We present an ab initio correlated approach to study molecules that interact strongly with quantum fields in an optical cavity. Quantum electrodynamics coupled cluster theory provides a nonperturbative description of cavity-induced effects in ground and excited states. Using this theory, we show how quantum fields can be used to manipulate charge transfer and photochemical properties of molecules. We propose a strategy to lift electronic degeneracies and induce modifications in the ground-state potential energy surface close to a conical intersection.

In recent years, social media has become an important platform for political discourse, being a site of both political conversations between voters and political advertisements from campaigns. While their individual influences on public discourse are well documented, the interplay between individual-level cognitive biases, social influence processes, dueling campaign efforts, and social media platforms remains unexamined. We introduce an agent-based model that integrates these dynamics and illustrates how their combination can lead to the formation of echo chambers. We find that the range of political viewpoints that individuals are willing to consider is a key determinant in the formation of polarized networks and the emergence of echo chambers and show that aggressive political campaigns can have counterproductive outcomes by radicalizing supporters and alienating moderates. Our model results demonstrate how certain elements of public discourse and political polarization can be understood as the result of an interactive process of shifting individual opinions, evolving social networks, and political campaigns. We also introduce a dynamic empirical case, retweet networks from the final stage of the 2016 U.S. presidential election, to show how our proposed model can be calibrated with real-world behavior.

We study the low-frequency properties of the bulk photovoltaic effect in topological semimetals. The bulk photovoltaic effect is a nonlinear optical effect that generates dc photocurrents under uniform irradiation, which is allowed by noncentrosymmetry. It is a promising mechanism for a terahertz photodetection based on topological semimetals. Here, we systematically investigate the low-frequency behavior of the second-order optical conductivity in point-node semimetals. Through symmetry and power-counting analysis, we show that Dirac and Weyl points with tilted cones show the leading low-frequency divergence. In particular, we find new divergent behaviors of the conductivity of Dirac and Weyl points under circularly polarized light, where the conductivity scales as ${\omega }^{-2}$ and ${\omega }^{-1}$ near the gap-closing point in two and three dimensions, respectively. We provide a further perspective on the low-frequency bulk photovoltaic effect by revealing the complete quantum geometric meaning of the second-order optical conductivity tensor. The bulk photovoltaic effect has two origins, which are the transition of electron position and the transition of electron velocity during the optical excitation, and the resulting photocurrents are, respectively, called the shift current and the injection current. Based on an analysis of two-band models, we show that the injection current is controlled by the quantum metric and Berry curvature, whereas the shift current is governed by the Christoffel symbols near the gap-closing points in semimetals. Finally, for further demonstrations of our theory beyond simple two-band models, we perform first-principles calculations on the shift and injection photocurrent conductivities as well as geometric quantities of antiferromagnetic ${\mathrm{MnGeO}}_3$ and ferromagnetic PrGeAl, respectively, as representatives of real magnetic Dirac and Weyl semimetals. Our calculations reveal gigantic peaks in many nonvanishing elements of photoconductivity tensors below a photon energy of about 0.2 eV in both ${\mathrm{MnGeO}}_3$ and PrGeAl. In particular, we show the ${\omega }^{-1}$ enhancement of the shift conductivity tensors due to the divergent behavior of the geometric quantities near the Dirac and Weyl points as well as slightly gapped topological nodes. Moreover, the low-frequency bulk photovoltaic effect is tunable by carrier doping and magnetization orientation rotation. Our work brings new insights into the structure of nonlinear optical responses as well as the design of semimetal-based terahertz photodetectors.

We present an unconstrained tree-tensor-network approach to the study of lattice gauge theories in two spatial dimensions, showing how to perform numerical simulations of theories in the presence of fermionic matter and four-body magnetic terms, at zero and finite density, with periodic and open boundary conditions. We exploit the quantum-link representation of the gauge fields and demonstrate that a fermionic rishon representation of the quantum links allows us to efficiently handle the fermionic matter while finite densities are naturally enclosed in the tensor network description. We explicitly perform calculations for quantum electrodynamics in the spin-one quantum-link representation on lattice sizes of up to $16\times 16$ sites, detecting and characterizing different quantum regimes. In particular, at finite density, we detect signatures of a phase separation as a function of the bare mass values at different filling densities. The presented approach can be extended straightforwardly to three spatial dimensions.

We report on the optical preparation of coherent superpositions of exciton and biexciton states manifested in temporal nonlinear oscillations in interacting exciton gases. The effect is illustrated for atomically thin semiconductors, where the reflected light reveals these interactions in a unique way. The occurring nonlinear coherent oscillations are counteracted by incoherent excitation-induced dephasing, a phenomenon which originates from a new type of quantum interference between excitons and the two-exciton scattering continuum. To improve the experimental accessibility, we discuss different methods to control the oscillation modulation depth by modifying the mutual interplay of the exciton-biexciton superposition and excitation-induced dephasing. We find that the coherent optical response can be manipulated by the polarization degree of the exciting light field, the laser detuning, external magnetic fields, and quantum coherent feedback. The extraordinary temporal behavior and its control distinguishes the nonlinear coherent oscillations from atomic Rabi oscillations and enables their engineering based on our proposed control schemes.

An ultimate goal of quantum computing is to perform calculations beyond the reach of any classical computer. It is therefore imperative that useful quantum computers be very difficult to simulate classically, otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits $N$ or the depth $D$ of the circuit. This difficulty has triggered recent experiments on deep, random circuits that aim to demonstrate that quantum devices may already perform tasks beyond the reach of classical computing. These real quantum computing devices, however, suffer from many sources of decoherence and imprecision which limit the degree of entanglement that can actually be reached to a fraction of its theoretical maximum. They are characterized by an exponentially decaying fidelity $\mathcal{F}\sim (1-\epsilon {)}^{ND}$ with an error rate $\epsilon$ per operation as small as $\approx 1\%$ for current devices with several dozen qubits or even smaller for smaller devices. In this work, we provide new insight on the computing capabilities of real quantum computers by demonstrating that they can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer. Our algorithms compress the representations of quantum wave functions using matrix product states, which are able to capture states with low to moderate entanglement very accurately. This compression introduces a finite error rate $\epsilon$ so that the algorithms closely mimic the behavior of real quantum computing devices. The computing time of our algorithm increases only linearly with $N$ and $D$ in sharp contrast with exact simulation algorithms. We illustrate our algorithms with simulations of random circuits for qubits connected in both one- and two-dimensional lattices. We find that $\epsilon$ can be decreased at a polynomial cost in computing power down to a minimum error ${\epsilon }_{\infty }$. Getting below ${\epsilon }_{\infty }$ requires computing resources that increase exponentially with ${\epsilon }_{\infty }/\epsilon$. For a two-dimensional array of $N=54$ qubits and a circuit with control-$Z$ gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours. For more complex gates such as a swap gate followed by a controlled rotation, the error rate increases by a factor 3 for similar computing time. Our results suggest that, despite the high fidelity reached by quantum devices, only a tiny fraction $(\sim {10}^{-8})$ of the system Hilbert space is actually being exploited.

Reservoir computing is a relatively recent computational paradigm that originates from a recurrent neural network and is known for its wide range of implementations using different physical technologies. Large reservoirs are very hard to obtain in conventional computers, as both the computation complexity and memory usage grow quadratically. We propose an optical scheme performing reservoir computing over very large networks potentially being able to host several millions of fully connected photonic nodes thanks to its intrinsic properties of parallelism and scalability. Our experimental studies confirm that, in contrast to conventional computers, the computation time of our optical scheme is only linearly dependent on the number of photonic nodes of the network, which is due to electronic overheads, while the optical part of computation remains fully parallel and independent of the reservoir size. To demonstrate the scalability of our optical scheme, we perform for the first time predictions on large spatiotemporal chaotic datasets obtained from the Kuramoto-Sivashinsky equation using optical reservoirs with up to 50 000 optical nodes. Our results are extremely challenging for conventional von Neumann machines, and they significantly advance the state of the art of unconventional reservoir computing approaches, in general.

Experimental studies of protein-pattern formation have stimulated new interest in the dynamics of reaction-diffusion systems. However, a comprehensive theoretical understanding of the dynamics of such highly nonlinear, spatially extended systems is still missing. Here, we show how a description in phase space, which has proven invaluable in shaping our intuition about the dynamics of nonlinear ordinary differential equations, can be generalized to mass-conserving reaction-diffusion (MCRD) systems. We present a comprehensive analysis of two-component MCRD systems, which serve as paradigmatic minimal systems that encapsulate the core principles and concepts of the local equilibria theory introduced in the paper. The key insight underlying this theory is that shifting local (reactive) equilibria—controlled by the local total density—give rise to concentration gradients that drive diffusive redistribution of total density. We show how this dynamic interplay can be embedded in the phase plane of the reaction kinetics in terms of simple geometric objects: the reactive nullcline (line of reactive equilibria) and the diffusive flux-balance subspace. On this phase-space level, physical insight can be gained from geometric criteria and graphical constructions. The effects of nonlinearities on the global dynamics are simply encoded in the curved shape of the reactive nullcline. In particular, we show that the pattern-forming “Turing instability” in MCRD systems is a mass-redistribution instability and that the features and bifurcations of patterns can be characterized based on regional dispersion relations, associated to distinct spatial regions (plateaus and interfaces) of the patterns. In an extensive outlook section, we detail concrete approaches to generalize local equilibria theory in several directions, including systems with more than two components, weakly broken mass conservation, and active matter systems.

To what extent does Noether’s principle apply to quantum channels? Here, we quantify the degree to which imposing a symmetry constraint on quantum channels implies a conservation law and show that this relates to physically impossible transformations in quantum theory, such as time reversal and spin inversion. In this analysis, the convex structure and extremal points of the set of quantum channels symmetric under the action of a Lie group $G$ becomes essential. It allows us to derive bounds on the deviation from conservation laws under any symmetric quantum channel in terms of the deviation from closed dynamics as measured by the unitarity of the channel $\mathcal{E}$. In particular, we investigate in detail the U(1) and SU(2) symmetries related to energy and angular momentum conservation laws. In the latter case, we provide fundamental limits on how much a spin-$j_A$ system can be used to polarize a larger spin-$j_B$ system, and on how much one can invert spin polarization using a rotationally symmetric operation. Finally, we also establish novel links between unitarity, complementary channels, and purity that are of independent interest.

The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested toward its solution. These methods are often grouped into two broad families. On the one hand, are methods such as umbrella sampling and metadynamics that build a bias potential based on few order parameters or collective variables. On the other hand, are tempering methods such as replica exchange that combine different thermodynamic ensembles in one single expanded ensemble. We instead adopt a unifying perspective, focusing on the target probability distribution sampled by the different methods. This allows us to introduce a new class of collective-variables-based bias potentials that can be used to sample any of the expanded ensembles normally sampled via replica exchange. We also provide a practical implementation by properly adapting the iterative scheme of the recently developed on-the-fly probability enhanced sampling method [M. Invernizzi and M. Parrinello, J. Phys. Chem. Lett. 11, 2731 (2020)], which was originally introduced for metadynamicslike sampling. The resulting method is very general and can be used to achieve different types of enhanced sampling. It is also reliable and simple to use, since it presents only few and robust external parameters and has a straightforward reweighting scheme. Furthermore, it can be used with any number of parallel replicas. We show the versatility of our approach with applications to multicanonical and multithermal-multibaric simulations, thermodynamic integration, umbrella sampling, and combinations thereof.

We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a stay-at-home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov chain Monte Carlo methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its subregions in order to account for the wide disparities in population size and density. Without prior information on nonpharmaceutical interventions, the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing stay-at-home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.

Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional surfaces, such as the cell membrane. The peculiarities of diffusion on two-dimensional surfaces may lead to nontrivial reaction kinetics, such as a concentration-dependent rate of association between two molecules. However, traditionally, the kinetics of biomolecular association reactions has been modeled using the law of mass action, which assumes that the rate of reaction is a concentration-independent constant. In this paper, using multiscale molecular simulation, we investigate the concentration dependence of diffusion-limited association reactions on 2D surfaces. In particular, we quantify the influence of short-ranged pair interactions on the concentration dependence of the reaction rates and codify it in an empirical law. Using this law in a chemical kinetic model, we find that the steady-state behaviors of simple chemical systems are drastically modified by the presence of concentration-dependent rates. In particular, we find that it leads to suppression of intrinsic noise in dimerization reaction and destabilizes robust oscillation in Lotka-Volterra predator-prey systems. In fact, we see a transition from robust to fine-tuned behavior in the steady-state oscillations. In addition, we show that concentration-dependent reaction rates arise naturally in stochastic predator-prey systems due to intrinsic noise. We comment on the consequences of these results and discuss their implications in the modeling of complex chemical and biological systems. In particular, we comment on the range of validity of the law of mass action, which is a staple in all theoretical modeling of these systems.

Thouless’ quantization of adiabatic particle transport permits one to associate an integer topological charge with each atom of an electronically gapped material. If these charges are additive and independent of atomic positions, they provide a rigorous definition of atomic oxidation states and atoms can be identified as integer-charge carriers in ionic conductors. Whenever these conditions are met, charge transport is necessarily convective; i.e., it cannot occur without substantial ionic flow, a transport regime that we dub trivial. We show that the topological requirements that allow these conditions to be broken are the same that would determine a Thouless’ pump mechanism if the system were subject to a suitably defined time-periodic Hamiltonian. The occurrence of these requirements determines a nontrivial transport regime whereby charge can flow without any ionic convection, even in electronic insulators. These results are first demonstrated with a couple of simple molecular models that display a quantum-pump mechanism upon introduction of a fictitious time dependence of the atomic positions along a closed loop in configuration space. We finally examine the impact of our findings on the transport properties of nonstoichiometric alkali-halide melts, where the same topological conditions that would induce a quantum-pump mechanism along certain closed loops in configuration space also determine a nontrivial transport regime such that most of the total charge current results to be uncorrelated from the ionic ones.

Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a topological circuit, for which braided circuits represent one candidate model. Given the large overhead associated with encoded circuits, it is paramount to reduce their size in terms of computation time and qubit number through circuit compression. While these optimizations have typically been performed in the language of three-dimensional diagrams, such a representation does not allow an efficient, general, and scalable approach to reduction or verification. We propose the use of the ZX-calculus as an intermediate language for braided circuit compression, demonstrating advantage by comparing results using this approach with those previously obtained for the compression of $|A⟩$ and $|Y⟩$ state distillation circuits. We then provide a benchmark of our method against a small set of $\text{Clifford}+T$ circuits, yielding compression percentages of $\sim 77\%$. Our results suggest that the overheads of braided, defect-based circuits are comparable to those of their lattice-surgery counterparts, restoring the potential of this model for surface-code quantum computation.

Thermal transport phenomena are ubiquitous and play a critical role in the performance of various microelectronic and energy-conversion devices. Binary rocksalt and zinc blende compounds, despite their rather simple crystal structures, exhibit an extraordinary range of lattice thermal conductivity (${\kappa }_{\mathrm{L}}$) spanning over 3 orders of magnitude. A comprehensive understanding of the underlying heat transfer mechanism through the development of microscopic theories is therefore of fundamental importance, yet it remains elusive because of the challenges arising from explicitly treating higher-order anharmonicity. Recent theoretical and experimental advances have revealed the essential role of quartic anharmonicity in suppressing heat transfer in zinc blende boron arsenide (BAs) with ultrahigh ${\kappa }_{\mathrm{L}}$. However, critical questions concerning the general effects of higher-order anharmonicity in the broad classes and chemistries of binary solids are still unanswered. Using our recently developed high-throughput phonon framework based on first-principles density functional theory calculations, we systematically investigate the lattice dynamics and thermal transport properties of 37 binary compounds with rocksalt and zinc blende structures at room temperature, with a particular focus on unraveling the impacts of quartic anharmonicity on ${\kappa }_{\mathrm{L}}$. Our advanced theoretical model for computing ${\kappa }_{\mathrm{L}}$ embraces current state-of-the-art methods, featuring a complete treatment of quartic anharmonicity for both phonon frequencies and lifetimes at finite temperatures, as well as contributions from off-diagonal terms in the heat-flux operator. We find the impacts of quartic anharmonicity on ${\kappa }_{\mathrm{L}}$ to be strikingly different in rocksalt and zinc blende compounds, owing to the countervailing effects on finite-temperature-induced shifts in phonon frequencies and scattering rates. By correlating ${\kappa }_{\mathrm{L}}$ with the phonon scattering phase space, we outline a qualitative but efficient route to assess the importance of four-phonon scattering from harmonic phonon calculations. Among notable examples, in zinc blende HgTe, we identify an unprecedented sixfold reduction in ${\kappa }_{\mathrm{L}}$ due to four-phonon scattering, which dominates over the three-phonon scattering in the acoustic region at room temperature. We also demonstrate a possible breakdown of the phonon gas model in rocksalt AgCl, wherein the phonon states are significantly broadened due to strong intrinsic anharmonicity, inducing off-diagonal contributions to ${\kappa }_{\mathrm{L}}$ comparable to the diagonal ones. The deep physical insights gained in this work can be used to guide the rational design of thermal management materials.

The general theory of dark solitons relies on repulsive interactions and, therefore, predicts the impossibility to form dark-soliton bound states. One important exception to this prediction is the observation of bound solitons in nonlocal nonlinear media. Here, we report that exciton-polariton superfluids can also sustain dark-soliton molecules, although the interactions are fully local. With a novel all-optical technique, we create two dark solitons that bind together to form an unconventional dark-soliton molecule. We demonstrate that the stability of this structure and the separation distance between two dark solitons is tightly connected to the driven-dissipative nature of the polariton fluid.

The light-matter interaction can be utilized to qualitatively alter physical properties of materials. Recent theoretical and experimental studies have explored this possibility of controlling matter by light based on driving many-body systems via strong classical electromagnetic radiation, leading to a time-dependent Hamiltonian for electronic or lattice degrees of freedom. To avoid inevitable heating, pump-probe setups with ultrashort laser pulses have so far been used to study transient light-induced modifications in materials. Here, we pursue yet another direction of controlling quantum matter by modifying quantum fluctuations of its electromagnetic environment. In contrast to earlier proposals on light-enhanced electron-electron interactions, we consider a dipolar quantum many-body system embedded in a cavity composed of metal mirrors and formulate a theoretical framework to manipulate its equilibrium properties on the basis of quantum light-matter interaction. We analyze hybridization of different types of the fundamental excitations, including dipolar phonons, cavity photons, and plasmons in metal mirrors, arising from the cavity confinement in the regime of strong light-matter interaction. This hybridization qualitatively alters the nature of the collective excitations and can be used to selectively control energy-level structures in a wide range of platforms. Most notably, in quantum paraelectrics, we show that the cavity-induced softening of infrared optical phonons enhances the ferroelectric phase in comparison with the bulk materials. Our findings suggest an intriguing possibility of inducing a superradiant-type transition via the light-matter coupling without external pumping. We also discuss possible applications of the cavity-induced modifications in collective excitations to molecular materials and excitonic devices.

We present a novel, nonparametric form for compactly representing entangled many-body quantum states, which we call a “Gaussian process state.” In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way, the nonlocal physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable, and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a “universal approximator” for quantum states, able to capture any entangled many-body state with increasing data-set size. We develop two numerical approaches which can learn this form directly—a fragmentation approach and direct variational optimization—and apply these schemes to the fermionic Hubbard model. We find competitive or superior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.

The stability and outstanding coherence of dopants and other atomlike defects in tailored host crystals make them a leading platform for the implementation of distributed quantum information processing and sensing in quantum networks. Albeit the required efficient light-matter coupling can be achieved via the integration into nanoscale resonators, in this approach the proximity of interfaces is detrimental to the coherence of even the least-sensitive emitters. Here, we establish an alternative: By integrating a $19\mu \mathrm{m}$ thin crystal into a cryogenic Fabry-Perot resonator with a quality factor of $9\times {10}^6$, we achieve a two-level Purcell factor of 530(50). In our specific system, erbium-doped yttrium orthosilicate, this leads to a 59(6)-fold enhancement of the emission rate with an out-coupling efficiency of 46(8)%. At the same time, we demonstrate that the emitter properties are not degraded in our approach. We thus observe ensemble-averaged optical coherence up to 0.54(1) ms, which exceeds the 0.19(2) ms lifetime of dopants at the cavity field maximum. While our approach is also applicable to other solid-state quantum emitters, such as color centers in diamond, our system emits at the minimal-loss wavelength of optical fibers and thus enables coherent and efficient nodes for long-distance quantum networks.