Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an elementary band representation (atomic limit band) splits into a particular set of bands. For the first time, we obtain a complete classification of the fragile topological phases, which can be diagnosed by symmetry eigenvalues, to find an incredibly rich structure that far surpasses that of stable or strong topological states. We find and enumerate hundreds of thousands of different fragile topological phases diagnosed by symmetry eigenvalues, and we link the mathematical structure of these phases to that of affine monoids in mathematics. Furthermore, for the first time, we predict and calculate (hundreds of realistic) materials where fragile topological bands appear, and we showcase the very best ones.

We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree cluster protects the information from transmission loss and enables long-range quantum communication through a chain of repeater stations. As opposed to conventional approaches that are limited by the two-way communication time, the overall transmission rate of the current quantum repeater protocol is determined by the local processing time enabling very high communication rates. We further show that such a repeater can be constructed with as little as two stationary qubits and one quantum emitter per repeater station, which significantly increases the experimental feasibility. We discuss potential implementations with diamond defect centers and semiconductor quantum dots efficiently coupled to photonic nanostructures and outline how such systems may be integrated into repeater stations.

High-spin states play a key role in chemical reactions found in nature. In artificial molecular systems, singlet fission produces a correlated triplet-pair state, a spin-bearing excited state that can be harnessed for more efficient solar-energy conversion and photocatalysis. In particular, triplet-pair states with overall quintet character (total spin $S=2$) have been discovered, but many of the fundamental properties of these biexciton states remain unexplored. The net spin of these pair states makes spin-sensitive probes attractive for their characterization. Combined with their surprisingly long spin coherence (of order microseconds), this opens up techniques relying on coherent spin control. Here we apply coherent manipulation of triplet-pair states to (i) isolate their spectral signatures from coexisting free triplets and (ii) selectively couple quintet and triplet states to specific nuclear spins. Using this approach, we separate quintet and triplet transitions and extract the relaxation dynamics and hyperfine couplings of the fission-borne spin states. Our results highlight the distinct properties of correlated and free triplet excitons and demonstrate optically induced nuclear spin polarization by singlet fission.

Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modeling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system provides a qualitatively better model than the classical single-layer aggregated network. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated to the multilayer and to the corresponding aggregated graph. We find that there exists a maximum amount of additional information that a multilayer model can encode with respect to the equivalent single-layer graph. We show how our complexity measure can be used to obtain low-dimensional representations of multidimensional systems, to cluster multilayer networks into a small set of meaningful superfamilies, and to detect tipping points in the evolution of different time-varying multilayer graphs. Interestingly, the low-dimensional multiplex networks obtained with the proposed method also retain most of the dynamical properties of the original systems, as demonstrated for instance by the preservation of the epidemic threshold in the multiplex susceptible-infected-susceptible model. These results suggest that information-theoretic approaches can be effectively employed for a more systematic analysis of static and time-varying multidimensional complex systems.

The interaction-energy landscapes (ELs) and magnetization dynamics of two-dimensional ensembles of dipole-coupled magnetic nanoparticles are theoretically investigated. Extended nanostructures are modeled by considering nonoverlapping nanoparticles (NPs) in a square unit cell with periodic boundary conditions. The local minima and connecting transition states of the EL are determined systematically for representative NP arrangements having different degrees of disorder. The topology of the ergodic networks of stationary points is analyzed from both local and energy perspectives by using kinetic networks and disconnectivity graphs. We show that increasing the degree of disorder not only increases, most significantly, the number of local minima and transition states but also changes the shape of the EL in a very profound way. While slightly disordered ensembles correspond to good structure seekers, which are funneled towards the global minima, strongly disordered systems show very rough landscapes with multiple low-energy local minima separated by relatively large energy barriers. The consequences of this transition on the long-time Markovian dynamics of the nanostructures are quantified by calculating the field-free magnetic relaxation after saturation and after quenching. The simulations indicate that the relaxation of weakly disordered systems follows a slightly stretched exponential law, with a single characteristic timescale for a wide range of temperatures. In contrast, strongly disordered systems show a much more complicated relaxation dynamics involving multiple timescales, slowing down and trapping, which is reminiscent of spin glasses.

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood about the QAOA’s performance beyond its lowest-depth variant. An essential but missing ingredient for understanding and deploying the QAOA is a constructive approach to carry out the outer-loop classical optimization. We provide an in-depth study of the performance of the QAOA on MaxCut problems by developing an efficient parameter-optimization procedure and revealing its ability to exploit nonadiabatic operations. Building on observed patterns in optimal parameters, we propose heuristic strategies for initializing optimizations to find quasioptimal $p$-level QAOA parameters in $O[\mathrm{poly}(p)]$ time, whereas the standard strategy of random initialization requires $2^{O(p)}$ optimization runs to achieve similar performance. We then benchmark the QAOA and compare it with quantum annealing, especially on difficult instances where adiabatic quantum annealing fails due to small spectral gaps. The comparison reveals that the QAOA can learn via optimization to utilize nonadiabatic mechanisms to circumvent the challenges associated with vanishing spectral gaps. Finally, we provide a realistic resource analysis on the experimental implementation of the QAOA. When quantum fluctuations in measurements are accounted for, we illustrate that optimization is important only for problem sizes beyond numerical simulations but accessible on near-term devices. We propose a feasible implementation of large MaxCut problems with a few hundred vertices in a system of 2D neutral atoms, reaching the regime to challenge the best classical algorithms.

Because of the broken time-translation symmetry, in periodically driven vibrational systems fluctuations of different vibration components have different intensities. Fluctuations of one of the components are often squeezed, whereas fluctuations of the other component, which is shifted in phase by $\pi /2$, are increased. Squeezing is a multifaceted phenomenon; it attracts much attention from the perspective of high-precision measurements. Here we demonstrate a new and hitherto unappreciated side of squeezing: its direct manifestation in the spectra of driven vibrational systems. With a weakly damped nanomechanical resonator, we study the spectrum of thermal fluctuations of a resonantly driven nonlinear mode. In the attained sideband-resolved regime, we show that the asymmetry of the spectrum directly characterizes the squeezing. This opens a way to deduce squeezing of thermal fluctuations in strongly underdamped resonators, for which a direct determination by a standard homodyne measurement is impeded by frequency fluctuations. The experimental and theoretical results are in excellent agreement. We further extend the theory to also describe the spectral manifestation of squeezing of quantum fluctuations.

Active matter, composed of self-propelled entities, forms a wide class of out-of-equilibrium systems that display striking collective behaviors, among which, the so-called active turbulence where spatially and time-disordered flow patterns spontaneously arise in a variety of active systems. De facto, the active turbulence naming suggests a connection with a second seminal class of out-of-equilibrium systems, inertial turbulence, even though the latter is of very different nature with energy injected at global system scale rather than at the elementary scale of single constituents. Indeed, the existence of a possible strong tie between active and canonical turbulence remains an open question and a field of profuse research. Using an assembly of self-propelled interfacial particles, we show experimentally that the statistical properties of particles’ velocities display a turbulentlike behavior, as described by the celebrated 1941 phenomenology of Kolmogorov. Moreover, the analogy between the dynamics of the self-propelled particles and inertial turbulence is observed to hold consistently both in the Eulerian and Lagrangian frameworks. Unlike the swimmers’ velocities distribution, the subsurface fluid flow is found not turbulent, thus making Marangoni surfers’ assemblies different from other active systems generating turbulence, such as living matter. Identifying an active system in the universality class of inertial turbulence not only benefits its future development but may also provide new insights into the long-standing description of turbulent flows, arguably one of the biggest remaining mysteries in classical physics.

As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from severe scalability issues and can be computed only for systems of a very modest size of around six sites. In order to address large many-body systems, we propose a renormalization-type approach based on a class of local linear transformations called connectors, which can be used to coarse grain the system in a way that preserves the property under investigation. Repeated coarse graining produces a system of manageable size, whose properties can then be explored by means of the usual techniques for small systems. In the case of a successful detection of the desired property, the method outputs a linear witness which admits an exact tensor network representation composed of connectors. We demonstrate the power of our method by certifying entanglement, Bell nonlocality, and supraquantum Bell nonlocality in systems with hundreds of sites using a normal desktop computer.

We show that the commonly used lowest-order theory of phonon-phonon interactions frequently fails to accurately describe the anharmonic phonon decay rates and thermal conductivity ($\kappa$), even among strongly bonded crystals. Applying a first-principles theory that includes both the lowest-order three-phonon and the higher-order four-phonon processes to 17 zinc blende semiconductors, we find that the lowest-order theory drastically overestimates the measured $\kappa$ for many of these materials, while inclusion of four-phonon scattering gives significantly improved agreement with measurements. We identify new selection rules on three-phonon processes that help explain many of these failures in terms of anomalously weak anharmonic phonon decay rates predicted by the lowest-order theory competing with four-phonon processes. We also show that zinc blende compounds containing boron (B), carbon (C), or nitrogen (N) atoms have exceptionally weak four-phonon scattering, much weaker than in compounds that do not contain B, C, or N atoms. This new understanding helps explain the ultrahigh $\kappa$ in several technologically important materials like cubic boron arsenide, boron phosphide, and silicon carbide. At the same time, it not only makes the possibility of achieving high $\kappa$ in materials without B, C, or N atoms unlikely, but it also suggests that it may be necessary to include four-phonon processes in many future studies. Our work gives new insights into the nature of anharmonic processes in solids and demonstrates the broad importance of higher-order phonon-phonon interactions in assessing the thermal properties of materials.

We present a unified and nonperturbative method for calculating spectral and transport properties of Hamiltonians with simultaneous Holstein (diagonal) and Peierls (off-diagonal) electron-phonon coupling. Our approach is motivated by the separation of energy scales in organic molecular crystals, in which electrons couple to high-frequency intramolecular Holstein modes and to low-frequency intermolecular Peierls modes. We treat Peierls modes as quasiclassical dynamic disorder, while Holstein modes are included with a Lang-Firsov polaron transformation and no narrow-band approximation. Our method reduces to the popular polaron picture due to Holstein coupling and the dynamic disorder picture due to Peierls coupling. We derive an expression for efficient numerical evaluation of the frequency-resolved optical conductivity based on the Kubo formula and obtain the dc mobility from its zero-frequency component. We also use our method to calculate the electron-addition Green’s function corresponding to the inverse photoemission spectrum. For realistic parameters, temperature-dependent dc mobility is largely determined by the Peierls-induced dynamic disorder with minor quantitative corrections due to polaronic band narrowing, and an activated regime is not observed at relevant temperatures. In contrast, for frequency-resolved observables, a quantum-mechanical treatment of the Holstein coupling is qualitatively important for capturing the phonon replica satellite structure.

The demonstration of superconductivity in nickelate analogs of high $T_c$ cuprates provides new perspectives on the physics of correlated electron materials. The degree to which the nickelate electronic structure is similar to that of cuprates is an important open question. This paper presents results of a comparative study of the many-body electronic structure and theoretical phase diagram of the isostructural materials ${\mathrm{CaCuO}}_2$ and ${\mathrm{NdNiO}}_2$. Both ${\mathrm{NdNiO}}_2$ and ${\mathrm{CaCuO}}_2$ are found to be charge transfer materials. Important differences include the proximity of the oxygen $2p$ bands to the Fermi level, the bandwidth of the transition metal-derived $3d$ bands, and the presence, in ${\mathrm{NdNiO}}_2$, of both Nd-derived $5d$ states crossing the Fermi level and a van Hove singularity that crosses the Fermi level as the out-of-plane momentum is varied. The low-energy physics of ${\mathrm{NdNiO}}_2$ is found to be that of a single Ni-derived correlated band, with additional accompanying weakly correlated bands of Nd-derived states that dope the Ni-derived band. The effective correlation strength of the Ni-derived $d$ band crossing the Fermi level in ${\mathrm{NdNiO}}_2$ is found to be greater than that of the Cu-derived $d$ band in ${\mathrm{CaCuO}}_2$, but the predicted magnetic transition temperature of ${\mathrm{NdNiO}}_2$ is substantially lower than that of ${\mathrm{CaCuO}}_2$ because of the smaller bandwidth.

The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [J. Huh et al., Nat. Photonics 9, 615 (2015)] in a two-mode superconducting device. In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode. Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states. We show the reprogrammability of our implementation by extracting the spectra of photoelectron processes in ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{O}}_3$, ${\mathrm{NO}}_2$, and ${\mathrm{SO}}_2$. The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.

The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved charge correlations are still in their infancy. Such information is crucial in order to help discern the connection between CDW and pseudogap phenomena, and to understand the extent to which charge correlations in general shape the phase diagram. We report a resonant inelastic x-ray scattering study of the underdoped cuprate superconductor ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ ($T_c=70\mathrm{K}$). At 250 K, above the previously established temperature $T_{\mathrm{CDW}}\approx 200\mathrm{K}$ that signifies the onset of quasistatic short-range CDW order, we observe significant dynamic correlations that are broadly peaked at about 40 meV and centered at the two-dimensional wave vector ${\mathit{q}}_{\mathrm{CDW}}$. This energy scale is comparable to both the superconducting gap and the low-energy pseudogap. At 70 K, we observe a quasistatic CDW peak at ${\mathit{q}}_{\mathrm{CDW}}$, but the dynamic correlations around 40 meV remain virtually unchanged, and we identify a new feature: dynamic correlations well above the optic phonon range that are broadly peaked in the 150–200 meV range. A similar energy scale was previously identified in other experiments as a high-energy pseudogap. The observation of three distinct features in the charge response is highly unusual for a CDW system and suggests that charge order in the cuprates is complex. We demonstrate that other single-layer cuprates exhibit approximately the same relative strength of high- to low-temperature energy-integrated charge signal, which points to the universal existence of significant dynamic correlations. Intriguingly, the two energy scales identified here are also comparable to those of the superconducting glue function extracted from other spectroscopic techniques, consistent with a dual charge and magnetic nature of the pairing glue. We further determine the paramagnon dispersion along [1, 0], across ${\mathit{q}}_{\mathrm{CDW}}$, and find it to be consistent with magnetic excitations measured by inelastic neutron scattering. Unlike for some other cuprates, our result points to the absence of a discernible coupling between charge and magnetic excitations.

The precise engineering of quantum states, a basic prerequisite for technologies such as quantum-enhanced sensing or quantum computing, becomes more challenging with increasing dimension of the system Hilbert space. Standard preparation techniques then require a large number of operations or slow adiabatic evolution and give access to only a limited set of states. Here, we use quantum optimal control theory to overcome this problem and derive shaped radio-frequency pulses to experimentally navigate the Stark manifold of a Rydberg atom. We demonstrate that optimal control, beyond improving the fidelity of an existing protocol, also enables us to accurately generate a nonclassical superposition state that cannot be prepared with reasonable fidelity using standard techniques. Optimal control thus substantially enlarges the range of accessible states. Our joint experimental and theoretical work establishes quantum optimal control as a key tool for quantum engineering in complex Hilbert spaces.

Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize. Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian—a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade. Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs. We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations. We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.

We investigate the connection between the time evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramér-Rao bound, we find that the rate of change of the average of any observable is bounded from above by its variance times the temporal Fisher information. As a consequence of this bound, we obtain a speed limit on the evolution of stochastic observables: Changing the average of an observable requires a minimum amount of time given by the change in the average squared, divided by the fluctuations of the observable times the thermodynamic cost of the transformation. In particular, for relaxation dynamics, which do not depend on time explicitly, we show that the Fisher information is a monotonically decreasing function of time and that the minimal required time is determined by the initial preparation of the system. We further show that the monotonicity of the Fisher information can be used to detect hidden variables in the system and demonstrate our findings for simple examples of continuous and discrete random processes.

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface acoustic wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later recapture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit’s final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signaling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon’s self-interference, or erased.

Quantum computing and quantum simulation can be implemented by concatenation of one- and two-qubit gates and interactions. For most physical implementations, however, it may be advantageous to explore state components and interactions that depart from this universal paradigm and offer faster or more robust access to more advanced operations on the system. In this article, we show that adiabatic passage along the dark eigenstate of excitation exchange interactions can be used to implement fast multiqubit Toffoli (${\mathrm{C}}_k$-NOT) and fan-out (C-${\text{NOT}}^k$) gates. This mechanism can be realized by simultaneous excitation of atoms to Rydberg levels, featuring resonant exchange interaction. Our theoretical estimates and numerical simulations show that these multiqubit Rydberg gates are possible with errors below 1% for up to 20 qubits. The excitation exchange mechanism is ubiquitous across experimental platforms, and we show that similar multiqubit gates can be implemented in superconducting circuits.