It is frequently hypothesized that cortical networks operate close to a critical point. Advantages of criticality include rich dynamics well suited for computation and critical slowing down, which may offer a mechanism for dynamic memory. However, mean-field approximations, while versatile and popular, inherently neglect the fluctuations responsible for such critical dynamics. Thus, a renormalized theory is necessary. We consider the Sompolinsky-Crisanti-Sommers model which displays a well studied chaotic as well as a magnetic transition. Based on the analog of a quantum effective action, we derive self-consistency equations for the first two renormalized Greens functions. Their self-consistent solution reveals a coupling between the population level activity and single neuron heterogeneity. The quantitative theory explains the population autocorrelation function, the single-unit autocorrelation function with its multiple temporal scales, and cross correlations.

We perform first-principles density functional calculations to elucidate structural, electronic, and magnetic properties at the interface of $\left(0001\right){\mathrm{Cr}}_2{\mathrm{O}}_3-\left(111\right)\mathrm{Pt}$ bilayers. This investigation is motivated by the fact that, despite the promise of ${\mathrm{Cr}}_2{\mathrm{O}}_3-\mathrm{Pt}$ heterostructures in a variety of antiferromagnetic spintronic applications, many key structural, electronic, and magnetic properties at the ${\mathrm{Cr}}_2{\mathrm{O}}_3-\mathrm{Pt}$ interface are poorly understood. We first analyze all inequivalent lateral interface alignments to determine the lowest energy interfacial structure. For all lateral alignments including the lowest energy one, we observe an accumulation of electrons at the interface between ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and Pt. We find an unexpected reversal of the magnetic moments of the interface Cr ions in the presence of Pt compared to surface Cr moments in vacuum-terminated $\left(0001\right){\mathrm{Cr}}_2{\mathrm{O}}_3$. We also find that the heterostructure exhibits a magnetic proximity effect in the first three Pt layers at the interface with ${\mathrm{Cr}}_2{\mathrm{O}}_3$, providing a mechanism by which the anomalous Hall effect can occur in $\left(0001\right){\mathrm{Cr}}_2{\mathrm{O}}_3-\left(111\right)\mathrm{Pt}$ bilayers. Our results provide the basis for a more nuanced interpretation of magnetotransport experiments on $\left(0001\right){\mathrm{Cr}}_2{\mathrm{O}}_3-\left(111\right)\mathrm{Pt}$ bilayers and should inform future development of improved antiferromagnetic spintronic devices based on the ${\mathrm{Cr}}_2{\mathrm{O}}_3-\mathrm{Pt}$ material system.

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of $n$-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance ${\sigma }_N^2\left(R\right)$ associated with a spherical sampling window of radius $R$ (which encodes pair correlations) and an integral measure derived from it ${\mathrm{\Sigma }}_N(R_i,R_j)$ that depends on two specified radial distances $R_i$ and $R_j$. Across the first three space dimensions ($d=1,2,3$), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale $R$. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of $R$. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius $R$ [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in probabilistic graphical models (PGMs) still lack corresponding TN-based adaptations. In this paper, we advance the connection between PGMs and TNs by formulating and implementing tensor-based solutions for the following inference tasks: (A) computing the partition function, (B) computing the marginal probability of sets of variables in the model, (C) determining the most likely assignment to a set of variables, (D) the same as (C) but after having marginalized a different set of variables, and (E) generating samples from a learned probability distribution using a generalized method. Our study is motivated by recent technical advances in the fields of quantum circuit simulation, quantum many-body physics, and statistical physics. Through an experimental evaluation, we demonstrate that the integration of these quantum technologies with a series of algorithms introduced in this study significantly improves the performance efficiency of existing methods for solving probabilistic inference tasks.

In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions $d=1–4$, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions $d=2–8$, which have only recently been made possible due to a highly parallelized algorithm.

Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is nonuniform in real space, accurately representing the state with a limited number of degrees of freedom hinges on appropriately configuring the TN to align with the entanglement pattern. However, a proposal has yet to show a structural search of ER due to its high computational cost and the lack of flexibility in its algorithm. In this study, we conducted an optimal structural search of TN, including ER, based on the reconstruction of their local structures with respect to variational energy. First, we demonstrated that our algorithm for the spin-$1/2$ tetramer singlets model could calculate exact ground energy using the multiscale entanglement renormalization ansatz (MERA) structure as an initial TN structure. Subsequently, we applied our algorithm to the random XY models with the two initial structures: MERA and the suitable structure underlying the strong disordered renormalization group. We found that, in both cases, our algorithm achieves improvements in variational energy, fidelity, and entanglement entropy. The degree of improvement in these quantities is superior in the latter case compared to the former, suggesting that utilizing an existing TN design method as a preprocessing step is important for maximizing our algorithm's performance.

We analyze a quantized pumping in a nonlinear non-Hermitian photonic system with nonadiabatic driving. The photonic system is made of a waveguide array, where the distances between adjacent waveguides are modulated. It is described by the Su-Schrieffer-Heeger model together with a saturated nonlinear gain term and a linear loss term. A topological interface state between the topological and the trivial phases is stabilized by the combination of a saturated nonlinear gain term and a linear loss term. We study the pumping of the topological interface state. We define the transfer-speed ratio $\omega /\mathrm{\Omega }$ by the ratio of the pumping speed $\omega$ of the center of mass of the wave packet to the driving speed $\mathrm{\Omega }$ of the topological interface. It is quantized topologically as $\omega /\mathrm{\Omega }=1$ in the adiabatic limit. It remains to be quantized dynamically unless the driving is not too fast even in the nonadiabatic regime. On the other hand, the wave packet collapses and there is no quantized pumping when the driving is too fast. In addition, the stability against disorder is more enhanced by stronger nonlinearity.

For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation. We describe a general procedure to construct efficient quantum circuits for the cost function evaluation required by VQAs. To mitigate the barren plateau problem during the optimization, we propose an adaptive multigrid strategy. The approach is illustrated for the nonlinear Burgers equation. We classically optimize quantum circuits to represent the desired ground-state solutions, run them on IBM Q System One and Quantinuum System Model H1, and demonstrate that current quantum computers are capable of accurately reproducing the exact results.

Spin squeezing has important applications in the field of quantum metrology and quantum information processing. Here we propose that coherent population trapping is well suitable for establishing cavity dissipation mechanism and generating a spin-squeezed state. An ensemble of $N$ double $\mathrm{\Lambda }$-type atoms is placed inside the two-mode optical cavity, where one $\mathrm{\Lambda }$ subsystem is driven resonantly by two strong control fields to form a dark resonance and the other $\mathrm{\Lambda }$ subsystem is coupled by two cavity vacuum fields and two external fields with large detunings. Due to the dark resonance, the atoms are trapped in a dark state and one has the maximal coherence between the two ground states. Two double off-resonance stimulated Raman scattering interactions are induced between fields and dressed atoms to establish a dissipative quantum dynamical process based on a collective cavity reservoir. As a result, strong stable spin squeezing is generated, which is verified by our numerical and analytical results.

In experiments conducted on a weakly confined 2D assembly of deformable cylinders subject ed to rapid in-plane shear loading, we have identified the key obstacle in achieving compaction. This obstacle involves a dynamic transition between mechanical instabilities, progressing from in-plane rearrangement to out-of-plane popping as the density increases. The popping effect reinforces the frictional constraints from the confining wall and restricts particle mobility, impeding the system from attaining greater compaction. We quantify this transition and demonstrate that interparticle friction contributes to smoothing the transition.

Emitters of single photons are essential resources for emerging quantum technologies and developed within different platforms including nonlinear optics and atomic and solid-state systems. The energy-level structures of emission processes are critical for reaching and controlling high-quality sources. The most commonly applied test uses a Hanbury Brown and Twiss (HBT) setup to determine the emitter energy-level structure based on fitting temporal correlations of photon detection events. However, only partial information about the emission process is extracted from such detection, that might be followed by an inconclusive fitting of the data. This process predetermines our limited ability to quantify and understand the dynamics in the photon emission process that are of importance for the applications in communication, sensing, and computing. In this work, we present a complete analysis based on all normalized coincidences between detection and no-detection events recorded in the same HBT setup to certify expected properties of an emitted photonic state. As a proof of concept we apply our methodology to single nitrogen-vacancy centers in diamond, in which case the certification conclusively rejects a model based on a two-level emitter that radiates a photonic state mixed with any classical noise background.

We present a thorough investigation of the physical properties and superconductivity of the binary intermetallic ${\mathrm{V}}_2{\mathrm{Ga}}_5$. Electrical resistivity and specific heat measurements show that ${\mathrm{V}}_2{\mathrm{Ga}}_5$ enters its superconducting state below $T_{sc}=$ 3.5 K, with a critical field of $H_{\mathrm{c}2,\perp \mathrm{c}}\left(H_{\mathrm{c}2,\left|\right|\mathrm{c}}\right)=6.5\left(4.1\right)$ kOe. With $H\perp c$, the peak effect was observed in resistivity measurements, indicating the ultrahigh quality of the single crystal studied. The resistivity measurements under high pressure reveal that the $T_{sc}$ is suppressed linearly with pressure and reaches absolute zero around 20 GPa. Specific heat and muon spin relaxation measurements indicate that the two-gap $s$-wave model best describes the superconductivity of ${\mathrm{V}}_2{\mathrm{Ga}}_5$. The bands near the Fermi level around the $Z$ and $\mathrm{\Gamma }$ points are observed and analyzed by the angle-resolved photoemission spectroscopy measurements and first-principles band structure calculations. We therefore conclude that ${\mathrm{V}}_2{\mathrm{Ga}}_5$ is a phonon-mediated two-gap $s$-wave superconductor.

The transport and capture of photo-induced electronic excitations is of fundamental interest to the design of energy efficient quantum technologies and to the study of potential quantum effects in biology. Using a simple quantum optical model, we examine the influence of coherence, entanglement, and cooperative dissipation on the transport and capture of excitation energy. We demonstrate that the rate of energy extraction is optimized under conditions that minimize the quantum coherence and entanglement of the system, which is a consequence of spontaneous parity time-reversal symmetry breaking. We then examine the effects of vibrational disorder and show that dephasing can be used to enhance the transport of delocalized excitations in settings relevant to biological photosynthesis. Our results highlight the rich, emergent behavior associated with the quantum-to-classical transition with relevance to the design of room-temperature quantum devices.

Anticipating bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. Before the annihilation of a system's equilibrium point by means of a bifurcation, the system's internal feedbacks that stabilize the initial state weaken and eventually vanish, a process referred to as critical slowing down (CSD). In one-dimensional systems, this motivates the use of variance and lag-1 autocorrelation as indicators of CSD. However, the applicability of variance is limited to time- and state-independent driving noise, strongly constraining the generality of this CSD indicator. In multidimensional systems, the use of these indicators is often preceded by a dimension reduction in order to obtain a one-dimensional time series. Many common techniques for such an extraction of a one-dimensional time series generally incur the risk of missing CSD in practice. Here, we propose a data-driven approach based on estimating a multidimensional Langevin equation to detect local stability changes and anticipate bifurcation-induced transitions in systems with generally time- and state-dependent noise. Our approach substantially generalizes the conditions under which CSD can reliably be detected, as demonstrated in a suite of examples. In contrast to existing approaches, changes in deterministic dynamics can be clearly discriminated from changes in the driving noise using our method. This substantially reduces the risk of false or missed alarms of conventional CSD indicators in settings with time-dependent or multiplicative noise. In multidimensional systems, our method can greatly advance the understanding of the coupling between system components and can avoid risks of missing CSD due to dimension reduction, which existing approaches suffer from.

Information in the form of data, which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded is an important and open problem in many settings. In this work we develop a statistical physics framework that allows one to determine analytically the fair price of information exchanged between players in a game of chance. For definiteness, we consider a game where $N$ players bet on the binary outcome of a stochastic process and share the entry fees pot if successful. We assume that one player holds information about past outcomes of the game, which they may either use exclusively to improve their betting strategy or offer to sell to another player. We find a sharp transition as the number of players $N$ is tuned across a critical value, between a phase where the transaction is always profitable for the seller and one where it may not be. In both phases, different regimes are possible, depending on the “quality” of information being put up for sale: we observe symbiotic regimes, where both parties collude effectively to rig the game in their favor, competitive regimes, where the transaction is unappealing to the data holder as it overly favors a competitor for scarce resources, and even prey-predator regimes, where an exploitative data holder could be giving away bad-quality data to undercut a competitor. Our analytical framework can be generalized to more complex settings and constitutes a flexible tool to address the rich and timely problem of pricing information in games of chance.

We investigate both analytically and numerically the wavepacket's dynamics in momentum space for a Floquet non-Hermitian system with a periodically kicked driven potential. We have deduced the exact expression of a time-evolving wavepacket under the condition of quantum resonance. With this analytical expression, we can investigate thoroughly the temporal behaviors of the directed transport, mean energy, and quantum scrambling. We find interestingly that, by tuning the relative phase between the real part and imaginary part of the kicking potential, one can manipulate the directed transport, mean energy, and quantum scrambling efficiently: When the phase equals to $\pi /2$, we observe a maximum directed transport and mean energy, while a minimum scrambling phenomenon protected by the $\mathcal{PT}$ symmetry; when the phase is $\pi$, both the directed transport and the time dependence of the energy are suppressed; in contrast, the quantum scrambling is enhanced by the non-Hermiticity. For the quantum nonresonance case, we numerically find that the quantum interference effects lead to dynamical localization, characterized by the suppression of the directed transport, the time dependence of the energy, and quantum scrambling. Interestingly, these suppression effects can be adjusted by the phase of the non-Hermitian kicking potential. Possible applications of our findings are discussed.

In this paper, we propose a method for denoising experimental density matrices that combines standard quantum state tomography with an attention-based neural network architecture. The algorithm learns the noise from the data itself, without a priori knowledge of its sources. Firstly, we show how the proposed protocol can improve the averaged fidelity of reconstruction over linear inversion and maximum likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. Next, we demonstrate its use for out-of-distribution data in realistic scenarios. In particular, we consider squeezed states of few spins in the presence of depolarizing noise and measurement/calibration errors and certify its metrologically useful entanglement content. The protocol introduced here targets experiments involving few degrees of freedom and afflicted by a significant amount of unspecified noise. These include NISQ devices and platforms such as trapped ions or photonic qudits.