The surface code, with a simple modification, exhibits ultrahigh error-correction thresholds when the noise is biased toward dephasing. Here, we identify features of the surface code responsible for these ultrahigh thresholds. We provide strong evidence that the threshold error rate of the surface code tracks the hashing bound exactly for all biases and show how to exploit these features to achieve significant improvement in the logical failure rate. First, we consider the infinite bias limit, meaning pure dephasing. We prove that the error threshold of the modified surface code for pure dephasing noise is 50%, i.e., that all qubits are fully dephased, and this threshold can be achieved by a polynomial time-decoding algorithm. We demonstrate that the subthreshold behavior of the code depends critically on the precise shape and boundary conditions of the code. That is, for rectangular surface codes with standard rough or smooth open boundaries, it is controlled by the parameter $g=\gcd (j,k)$, where $j$ and $k$ are dimensions of the surface code lattice. We demonstrate a significant improvement in the logical failure rate with pure dephasing for coprime codes that have $g=1$ and closely related rotated codes, which have a modified boundary. The effect is dramatic: The same logical failure rate achievable with a square surface code and $n$ physical qubits can be obtained with a coprime or rotated surface code using only $O(\sqrt{n})$ physical qubits. Finally, we use approximate maximum-likelihood decoding to demonstrate that this improvement persists for a general Pauli noise biased toward dephasing. In particular, comparing with a square surface code, we observe a significant improvement in the logical failure rate against biased noise using a rotated surface code with approximately half the number of physical qubits.

Modulational instability in passive optical resonators, the triggering mechanism of frequency comb and pulse train generation, is shown to exhibit transitions between regimes involving period-one (P1) versus period-two (P2) dynamical evolutions. The latter is a signature of parametric resonance occurring in the system, which can arise either from intrinsic cavity periodicity or from spatial modulation of the cavity parameters. We characterize the P1-P2 transition for both cases, employing a fiber resonator where the intracavity fiber can be either uniform or dispersion modulated. The key element of our setup is a time lens which we exploit to resolve the temporal dynamics over successive round trips, allowing crystal-clear evidence of the existence of P1-P2 transitions for suitable changes of cavity parameters, as well as for the successful characterization of the relative temporal patterns. Our findings reveal new regimes where the averaged model known as the Lugiato-Lefever equation turns out to be inadequate to explain the dynamics, whereas the results are correctly predicted and described on the basis of the full Ikeda map.

We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatically sort the input under minimal assumptions, yet partially preserves information contained in the states. We quantify analytically its performance for an arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that have been sampled from two unknown probability distributions. We find that the quantum protocol fully exploits the dimensionality of the quantum data to achieve a much higher performance, provided the data are at least three dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known.

We report on the investigation of the three-dimensional single-atom-resolved distributions of bosonic Mott insulators in momentum space. First, we measure the two-body and three-body correlations deep in the Mott regime, finding a perfectly contrasted bunching whose periodicity reproduces the reciprocal lattice. In addition, we show that the two-body correlation length is inversely proportional to the in-trap size of the Mott state with a prefactor in agreement with the prediction for an incoherent state occupying a uniformly filled lattice. Our findings indicate that the momentum-space correlations of a Mott insulator at small tunneling are those of a many-body ground state with Gaussian statistics. Second, in the Mott insulating regime with increasing tunneling, we extract the spectral weight of the quasiparticles from the momentum-density profiles. On approaching the transition towards a superfluid, the momentum spread of the spectral weight is found to decrease as a result of the increased mobility of the quasiparticles. While the shapes of the observed spectral weight agree with those predicted by perturbative many-body calculations for homogeneous systems, the fitted mobilities are larger than the theoretical ones, mostly because of the coexistence of various phases in the trap.

Understanding the unique properties of ultra-wide band gap semiconductors requires detailed information about the exact nature of point defects and their role in determining the properties. Here, we report the first direct microscopic observation of an unusual formation of point defect complexes within the atomic-scale structure of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ using high resolution scanning transmission electron microscopy (STEM). Each complex involves one cation interstitial atom paired with two cation vacancies. These divacancy-interstitial complexes correlate directly with structures obtained by density functional theory, which predicts them to be compensating acceptors in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$. This prediction is confirmed by a comparison between STEM data and deep level optical spectroscopy results, which reveals that these complexes correspond to a deep trap within the band gap, and that the development of the complexes is facilitated by Sn doping through increased vacancy concentration. These findings provide new insight on this emerging material’s unique response to the incorporation of impurities that can critically influence their properties.

The dynamics and structure of nonequilibrium liquids, driven by nonconservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations, and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials.

The slipperiness of ice is an everyday-life phenomenon, which, surprisingly, remains controversial despite a long scientific history. The very small friction measured on ice is classically attributed to the presence of a thin self-lubricating film of meltwater between the slider and the ice. But while the macroscale friction behavior of ice and snow has been widely investigated, very little is known about the interfacial water film and its mechanical properties. In this work, we develop a stroke-probe force measurement technique to uncover the microscopic mechanisms underlying ice lubrication. We simultaneously measure the shear friction of a bead on ice and quantify the in situ mechanical properties of the interfacial film, as well as its thickness, under various regimes of speed and temperature. In contrast with standard views, meltwater is found to exhibit a complex viscoelastic rheology, with a viscosity up to 2 orders of magnitude larger than pristine water. The unconventional rheology of meltwater provides a new, consistent, rationale for ice slipperiness. Hydrophobic coatings are furthermore shown to strongly reduce friction due to a surprising change in the local viscosity, providing an unexpected explanation for waxing effects in winter sports. Beyond ice friction, our results suggest new avenues towards self-healing lubricants to achieve ultralow friction.

Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row “phalanx” formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory.

Many existing quantum supervised learning (SL) schemes consider data given a priori in a classical description. With only noisy intermediate-scale quantum (NISQ) devices available in the near future, their quantum speedup awaits the development of quantum random access memories (qRAMs) and fault-tolerant quantum computing. However, there also exist a multitude of SL tasks whose data are acquired by sensors, e.g., pattern classification based on data produced by imaging sensors. Solving such SL tasks naturally requires an integrated approach harnessing tools from both quantum sensing and quantum computing. We introduce supervised learning assisted by an entangled sensor network (SLAEN) as a means to carry out SL tasks at the physical layer. The entanglement shared by the sensors in SLAEN boosts the performance of extracting global features of the object under investigation. We leverage SLAEN to construct an entanglement-assisted support-vector machine for data classification and entanglement-assisted principal component analyzer for data compression. In both schemes, variational circuits are employed to seek the optimum entangled probe states and measurement settings to maximize the entanglement-enabled enhancement. We observe that SLAEN enjoys an appreciable entanglement-enabled performance gain, even in the presence of loss, over conventional strategies in which classical data are acquired by separable sensors and subsequently processed by classical SL algorithms. SLAEN is realizable with available technology, opening a viable route toward building NISQ devices that offer unmatched performance beyond what the optimum classical device is able to afford.

While quantum mechanics imposes a fundamental limit on the precision of interferometric measurements of mechanical motion due to measurement backaction, the nonlinear nature of the coupling also leads to parametric instabilities that place practical limits on the sensitivity by limiting the power in the interferometer. Such instabilities have been extensively studied in the context of gravitational wave detectors, and their presence has recently been reported in Advanced LIGO. Here, we observe experimentally and describe theoretically a new type of optomechanical instability that arises in two-tone backaction-evading (BAE) measurements, a protocol designed to overcome the standard quantum limit. We demonstrate the effect in the optical domain with a photonic crystal nanobeam cavity and in the microwave domain with a micromechanical oscillator coupled to a microwave resonator. In contrast to the well-known parametric oscillatory instability that occurs in single-tone, blue-detuned pumping, and results from a two-mode squeezing interaction between the optical and mechanical modes, the parametric instability in balanced two-tone optomechanics results from single-mode squeezing of the mechanical mode in the presence of small detuning errors in the two pump frequencies. Counterintuitively, the instability occurs even in the presence of perfectly balanced intracavity fields and can occur for both signs of detuning errors. We find excellent quantitative agreement with our theoretical predictions. Since the constraints on tuning accuracy become stricter with increasing probe power, the instability imposes a fundamental limitation on BAE measurements as well as other two-tone schemes, such as dissipative squeezing of optical and microwave fields or of mechanical motion. In addition to identifying a new limitation in two-tone BAE measurements, the results also introduce a new type of nonlinear dynamics in cavity optomechanics.

The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating. This dependence motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime. We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation. Using a double-quench protocol, we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions. We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space. Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization. The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering.

When embryonic stem cells differentiate, the mechanical properties of their nuclei evolve en route to their terminal state. Measurements of the deformability of cell nuclei in the transitional state that intervenes between the embryonic stem-cell state and the differentiation primed state of mouse stem cells indicate that such nuclei are auxetic; i.e., they have a negative Poisson’s ratio. We show, using a theoretical model, how this remarkable mechanical behavior results from the coupling between chromatin compaction states and nuclear shape. Our biophysical approach, which treats chromatin as an active polymer system whose mechanics is modulated by nucleosome binding and unbinding, reproduces experimental results. It provides testable predictions for changes in chromatin compaction as a function of applied force, for the correlations of chromatin compaction and nuclear shape, and for the in-phase and out-of-phase response of these quantities to an applied uniaxial oscillatory force. Our model yields a biophysical interpretation of the epigenetic landscape of stem cells, also suggesting how this landscape might be probed experimentally.

Mobile quantum impurities interacting with a fermionic bath form quasiparticles known as Fermi polarons. We demonstrate that a force applied to the bath particles can generate a drag force of similar magnitude acting on the impurities, realizing a novel, nonperturbative Coulomb drag effect. To prove this, we calculate the fully self-consistent, frequency-dependent transconductivity at zero temperature in the Baym-Kadanoff conserving approximation. We apply our theory to excitons and exciton polaritons interacting with a bath of charge carriers in a doped semiconductor embedded in a microcavity. In external electric and magnetic fields, the drag effect enables electrical control of excitons and may pave the way for the implementation of gauge fields for excitons and polaritons. Moreover, a reciprocal effect may facilitate optical manipulation of electron transport. Our findings establish transport measurements as a novel, powerful tool for probing the many-body physics of mobile quantum impurities.

The standard model of Earth’s core evolution has the bulk composition set at formation, with slow cooling beneath a solid mantle providing power for geomagnetic field generation. However, controversy surrounding the incorporation of oxygen, a critical light element, and the rapid cooling rates needed to maintain the early dynamo have called this model into question. The predicted cooling rates imply early core temperatures that far exceed estimates of the lower mantle solidus, suggesting that early core evolution was governed by interaction with a molten lower mantle. Here we develop ab initio techniques to compute the chemical potentials of arbitrary solutes in solution and use them to calculate oxygen partitioning between liquid Fe-O metal and silicate melts at the pressure-temperature ($P\text{−}T$) conditions expected for the early core-mantle system. Our distribution coefficients are compatible with those obtained by extrapolating experimental data at lower $P\text{−}T$ values and reveal that oxygen strongly partitions into metal at core conditions via an exothermic reaction. Our results suggest that the bulk of Earth’s core was undersaturated in oxygen compared to the FeO content of the magma ocean during the latter stages of its formation, implying the early creation of a stably stratified oxygen-enriched layer below the core-mantle boundary (CMB). FeO partitioning is accompanied by heat release due to the exothermic reaction. If the reaction occurred at the CMB, this heat sink could have significantly reduced the heat flow driving the core convection and magnetic field generation.

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green’s functions grow linearly with rate $\alpha$ in generic systems, with an extra logarithmic correction in 1D. The rate $\alpha$—an experimental observable—governs the exponential growth of operator complexity in a sense we make precise. This exponential growth prevails beyond semiclassical or large-$N$ limits. Moreover, $\alpha$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents ${\lambda }_L\le 2\alpha$, which complements and improves the known universal low-temperature bound ${\lambda }_L\le 2\pi T$. We illustrate our results in paradigmatic examples such as nonintegrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally, we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.

As electrical control of Néel order opens the door to reliable antiferromagnetic spintronic devices, understanding the microscopic mechanisms of antiferromagnetic switching is crucial. Spatially resolved studies are necessary to distinguish multiple nonuniform switching mechanisms; however, progress has been hindered by the lack of tabletop techniques to image the Néel order. We demonstrate spin Seebeck microscopy as a sensitive tabletop method for imaging antiferromagnetism in thin films and apply this technique to study spin-torque switching in $\mathrm{Pt}/\mathrm{NiO}$ and $\mathrm{Pt}/\mathrm{NiO}/\mathrm{Pt}$ heterostructures. We establish the interfacial antiferromagnetic spin Seebeck effect in NiO as a probe of surface Néel order. By imaging before and after applying current-induced spin torque, we resolve spin domain rotation and domain wall motion. We correlate the changes in spin Seebeck images with electrical measurements of the average Néel orientation through the spin Hall magnetoresistance, confirming that we image antiferromagnetic order.

Non-Hermiticity enriches topological phases beyond the existing Hermitian framework. Whereas their unusual features with no Hermitian counterparts were extensively explored, a full understanding about the role of symmetry in non-Hermitian physics has still been elusive, and there remains an urgent need to establish their topological classification in view of rapid theoretical and experimental progress. Here, we develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, pointlike and linelike vacant regions. On the basis of these concepts and $K$-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps, and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons. Our work establishes a theoretical framework for the fundamental and comprehensive understanding of non-Hermitian topological phases and paves the way toward uncovering unique phenomena and functionalities that emerge from the interplay of non-Hermiticity and topology.

Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is experienced only by one of the components. The second nondisordered “clean” component plays the role of a bath of adjustable size that is collisionally coupled to the “dirty” component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling, and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.

Stochastic processes underlie a vast range of natural and social phenomena. Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g., traffic congestion, are effectively probabilistic because we cannot track all relevant variables. To simulate a stochastic system’s future behavior, information about its past must be stored, and thus memory is a key resource. Quantum information processing promises a memory advantage for stochastic simulation. Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the required information in fewer dimensions than any classical simulator, thereby achieving a quantum advantage in minimal memory requirements using an individual simulator. This advantage is in contrast to recent proof-of-concept experiments, where the memory saving would only become accessible in the limit of a large number of parallel simulations. In those examples, the minimal memory registers of individual quantum simulators had the same dimensionality as their classical counterparts. Our photonic experiment thus establishes the potential of new, practical resource savings in the simulation of complex systems.

Measurement-device-independent quantum key distribution (MDI-QKD) can eliminate detector side channels and prevent all attacks on detectors. The future of MDI-QKD is a quantum network that provides service to many users over untrusted relay nodes. In a real quantum network, the losses of various channels are different and users are added and deleted over time. To adapt to these features, we propose a type of protocol that allows users to independently choose their optimal intensity settings to compensate for different channel losses. Such a protocol enables a scalable high-rate MDI-QKD network that can easily be applied for channels of different losses and allows users to be dynamically added or deleted at any time without affecting the performance of existing users.