Programmable quantum devices are now able to probe wave functions at unprecedented levels. This is based on the ability to project the many-body state of atom and qubit arrays onto a measurement basis which produces snapshots of the system wave function. Extracting and processing information from such observations remains, however, an open quest. One often resorts to analyzing low-order correlation functions—that is, discarding most of the available information content. Here, we introduce wave-function networks—a mathematical framework to describe wave-function snapshots based on network theory. For many-body systems, these networks can become scale-free—a mathematical structure that has found tremendous success and applications in a broad set of fields, ranging from biology to epidemics to Internet science. We demonstrate the potential of applying these techniques to quantum science by introducing protocols to extract the Kolmogorov complexity corresponding to the output of a quantum simulator and implementing tools for fully scalable cross-platform certification based on similarity tests between networks. We demonstrate the emergence of scale-free networks analyzing experimental data obtained with a Rydberg quantum simulator manipulating up to 100 atoms. Our approach illustrates how, upon crossing a phase transition, the simulator complexity decreases while correlation length increases—a direct signature of buildup of universal behavior in data space. Comparing experiments with numerical simulations, we achieve cross-certification at the wave-function level up to timescales of $4\mathrm{\mu }\mathrm{s}$ with a confidence level of 90% and determine experimental calibration intervals with unprecedented accuracy. Our framework is generically applicable to the output of quantum computers and simulators with in situ access to the system wave function and requires probing accuracy and repetition rates accessible to most currently available platforms.

We derive an exact solution for the steady state of a setup where two $XX$-coupled $N$-qubit spin chains (with possibly nonuniform couplings) are subject to boundary Rabi drives and common boundary loss generated by a waveguide (either bidirectional or unidirectional). For a wide range of parameters, this system has a pure entangled steady state, providing a means for stabilizing remote multiqubit entanglement without the use of squeezed light. Our solution also provides insights into a single boundary-driven dissipative $XX$ spin chain that maps to an interacting fermionic model. The nonequilibrium steady state exhibits surprising correlation effects, including an emergent pairing of hole excitations that arises from dynamically constrained hopping. Our system could be implemented in a number of experimental platforms, including circuit QED.

Systems driven far from equilibrium often retain structural memories of their processing history. This memory has, in some cases, been shown to dramatically alter the material response. For example, work hardening in crystalline metals can alter the hardness, yield strength, and tensile strength to prevent catastrophic failure. Whether memory of processing history can be similarly exploited in flowing systems, where significantly larger changes in structure should be possible, remains poorly understood. Here, we demonstrate a promising route to embedding such useful memories. We build on work showing that exposing a sheared dense suspension to acoustic perturbations of different power allows for dramatically tuning the sheared suspension viscosity and underlying structure. We find that, for sufficiently dense suspensions, upon removing the acoustic perturbations, the suspension shear jams with shear stress contributions from the maximum compressive and maximum extensive axes that reflect or “remember” the acoustic training. Because the contributions from these two orthogonal axes to the total shear stress are antagonistic, it is possible to tune the resulting suspension response in surprising ways. For example, we show that differently trained sheared suspensions exhibit (1) different susceptibility to the same acoustic perturbation, (2) orders of magnitude changes in their instantaneous viscosities upon shear reversal, and (3) even a shear stress that increases in magnitude upon shear cessation. We work through these examples to explain the underlying mechanisms governing each behavior. Then, to illustrate the power of this approach for controlling suspension properties, we demonstrate that flowing states well below the shear jamming threshold can be shear jammed via acoustic training. Collectively, our work paves the way for using acoustically induced memory in dense suspensions to generate rapidly and widely tunable materials.

Developing a thermodynamic theory of computation is a challenging task at the interface of nonequilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of nonequilibrium thermodynamics to generic nonstationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process—in particular, the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly.

The flux quantization is a key indication of electron pairing in superconductors. For example, the well-known $h/2e$ flux quantization is considered strong evidence for the existence of charge-$2e$, two-electron Cooper pairs. Here we report evidence for multicharge flux quantization in mesoscopic ring devices fabricated using the transition-metal kagome superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. We perform systematic magnetotransport measurements and observe unprecedented quantization of magnetic flux in units of $h/4e$ and $h/6e$ in magnetoresistance oscillations. Specifically, at low temperatures, magnetoresistance oscillations with period $h/2e$ are detected, as expected from the flux quantization for charge-$2e$ superconductivity. We find that the $h/2e$ oscillations are suppressed and replaced by resistance oscillations with $h/4e$ periodicity when the temperature is increased. Increasing the temperature further suppresses the $h/4e$ oscillations, and robust resistance oscillations with $h/6e$ periodicity emerge as evidence for charge-$6e$ flux quantization. Our observations provide the first experimental evidence for the existence of multicharge flux quanta and emergent quantum matter exhibiting higher-charge superconductivity in the strongly fluctuating region above the charge-$2e$ Cooper pair condensate, revealing new insights into the intertwined and vestigial electronic order in kagome superconductors.

Coherence time and gate fidelities in Rydberg atom quantum simulators and computers are fundamentally limited by the Rydberg state lifetime. Circular Rydberg states are highly promising candidates to overcome this limitation by orders of magnitude, as they can be effectively protected from decay due to their maximum angular momentum. We report the first realization of alkaline-earth circular Rydberg atoms trapped in optical tweezers, which provide unique and novel control possibilities due to the optically active ionic core. Specifically, we demonstrate creation of very high-$n$ ($n=79$) circular states of ${}^{88}\mathrm{Sr}$. We measure lifetimes as long as 2.55 ms at room temperature, which are achieved via cavity-assisted suppression of black-body radiation. We show coherent control of a microwave qubit encoded in circular states of nearby manifolds, and characterize the qubit coherence time via Ramsey and spin-echo spectroscopy. Finally, circular-state tweezer trapping exploiting the ${\mathrm{Sr}}^{+}$ core polarizability is quantified via measurements of the trap-induced light shift on the qubit. Our work opens routes for quantum simulations with circular Rydberg states of divalent atoms, exploiting the emergent toolbox associated with the optically active core ion.

First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon ($e\text{−}\mathrm{ph}$) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For $e\text{−}\mathrm{ph}$ interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress $e\text{−}\mathrm{ph}$ interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to $e\text{−}\mathrm{ph}$ interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of $e\text{−}\mathrm{ph}$ interactions. Furthermore, they accelerate state-of-the-art first-principles $e\text{−}\mathrm{ph}$ calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of $e\text{−}\mathrm{ph}$ interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter.

Given a unitary evolution $U$ on a multipartite quantum system and an ensemble of initial states, how well can $U$ be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity—what we call an “LOCC inequality.” We then apply our findings to the fundamental setting where $U$ implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the nonclassicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialized in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalized states of motion nor the detection of entanglement, which is never created at any point in the process.

Nonfullerene acceptors have caused a step change in organic optoelectronics research but little is known about the mechanism and factors limiting charge transport in these molecular materials. Here a joint computational-experimental investigation is presented to understand the impact of various sources of disorder on the electron transport in the nonfullerene acceptor O-IDTBR. We find that in single crystals of this material, electron transport occurs in the transient quantum delocalization regime with the excess charge delocalized over about three molecules on average, according to quantum-classical nonadiabatic molecular-dynamics simulations. In this regime, carrier delocalization and charge mobility (${\mu }_a=7{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$) are limited by dynamical disorder of off-diagonal and diagonal electron-phonon coupling. In molecular assemblies representing disordered thin films, the additional static disorder of off-diagonal electron-phonon coupling is sufficient to fully localize the excess electron on single molecules, concomitant with a transition of transport mechanism from transient quantum delocalization to small polaron hopping and a drop in electron mobility by about 1 order of magnitude. Yet, inclusion of static diagonal disorder resulting from electrostatic interactions arising from the acceptor-donor-acceptor (A-D-A) structure of O-IDTBR, are found to have the most dramatic impact on carrier mobility, resulting in a further drop of electron mobility by about 4–5 orders of magnitude to ${10}^{-5}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, in good agreement with thin-film electron mobility estimated from space-charge-limited-current measurements. Limitations due to diagonal disorder caused by electrostatic interactions are likely to apply to most nonfullerene acceptors. They imply that while A-D-A or A-DAD-A motifs are beneficial for photoabsorption and exciton transport, the electrostatic disorder they create can limit carrier transport in thin-film optoelectronic applications. This work shows the value of computational methods, in particular, nonadiabatic molecular-dynamics propagation of charge carriers, to distinguish different regimes of transport for different types of molecular packing.

Recent studies have shown that light propagating in a nonlinear, highly multimode system can thermalize in a manner totally analogous to that encountered in traditional statistical mechanics. At thermal equilibrium, the system’s entropy is at a maximum, in full accord with the second law of thermodynamics. In such arrangements, the entropy is extremized once the statistical power allocation among modes associated with this photon gas attains a Rayleigh-Jeans distribution that is fully characterized by an optical temperature $T$ and a chemical potential $\mu$. However, it has been theoretically argued that the variables $T$ and $\mu$ represent actual thermodynamic forces that control the exchange of the respective conjugate quantities between two subsystems. In this work, we report, for the first time, optical calorimetric measurements in nonlinear multimode fibers, which unambiguously demonstrate that both the temperature $T$ and the chemical potential $\mu$ dictate the flow of their associated extensive quantities, i.e., the energy and the optical power. Specifically, we study the process of light thermalization associated with two orthogonally polarized laser beams. Our observations are enabled by recently developed techniques that allow one to judiciously multiplex/demultiplex the optical power within various mode groups. Our results indicate that because of photon-photon collisions, “heat” only flows from a hot to a cold photon gas subsystem—thus providing an unequivocal demonstration of the second law in such all-optical thermodynamic arrangements. In addition to being fundamental, our findings provide a new approach to manipulate laser beams using thermodynamic principles.

Cat qubits, for which logical $|0⟩$ and $|1⟩$ are coherent states $|\pm \alpha ⟩$ of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number $|\alpha {|}^2$. A large two-photon dissipation rate ${\kappa }_2$ ensures fast qubit manipulation and short error-correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here, we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump, and it reaches a rate ${\kappa }_2/2\pi \approx 2\mathrm{MHz}$. With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. In addition, we illustrate how the phase of a quantum superposition between $|\alpha ⟩$ and $|-\alpha ⟩$ can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active.

Quantum networks can enable various applications such as distributed quantum computing, long-distance quantum communication, and network-based quantum sensing with unprecedented performances. One of the most important building blocks for a quantum network is a photonic quantum memory which serves as the interface between the communication channel and the local functional unit. A programmable quantum memory which can process a large stream of flying qubits and fulfill the requirements of multiple core functions in a quantum network is still to be realized. Here we report a high-performance quantum memory which can simultaneously store 72 optical qubits carried by 144 spatially separated atomic ensembles and support up to a thousand consecutive write or read operations in a random access way, 2 orders of magnitude larger than the previous record. Because of the built-in programmability, this quantum memory can be adapted on demand for several functions. As example applications, we realize quantum queue, stack, and buffer which closely resemble the counterpart devices for classical information processing. We further demonstrate the storage and reshuffle of four entangled pairs of photonic pulses with probabilistic arrival time and arbitrary release order via the memory, which is an essential requirement for the realization of quantum repeaters and efficient routing in quantum networks. Realization of this multipurpose programmable quantum memory thus constitutes a key enabling building block for future large-scale fully functional quantum networks.

A direct current through a metal-insulator-metal tunneling junction emits light when surface-plasmon polaritons (SPPs) are excited. Two distinct processes are believed to coexist in this light emission mediated by surface plasmons: inelastic tunneling, where electrons excite SPPs in the insulator gap, and hot-electron radiative decay, which occurs in the electrodes after elastic tunneling. Previous theoretical approaches to study light emission by inelastic tunneling have relied on Bardeen’s approximation where the electronic wave functions are considered only in the barrier of the junction. In this work, we introduce an extension to models of inelastic tunneling by incorporating the full quantum device solution of the Schrödinger equation, which can also account for processes in the metallic electrodes. The extension unveils the existence of long-range correlations of the current density across the barrier and enables us to establish the equivalence between two models widely used in the past: (i) a calculation of the inelastic transition rate between two states across the barrier based on Fermi’s golden rule and (ii) a calculation of the power transferred to plasmons by current fluctuations. Importantly, the new model accounts for processes that take place in the metallic electrodes and that could not be described within Bardeen’s approximation. Hence, it is no longer necessary to invoke a hot-electron mechanism to obtain a dependence on the geometry of metallic electrodes. The new framework enables to discuss the role of surface plasmons localized in different metal-insulator interfaces and to include possible nonlocal effects at the interfaces.

Dynamical perturbations modify the states of classical systems in surprising ways and give rise to important applications in science and technology. For example, Floquet engineering exploits the possibility of band formation in the frequency domain when a strong, periodic variation is imposed on parameters such as spring constants. We describe here Kapitza engineering, where a drive field oscillating at a frequency much higher than the characteristic frequencies for the linear response of a system changes the potential energy surface so much that maxima found at equilibrium become local minima, in precise analogy to the celebrated Kapitza pendulum where the unstable inverted configuration, with the mass above rather than below the fulcrum, actually becomes stable. Our starting point is a quantum field theory of the Ginzburg-Devonshire type, suitable for many condensed matter systems, including particularly ferroelectrics and quantum paralectrics. We show that an off-resonance oscillatory electric field generated by a laser-driven terahertz source can induce ferroelectric order in the quantum-critical limit. Heating effects are estimated to be manageable using pulsed radiation; “hidden” radiation-induced order can persist to low temperatures without further pumping due to stabilization by strain. We estimate the Ginzburg-Devonshire free-energy coefficients in ${\text{SrTiO}}_3$ using density-functional theory and the stochastic self-consistent harmonic approximation accelerated by a machine-learned force field. Although we find that ${\text{SrTiO}}_3$ is not an optimal choice for Kapitza stabilization, we show that scanning for further candidate materials can be performed at the computationally convenient density-functional theory level. We suggest second harmonic generation, soft-mode spectroscopy, and x-ray diffraction experiments to characterize the induced order.

A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different species of quasiparticles, which can get stuck at high enough density, realizing the quantum analog of jamming. We identify a family of interactions satisfying simple kinetic constraints and consider generic translationally invariant models built up from them. We study dynamics following a local unjamming perturbation in a jammed state. We show that they can be mapped into dynamics of ordinary unconstrained systems, but the nonlocality of the mapping changes the scales at which the phenomena manifest themselves. Scattering of quasiparticles, formation of bound states, and eigenstate localization become all visible at macroscopic scales. Depending on whether a symmetry is present or not, the microscopic details of the jammed state turn out to have either a marginal or a strong effect. In the former case or when the initial state is almost homogeneous, we show that even a product state is turned into a macroscopic quantum state.

In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction-diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a nonzero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common “normal form” that can be seen as a spatially extended generalization of the FitzHugh-Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal nonreciprocal Cahn-Hilliard equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. Our work, thus, generalizes previously studied nonreciprocal phase transitions and shows that interfaces are the relevant collective excitations governing the rich dynamical patterns of conserved fields.

We propose multilayer moiré structures in strong external magnetic fields as a novel platform for realizing highly tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudospin allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudospin-liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable toward relevant perturbations. We discuss how layer pseudospin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moiré systems, our approach provides a promising route toward the experimental realization and control of topologically ordered phases of matter.

The thermoelectric Nernst effect of solids converts heat flow to beneficial electronic voltages. Here, using a correlated topological semimetal with high carrier mobility $\mu$ in the presence of magnetic fluctuations, we demonstrate an enhancement of the Nernst effect close to a magnetic phase transition. A magnetic instability in NdAlSi modifies the carrier relaxation time on “hot spots” in momentum space, causing a strong band filling dependence of $\mu$. We quantitatively derive electronic band parameters from a novel two-band analysis of the Nernst effect $S_{xy}$, in good agreement with quantum oscillation measurements and band calculations. While the Nernst response of NdAlSi behaves much like conventional semimetals at high temperatures, an additional contribution $\mathrm{\Delta }{S}_{\mathrm{xy}}$ from electronic correlations appears just above the magnetic transition. Our work demonstrates the engineering of the relaxation time, or the momentum-dependent self-energy, to generate a large Nernst response independent of a material’s carrier density, i.e., for metals, semimetals, and semiconductors with large $\mu$.

The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.