The Josephson diode (JD) is a nonreciprocal circuit element that supports a larger critical current in one direction compared to the other. This effect has gained growing interest because of promising applications in superconducting electronic circuits with low power consumption. Some implementations of a JD rely on breaking the inversion symmetry in the material used to realize Josephson junctions (JJs), but recent theoretical proposals have suggested that the effect can also be engineered by combining two JJs hosting highly transmitting Andreev bound states in a Superconducting Quantum Interference Device (SQUID) at a small, but finite flux bias. We have realized a SQUID with two JJs fabricated in a proximitized InAs two-dimensional electron gas (2DEG). We demonstrate gate control of the diode efficiency from zero up to around $30\%$ at specific flux bias values which comes close to the maximum of $\sim 40\%$ predicated in Souto et al. [Phys. Rev. Lett. 129, 267702 (2022)]. The key ingredients to the JD effect in the SQUID arrangement is the presence of highly transmitting channels in the JJs, a flux bias, and an asymmetry between the two SQUID arms.

Superconducting circuits constitute a promising platform for future implementation of quantum processors and simulators. Arrays of capacitively coupled transmon qubits naturally implement the Bose-Hubbard model with attractive on-site interaction. The spectrum of such many-body systems is characterized by low-energy localized states defining the lattice analog of bright solitons. Here, we demonstrate that these bright solitons can be pinned in the system, and we find that a soliton moves while maintaining its shape. Its velocity obeys a scaling law in terms of the combined interaction and number of constituent bosons. In contrast, the source-to-drain transport of photons through the array occurs through extended states that have higher energy compared to the bright soliton. For weak coupling between the source or drain and the array, the populations of the source and drain oscillate in time; for chains of even length, their population remains low at all times, while it can reach half the number of total bosons in odd chains. Implications of our results for actual experimental realizations are discussed.

Quantifying the relations (e.g., similarity) between complex networks paves the way for studying the latent information shared across networks. However, fundamental relation metrics are not well-defined between networks. As a compromise, prevalent techniques measure network relations in data-driven manners, which are inapplicable to analytic derivations in physics. To resolve this issue, we present a theory for obtaining an optimal characterization of network topological properties. We show that a network can be fully represented by a Gaussian variable defined by a function of the Laplacian, which simultaneously satisfies network-topology-dependent smoothness and maximum entropy properties. Based on it, we can analytically measure diverse relations between complex networks. As illustrations, we define encoding (e.g., information divergence and mutual information), decoding (e.g., Fisher information), and causality (e.g., Granger causality and conditional mutual information) between networks. We validate our framework on representative networks (e.g., random networks, protein structures, and chemical compounds) to demonstrate that a series of science and engineering challenges (e.g., network evolution, embedding, and query) can be tackled from a new perspective. An implementation of our theory is released as a multiplatform toolbox.

The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order $s\in {\mathbb{R}}_{\ge 0}$. We show that the parameter $s$ can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength.

The benefits of noise to applications of nonlinear dynamical systems through mechanisms such as stochastic and coherence resonances have been well documented. Recent years have witnessed a growth of research in exploiting machine learning to predict nonlinear dynamical systems. It has been known that noise can act as a regularizer to improve the training performance of machine learning. Utilizing reservoir computing as a paradigm, we find that injecting noise to the training data can induce a resonance phenomenon with significant benefits to both short-term prediction of the state variables and long-term prediction of the attractor. The optimal noise level leading to the best performance in terms of the prediction accuracy, stability, and horizon can be identified by treating the noise amplitude as one of the hyperparameters for optimization. The resonance phenomenon is demonstrated using two prototypical high-dimensional chaotic systems.

Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum system is the central question of quantum chaos, but a rigorous quantum notion of ergodicity remains elusive. Closely related to the classical ergodic hierarchy is a less-known notion of cyclic approximate periodic transformations [see, e.g., I. Cornfield, S. Fomin, and Y. Sinai, Ergodic Theory (Springer-Verlag, New York, 1982)], which maps any “ergodic” dynamical system to a cyclic permutation on a circle and arguably represents the most elementary form of ergodicity. This paper shows that cyclic ergodicity generalizes to quantum dynamical systems, and provides a rigorous observable-independent definition of quantum ergodicity. It implies the ability to construct an orthonormal basis, where quantum dynamics transports any initial basis vector to have a sufficiently large overlap with each of the other basis vectors in a cyclic sequence. It is proven that the basis, maximizing the overlap over all such quantum cyclic permutations, is obtained via the discrete Fourier transform of the energy eigenstates, with overlaps given by specific measures of spectral rigidity. This relates quantum cyclic ergodicity to energy level statistics. The level statistics of Wigner-Dyson random matrices, usually associated with quantum chaos on empirical grounds, is derived as a special case of this general relation. To demonstrate generality, we prove that irrational flows on a 2D torus are classical and quantum cyclic ergodic, with spectral rigidity distinct from Wigner-Dyson. Finally, we motivate a quantum ergodic hierarchy of operators and discuss connections to eigenstate thermalization. This work provides a general framework for transplanting some rigorous concepts of ergodic theory to quantum dynamical systems.

Skutterudites are crystals with a cagelike structure that can be augmented with filler atoms (“rattlers”), usually leading to a reduction in thermal conductivity that can be exploited for thermoelectric applications. Here, we leverage the recently introduced Wigner formulation of thermal transport to elucidate the microscopic physics underlying heat conduction in skutterudites, showing that filler atoms can drive a crossover from the Boltzmann to the Wigner regimes of thermal transport, i.e., from particlelike conduction to wavelike tunneling. At temperatures where the thermoelectric efficiency of skutterudites is largest, wavelike tunneling can become comparable to particlelike propagation. We define a Boltzmann deviation descriptor able to differentiate the two regimes and relate the competition between the two mechanisms to the materials' chemistry, providing a design strategy to select rattlers and identify optimal compositions for thermoelectric applications.

The multiterminal Josephson effect aroused considerable interest recently, in connection with theoretical and experimental evidence for correlations among Cooper pairs, that is, the so-called Cooper quartets. It was further predicted that the spectrum of Andreev bound states in such devices could host Weyl-point singularities. However, the relative phase between the Cooper pair and quartet supercurrents has not yet been addressed experimentally. Here, we propose an experiment involving four-terminal Josephson junctions with two independent orthogonal supercurrents, and calculate the critical current contours (CCCs) from a multiterminal Josephson junction circuit theory. We predict a generically $\pi$-shifted contribution of both the local or nonlocal second-order Josephson harmonics. Furthermore, we show that these lead to marked nonconvex shapes for the CCCs in zero magnetic field where the dissipative state reenters into the superconducting one. Eventually, we discuss distinctive features of the nonlocal Josephson processes in the CCCs. The experimental observation of the latter could allow providing firm evidence of the $\pi$-shifted Cooper quartet current-phase relation.

Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of “influence”. While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the computation of nodes' influence, using a low-rank approximation we show that—in a variety of contexts—local and aggregate information about the neighborhoods of nodes is enough to reliably estimate how influential they are without the need to infer or reconstruct the whole map of interactions. Our framework is successful in approximating with high accuracy different incarnations of influence in systems as diverse as the WWW PageRank, trophic levels of ecosystems, upstreamness of industrial sectors in complex economies, and centrality measures of social networks, as long as the underlying network is not exceedingly sparse. We also discuss the implications of this “emerging locality” on the approximate calculation of nonlinear network observables.

We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: A chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output (average value and standard deviation) and efficiency of the engine are derived. We prove the efficiency is controlled by the “local entanglement gap,” the energy difference between the many-body ground state and the lowest-energy eigenstate of the local Hamiltonian. In all the examples analyzed in this work, for a large number of coupled subsystems, the average work output scales linearly or faster and dominates over fluctuations, while the efficiency limits to a constant. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output.

We perform a systematic analysis of continuously polydisperse hard-sphere fluids as a function of the degree of polydispersity within the framework of the mode-coupling theory of the glass transition (MCT). Our results show that a high degree of polydispersity tends to stabilize the liquid phase against vitrification, the magnitude of which depends on the shape of the polydispersity distribution. Furthermore, we report on a separation between the localization lengths of the smallest and largest particles. A diameter-resolved analysis of the intermediate scattering functions reveals that this separation significantly stretches the relaxation patterns, which we quantitatively study by an analysis of the dynamical exponents predicted by the theory. Our observations have strong implications for our understanding of the nature of dynamical heterogeneities and localization lengths in continuously polydisperse systems with hard-core interactions. These results suggest that the dynamics of the smallest particles is of central importance to understand structural relaxation of such systems, already in the mildly supercooled regime where MCT is usually applicable.

State-of-the-art techniques for simulating deeply supercooled liquids require a high degree of size polydispersity to be effective. While these techniques have enabled great insight into the microscopic dynamics near the glass transition, the effect of the large polydispersity on the dynamics has remained largely unstudied. Here we show that a particle's size not only has a strong correlation with its mobility, but we also observe that, as the mode-coupling temperature is crossed and the system becomes more deeply supercooled, a dynamic separation between small mobile and larger quiescent particles emerges at timescales corresponding to cage escape. Our results suggest that the cage escape of this population of mobile particles facilitates the later structural relaxation of the quiescent particles. In the deep supercooled regime, we show that particles of different sizes display varying degrees of breakdown of the Stokes-Einstein relation and have different activation energy barriers. Overall, this indicates that it is important to account for particle-size effects when generalizing results to other glass-forming systems.

The interplay between coherent and dissipative dynamics required in various control protocols of quantum technology has motivated studies of open-system degeneracies, referred to as exceptional points (EPs). Here, we introduce a scheme for fast quantum-state synthesis using exceptional-point engineering in a lossy chain of three superconducting resonators. We theoretically find that the rich physics of EPs can be used to identify regions in the parameter space that favor a fast and quasistable transfer of squeezing and entanglement or a fast reset of the system. For weakly interacting resonators with the coupling strength $g$, the obtained quasistabilization timescales are identified as $1/\left(2\sqrt{2}g\right)$, and reset infidelities below ${10}^{-5}$ are obtained with a waiting time of roughly $6/g$ in the case of weakly squeezed resonators. Our results shed light on the role of EPs in multimode Gaussian systems and pave the way for optimized distribution of squeezing and entanglement between different nodes of a photonic network using dissipation as a resource.

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.

The persistence of spin-polarized fuels is a crucial problem for polarized magnetic and inertial confinement fusion (ICF). The depolarizations of polarized deuterium-tritium (DT) fuels in indirectly driven ICF implosions are investigated with three-dimensional spin transport hydrodynamics simulations. The spin transport equations for deuterons and tritons are derived with the density matrix formalism, which are used to investigate the evolutions of spin eigenstate distributions of DT fuel. The depolarization of DT ions by strong self-generated magnetic fields and the mixings of DT ions with different spin states can be captured by the spin transport equation. The simulation results show that triton polarizations are sensitive to large scale magnetic fields generated by polar mode asymmetries. It is also found that the depolarization of tritons can be reduced by an optimized spin alignment of the polarized fuel. The methods and results can be used to optimize the design of polarized fusion targets and interpret polarized fusion experiments.

Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms. Here, we introduce two approximate quantum-state preparation methods for the noisy intermediate-scale quantum era inspired by the Grover-Rudolph algorithm, which partially solve the problem of loading real functions. Indeed, by allowing for an infidelity $\epsilon$ and under certain smoothness conditions, we prove that the complexity of the implementation of the Grover-Rudolph algorithm without ancillary qubits, first introduced by Möttönen et al., results into $\mathcal{O}\left(2^{k_0\left(\epsilon \right)}\right)$, with $n$ the number of qubits and $k_0\left(\epsilon \right)$ asymptotically independent of $n$. This leads to a dramatic reduction in the number of required two-qubit gates. Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions. Our variational Ansatz is explicitly tailored to the landscape of the function, leading to a quasioptimized number of hyperparameters. This allows us to achieve high fidelity in the loaded state with high speed convergence for the studied examples.