requirements: NQR transition frequency range applicable to clinical 1.5- and 3 T MRI systems, low temperature dependency, low toxicity, and tunability in frequency by chemical modification.

Knitting is not only a mere art and craft hobby but also a thousand-year-old technology. Unlike weaving, it can produce loose yet extremely stretchable fabrics with almost vanishing rigidity, a desirable property exhibited by hardly any bulk material. It also enables the engineering of arbitrarily shaped two- and three-dimensional objects with tunable mechanical response. In contrast with the extensive body of related empirical knowledge and despite a growing industrial interest, the physical ingredients underlying these intriguing mechanical properties remain poorly understood. To make some progress in this direction, we study a model tricot made of a single elastic thread knitted into a common pattern called stockinette. On the one hand, we experimentally investigate its tensile response and measure local displacements of the stitches during deformation. On the other hand, we derive a first-principle mechanical model for the displacement field based on the yarn-bending energy, the conservation of its total length, and the topological constraints on the constitutive stitches. Our model solves both the shape and mechanical response of the knit and agrees quantitatively with our measurements. This study thus provides a fundamental framework for the understanding of knitted fabrics, paving the way to thread-based smart materials.

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in $1+1\mathrm{D}$ bosonic systems, there is no nontrivial topological order, while in $2+1\mathrm{D}$ bosonic systems, the topological orders are classified by the following pair: a modular tensor category and a chiral central charge. In this paper, following a new line of thinking, we find that in $3+1\mathrm{D}$ the classification is much simpler than it was thought to be; we propose a partial classification of topological orders for $3+1\mathrm{D}$ bosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair $(G,{\omega }_4)$: a finite group $G$ and its group 4-cocycle ${\omega }_4\in {\mathcal{H}}^4[G;U(1)]$ (up to group automorphisms). Furthermore, all such $3+1\mathrm{D}$ topological orders can be realized by Dijkgraaf-Witten gauge theories.

Interference experiments provide a simple yet powerful tool to unravel fundamental features of quantum physics. Here we engineer a driven, time-dependent bilinear coupling that can be tuned to implement a robust $50:50$ beam splitter between stationary states stored in two superconducting cavities in a three-dimensional architecture. With this, we realize high-contrast Hong-Ou-Mandel interference between two spectrally detuned stationary modes. We demonstrate that this coupling provides an efficient method for measuring the quantum state overlap between arbitrary states of the two cavities. Finally, we showcase concatenated beam splitters and differential phase shifters to implement cascaded Mach-Zehnder interferometers, which can control the signature of the two-photon interference on demand. Our results pave the way toward implementation of scalable boson sampling, the application of linear optical quantum computing protocols in the microwave domain, and quantum algorithms between long-lived bosonic memories.

Creating large-scale entanglement lies at the heart of many quantum information processing protocols and the investigation of fundamental physics. For multipartite quantum systems, it is crucial to identify not only the presence of entanglement but also its detailed structure. This is because in a generic experimental situation with sufficiently many subsystems involved, the production of so-called genuine multipartite entanglement remains a formidable challenge. Consequently, focusing exclusively on the identification of this strongest type of entanglement may result in an all or nothing situation where some inherently quantum aspects of the resource are overlooked. On the contrary, even if the system is not genuinely multipartite entangled, there may still be many-body entanglement present in the system. An identification of the entanglement structure may thus provide us with a hint about where imperfections in the setup may occur, as well as where we can identify groups of subsystems that can still exhibit strong quantum-information-processing capabilities. However, there is no known efficient methods to identify the underlying entanglement structure. Here, we propose two complementary families of witnesses for the identification of such structures. They are based, respectively, on the detection of entanglement intactness and entanglement depth, each applicable to an arbitrary number of subsystems and whose evaluation requires only the implementation of solely two local measurements. Our method is also robust against noises and other imperfections, as reflected by our experimental implementation of these tools to verify the entanglement structure of five different eight-photon entangled states. In particular, we demonstrate how their entanglement structure can be precisely and systematically inferred from the experimental measurement of these witnesses. In achieving this goal, we also illustrate how the same set of data can be classically postprocessed to learn the most about the measured system.

Turing’s theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry, and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the mechanisms of pattern selection, are well understood in small networks. However, a general set of rules explaining how network topology determines fundamental system properties and constraints has not been found. Here we provide a first general theory of Turing network topology, which proves why three key features of a Turing system are directly determined by the topology: the type of restrictions that apply to the diffusion rates, the robustness of the system, and the phase relations of the molecular species.