The theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian describing these circuits. In many simplified versions of these networks, the modeling involves a singular Lagrangian that employs Kirchhoff’s laws to eliminate inherent constraints of the system. In this work, we demonstrate the failure of such singular theories for the quantization of realistic, nearly singular superconducting circuits. Instead, we rigorously prove the validity of a perturbative analysis within the Born-Oppenheimer approximation. In particular, we find that the limiting behavior of the low-energy dynamics obtained from the regularized approach exhibits a fixed-point structure flowing to one of a few universal fixed points as parasitic capacitance values go to zero. This singular limit of the regularized analysis is, in many cases, completely unlike the singular theory. Consequently, we conclude that classical network synthesis techniques which build on Kirchhoff’s laws must be critically examined prior to applying circuit quantization.

We report the experimental observation of the spin-wave moiré edge and cavity modes using Brillouin light scattering spectromicroscopy in a nanostructured magnetic moiré lattice consisting of two twisted triangle antidot lattices based on an yttrium iron garnet thin film. Spin-wave moiré edge modes are detected at an optimal twist angle and with a selective excitation frequency. At a given twist angle, the magnetic field acts as an additional degree of freedom for tuning the chiral behavior of the magnon edge modes. Micromagnetic simulations indicate that the edge modes emerge within the original magnonic band gap and at the intersection between a mini flatband and a propagation magnon branch. Our theoretical estimate for the Berry curvature of the magnon-magnon coupling suggests a nontrivial topology for the chiral edge modes and confirms the key role played by the dipolar interaction. Our findings shed light on the topological nature of the magnon edge mode for emergent moiré magnonics.

The correlation functions of quantum systems—central objects in quantum field theories—are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the application of sophisticated many-body theories to interesting problems. Here, we propose a multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains (QTTs), “qubits” describing exponentially different length scales. The ansatz then assumes a separation of length scales by decomposing the resulting high-dimensional tensors into tensor trains (also known as matrix product states). We numerically verify the ansatz for various equilibrium and nonequilibrium systems and demonstrate compression ratios of several orders of magnitude for challenging cases. Essential building blocks of diagrammatic equations, such as convolutions or Fourier transforms, are formulated in the compressed form. We numerically demonstrate the stability and efficiency of the proposed methods for the Dyson and Bethe-Salpeter equations. The QTT representation provides a unified framework for implementing efficient computations of quantum field theories.

We present results from three-dimensional hybrid-kinetic simulations of Alfvénic turbulence in a high-$\beta$, collisionless plasma. The key feature of such turbulence is the interplay between local wave-wave interactions between the fluctuations in the cascade and the nonlocal wave-particle interactions associated with kinetic microinstabilities driven by anisotropy in the thermal pressure (namely, firehose, mirror, and ion cyclotron). We present theoretical estimates for, and calculate directly from the simulations, the effective collisionality and plasma viscosity in pressure-anisotropic high-$\beta$ turbulence, demonstrating that, for strong Alfvénic turbulence, the effective parallel-viscous scale is comparable to the driving scale of the cascade. Below this scale, the kinetic-energy spectrum indicates an Alfvénic cascade with a slope steeper than $-5/3$ due to the anisotropic viscous stress. The magnetic-energy spectrum is shallower than $-5/3$ near the ion-Larmor scale due to fluctuations produced by the firehose instability. Most of the cascade energy ($\approx 80\%–90\%$) is dissipated as ion heating through a combination of Landau damping and anisotropic viscous heating. Our results have implications for models of particle heating in low-luminosity accretion onto supermassive black holes, the effective viscosity of the intracluster medium, and the interpretation of near-Earth solar-wind observations.

Orbital degrees of freedom play an essential role in metals, semiconductors, and strongly confined electronic systems. Experiments with ultracold atoms have used highly anisotropic confinement to explore low-dimensional physics, but they typically eliminate orbital degrees of freedom by preparing atoms in the motional ground states of the strongly confined directions. Here, we prepare multiband systems of spin-polarized fermionic potassium (${}^{40}\mathrm{K}$) in the quasi-one-dimensional (q1D) regime and quantify the strength of atom-atom correlations using radio-frequency spectroscopy. The activation of orbital degrees of freedom leads to a new phenomenon: a low-energy scattering channel that has even particle-exchange parity along the q1D axis, as if the underlying interactions were $s$-wave. This emergent exchange symmetry is enabled by orbital singlet wave functions in the strongly confined directions, which also confer high-momentum components to low-energy q1D collisions. We measure both the q1D odd-wave and even-wave “contact” parameters for the first time and compare them to theoretical predictions of one-dimensional many-body models. The strength and spatial symmetry of interactions are tuned by a $p$-wave Feshbach resonance and by transverse confinement strength. Near resonance, the even-wave contact approaches its theoretical unitary value, whereas the maximum observed odd-wave contact remains several orders of magnitude below its unitary limit. Low-energy scattering channels of multi-orbital systems, such as those found here, may provide new routes for the exploration of universal many-body phenomena.

Since the discovery of magic-angle twisted bilayer graphene, flat bands in Dirac materials have become a prominent platform for realizing strong correlation effects in electronic systems. Here we show that the symmetry group protecting the Dirac cone in such materials determines whether a Dirac band may be flattened by the tuning of a small number of parameters. We devise a criterion that, given a symmetry group, allows for the calculation of the number of parameters required to make the Dirac velocity vanish. This criterion is employed to study band flattening in twisted bilayer graphene and in surface states of 3D topological insulators. Following this discussion, we identify the symmetries under which the vanishing of the Dirac velocity implies the emergence of perfectly flat bands. Our analysis allows us to construct additional model Hamiltonians that display perfectly flat bands at certain points in the space of parameters: the first is a toy model of two coupled 3D topological insulator surfaces, and the second is a quasicrystalline generalization of the chiral model of twisted bilayer graphene.

The planted-coloring problem is a prototypical inference problem for which thresholds for Bayes-optimal algorithms, like belief propagation (BP), can be computed analytically. In this paper, we analyze the limits and performances of simulated annealing (SA), a Monte-Carlo-based algorithm that is more general and robust than BP, and thus of broader applicability. We show that SA is suboptimal in the recovery of the planted solution because it gets attracted by glassy states that, instead, do not influence the BP algorithm. At variance with previous conjectures, we propose an analytic estimation for the SA algorithmic threshold by comparing the spinodal point of the paramagnetic phase and the dynamical critical temperature. This is a fundamental connection between thermodynamical phase transitions and out-of-equilibrium behavior of Glauber dynamics. We also study an improved version of SA, called replicated SA (RSA), where several weakly coupled replicas are cooled down together. We show numerical evidence that the algorithmic threshold for the RSA coincides with the Bayes-optimal one. Finally, we develop an approximated analytical theory explaining the optimal performances of RSA and predicting the location of the transition toward the planted solution in the limit of a very large number of replicas. Our results for RSA support the idea that mismatching the parameters in the prior with respect to those of the generative model may produce an algorithm that is optimal and very robust.

Kinetoplast DNA (kDNA) is a two-dimensional Olympic-ring-like network of mutually linked DNA minicircles found in certain parasites called trypanosomes. Understanding the self-assembly and replication of this structure are not only major open questions in biology but can also inform the design of synthetic topological materials. Here, we report the first high-resolution, single-molecule study of kDNA network topology using AFM and steered molecular dynamics simulations. We map out the DNA density within the network and the distribution of linking number and valence of the minicircles. We also characterize the DNA hubs that surround the network and show that they cause a buckling transition akin to that of a 2D elastic thermal sheet in the bulk. Intriguingly, we observe a broad distribution of density and valence of the minicircles, indicating heterogeneous network structure and individualism of different kDNA structures. Finally, we estimate the 2D Young modulus of the network to be orders of magnitude smaller than that of other 2D materials. Our findings explain outstanding questions in the field and offer single-molecule insights into the properties of a unique topological material.

The 3D Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the 2D Ising transition. Yet, the emergence of conformal invariance in the 3D Ising transition has rarely been explored directly, mainly due to unavoidable mathematical or conceptual obstructions. Here, we design an innovative way to study the quantum version of the 3D Ising phase transition on spherical geometry, using the “fuzzy (noncommutative) sphere” regularization. We accurately calculate and analyze the energy spectra at the transition, and explicitly demonstrate the state-operator correspondence (i.e., radial quantization), a fingerprint of conformal field theory. In particular, we identify13 parity-even primary operators within a high accuracy and two parity-odd operators that were not known before. Our result directly elucidates the emergent conformal symmetry of the 3D Ising transition, a conjecture made by Polyakov half a century ago. More importantly, our approach opens a new avenue for studying 3D conformal field theories by making use of the state-operator correspondence and spherical geometry.

Alkali-doped fullerides are strongly correlated organic superconductors that exhibit high transition temperatures, exceptionally large critical magnetic fields, and a number of other unusual properties. The proximity to a Mott insulating phase is thought to be a crucial ingredient of the underlying physics and may also affect precursors of superconductivity in the normal state above $T_c$. We report on the observation of a sizable magneto-thermoelectric (Nernst) effect in the normal state of ${\mathrm{K}}_3{\mathrm{C}}_{60}$, which displays the characteristics of superconducting fluctuations. This nonquasiparticle Nernst effect emerges from an ordinary quasiparticle background below a temperature of 80 K, far above $T_c=20\mathrm{K}$. At the lowest fields and close to $T_c$, the scaling of the effect is captured by a model based on Gaussian fluctuations. The behavior at higher magnetic fields displays a symmetry between the magnetic length and the correlation length of the system. The temperature up to which we observe fluctuations is exceptionally high for a three-dimensional isotropic system, where fluctuation effects are expected to be suppressed.

Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.

Biological constraints often impose restrictions on plasticity rules such as locality and reward-based rather than supervised learning. Two learning rules that comply with these restrictions are weight (WP) and node (NP) perturbation. NP is often used in learning studies, in particular, as a benchmark; it is considered to be superior to WP and more likely neurobiologically realized, as the number of weights and, therefore, their perturbation dimension typically massively exceed the number of nodes. Here, we show that this conclusion no longer holds when we take two properties into account that are relevant for biological and artificial neural network learning: First, tasks extend in time and/or are trained in batches. This increases the perturbation dimension of NP but not WP. Second, tasks are (comparably) low dimensional, with many weight configurations providing solutions. We analytically delineate regimes where these properties let WP perform as well as or better than NP. Furthermore, we find that the changes in weight space directions that are irrelevant for the task differ qualitatively between WP and NP and that only in WP gathering batches of subtasks in a trial decreases the number of trials required. This may allow one to experimentally distinguish which of the two rules underlies a learning process. Our insights suggest new learning rules which combine for specific task types the advantages of WP and NP. If the inputs are similarly correlated, temporally correlated perturbations improve NP. Using numerical simulations, we generalize the results to networks with various architectures solving biologically relevant and standard network learning tasks. Our findings, together with WP’s practicability, suggest WP as a useful benchmark and plausible model for learning in the brain.

We use Monte Carlo and genetic algorithms to train neural-network feedback-control protocols for simulated fluctuating nanosystems. These protocols convert the information obtained by the feedback process into heat or work, allowing the extraction of work from a colloidal particle pulled by an optical trap and the absorption of entropy by an Ising model undergoing magnetization reversal. The learning framework requires no prior knowledge of the system, depends only upon measurements that are accessible experimentally, and scales to systems of considerable complexity. It could be used in the laboratory to learn protocols for fluctuating nanosystems that convert measurement information into stored work or heat.

Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly susceptible to photon loss, which inevitably diminishes their quantum non-Gaussian features. Here, we protect these non-Gaussian features against photon loss by compressing the phase-space distribution of a cat state. We achieve this compression with a deterministic technique based on the echoed conditional displacement operation in a circuit QED device. We present a versatile technique for creating robust non-Gaussian continuous-variable resource states in a highly linear bosonic mode and manipulating their phase-space distribution to achieve enhanced resilience against photon loss. Such compressed cat states offer an attractive avenue for obtaining new insights into quantum foundations and quantum metrology, as well as for developing inherently more protected bosonic code words for quantum error correction.

A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make it easier to interpret the significant latent factors of variation in the data, as well as to generate new data with desirable features. The methods for disentangling representations often rely on an adversarial scheme, in which representations are tuned to avoid discriminators from being able to reconstruct information about the data properties (labels). Unfortunately, adversarial training is generally difficult to implement in practice. Here we propose a simple, effective way of disentangling representations without any need to train adversarial discriminators and apply our approach to Restricted Boltzmann Machines, one of the simplest representation-based generative models. Our approach relies on the introduction of adequate constraints on the weights during training, which allows us to concentrate information about labels on a small subset of latent variables. The effectiveness of the approach is illustrated with four examples: the CelebA dataset of facial images, the two-dimensional Ising model, the MNIST dataset of handwritten digits, and the taxonomy of protein families. In addition, we show how our framework allows for analytically computing the cost, in terms of the log-likelihood of the data, associated with the disentanglement of their representations.

As experiments continue to increase in size and scope, a fundamental challenge of subsequent analyses is to recast the wealth of information into an intuitive and readily interpretable form. Often, each measurement conveys only the relationship between a pair of entries, and it is difficult to integrate these local interactions across a dataset to form a cohesive global picture. The classic localization problem tackles this question, transforming local measurements into a global map that reveals the underlying structure of a system. Here, we examine the more challenging bipartite localization problem, where pairwise distances are available only for bipartite data comprising two classes of entries (such as antibody-virus interactions, drug-cell potency, or user-rating profiles). We modify previous algorithms to solve bipartite localization and examine how each method behaves in the presence of noise, outliers, and partially observed data. As a proof of concept, we apply these algorithms to antibody-virus neutralization measurements to create a basis set of antibody behaviors, formalize how potently inhibiting some viruses necessitates weakly inhibiting other viruses, and quantify how often combinations of antibodies exhibit degenerate behavior.

Entanglement distribution via photons over long distances enables many applications, including quantum key distribution, which provides unprecedented privacy. The inevitable degradation of entanglement through noise accumulated over long distances remains one of the key challenges in this area. Exploiting the potential of higher-dimensional entangled photons promises to address this challenge, but poses extreme demands on the experimental implementation. Here, we present a long-range free-space quantum link, distributing entanglement over 10.2 km with flexible dimensionality of encoding by deploying a phase-stable nonlocal Franson interferometer. With this distribution of multidimensional energy-time entangled photons, we analyze the achievable key rate in a dimensionally adaptive quantum key distribution protocol that can be optimized with respect to any environmental noise conditions. Our approach enables and emphasizes the power of high-dimensional entanglement for quantum communication, yielding a positive asymptotic key rate well into the dawn of the day.

Ultralight axionlike particles can contribute to the dark matter near the Sun, leading to a distinct, stochastic signature in terrestrial experiments. We search for such particles through their neutron-spin coupling by reanalyzing approximately 40 days of data from a K-${}^3\mathrm{He}$ comagnetometer with a new frequency-domain likelihood-based formalism that properly accounts for stochastic effects over all axion coherence times relative to the experimental time span. Assuming that axions make up all of the dark matter in the Sun’s vicinity, we find a median 95% upper limit on the neutron-spin coupling of $2.4\times {10}^{-10}{\mathrm{GeV}}^{-1}$ for most axion masses from 0.4 to 4 feV, which is about 5 orders of magnitude more stringent than previous laboratory bounds in that mass range. Although several peaks in the experiment’s magnetic power spectrum suggest the rejection of a white-noise null hypothesis, further analysis of their line shapes yields no positive evidence for a dark-matter axion.

A central challenge in analog quantum simulation is to characterize desirable physical properties of quantum states produced in experiments. However, in conventional approaches, the extraction of arbitrary information requires performing measurements in many different bases, which necessitates a high level of control that present-day quantum devices may not have. Here, we propose and analyze a scalable protocol that leverages the ergodic nature of generic quantum dynamics, enabling the efficient extraction of many physical properties. The protocol does not require sophisticated controls and can be generically implemented in analog quantum simulation platforms today. Our protocol involves introducing ancillary degrees of freedom in a predetermined state to a system of interest, quenching the joint system under Hamiltonian dynamics native to the particular experimental platform, and then measuring globally in a single, fixed basis. We show that arbitrary information of the original quantum state is contained within such measurement data and can be extracted using a classical data-processing procedure. We numerically demonstrate our approach with a number of examples, including the measurements of entanglement entropy, many-body Chern number, and various superconducting orders in systems of neutral atom arrays, bosonic and fermionic particles on optical lattices, respectively, only assuming existing technological capabilities. Our protocol excitingly promises to overcome limited controllability and, thus, enhance the versatility and utility of near-term quantum technologies.