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.

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational Gaudin-type integrability, and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop “dressing tails” of higher-body terms, reminiscent of the dressed local integrals of motion found in many-body localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-$1/2$ systems disappears in the large-$S$ limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation.

The surprising insulating and superconducting states of narrow-band graphene twisted bilayers have been mostly discussed so far in terms of strong electron correlation, with little or no attention to phonons and electron-phonon effects. We found that, among the 33 492 phonons of a fully relaxed $\theta =1.08°$ twisted bilayer, there are few special, hard, and nearly dispersionless modes that resemble global vibrations of the moiré supercell, as if it were a single, ultralarge molecule. One of them, doubly degenerate at $\mathbf{\Gamma }$ with symmetry $A_1+B_1$, couples very strongly with the valley degrees of freedom, also doubly degenerate, realizing a so-called $E\otimes e$ Jahn-Teller (JT) coupling. The JT coupling lifts very efficiently all degeneracies which arise from the valley symmetry, and may lead, for an average atomic displacement as small as 0.5 m Å, to an insulating state at charge neutrality. This insulator possesses a nontrivial topology testified by the odd winding of the Wilson loop. In addition, freezing the same phonon at a zone boundary point brings about insulating states at most integer occupancies of the four ultraflat electronic bands. Following that line, we further study the properties of the superconducting state that might be stabilized by these modes. Since the JT coupling modulates the hopping between $AB$ and $BA$ stacked regions, pairing occurs in the spin-singlet Cooper channel at the inter-($AB\text{−}BA$) scale, which may condense a superconducting order parameter in the extended $s$-wave and/or $d\pm id$-wave symmetry.

In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, two-body operations with an ancilla to extract information about errors without causing backaction on the encoded information. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with a strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear oscillator. Such a cat qubit experiences only bit-flip noise, while the phase flips are exponentially suppressed. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric, bosonic-cat, and Gottesman-Kitaev-Preskill codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.

We propose a systematic approach to the nonequilibrium dynamics of strongly interacting many-body quantum systems, building upon the standard perturbative expansion in the Coulomb interaction. High-order series are derived from the Keldysh version of the determinantal diagrammatic quantum Monte Carlo algorithm, and the reconstruction beyond the weak-coupling regime of physical quantities is obtained by considering them as analytic functions of a complex-valued interaction $U$. Our advances rely on two crucial ingredients: (i) a conformal change of variable, based on the approximate location of the singularities of these functions in the complex $U$ plane, and (ii) a Bayesian inference technique, that takes into account additional known nonperturbative relations, in order to control the amplification of noise occurring at large $U$. This general methodology is applied to the strongly correlated Anderson quantum impurity model and is thoroughly tested both in and out of equilibrium. In the situation of a finite voltage bias, our method is able to extend previous studies, by bridging with the regime of unitary conductance and by dealing with energy offsets from particle-hole symmetry. We also confirm the existence of a voltage splitting of the impurity density of states and find that it is tied to a nontrivial behavior of the nonequilibrium distribution function. Beyond impurity problems, our approach could be directly applied to Hubbard-like models, as well as other types of expansions.

A single quantum of excitation of a mechanical oscillator is a textbook example of the principles of quantum physics. But mechanical oscillators, despite their pervasive presence in nature and modern technology, do not generically exist in an excited Fock state. In the past few years, careful isolation of gigahertz-frequency nanoscale oscillators has allowed experimenters to prepare such states at millikelvin temperatures. These developments illustrate the tension between the basic predictions of quantum mechanics—which should apply to all mechanical oscillators even at ambient conditions—and the extreme conditions required to observe those predictions. We resolve the tension by creating a single Fock state of a 40-THz vibrational mode in a crystal at room temperature and atmospheric pressure. After exciting a bulk diamond with a femtosecond laser pulse and detecting a Stokes-shifted photon, the Raman-active vibrational mode is prepared in the Fock state $|1⟩$ with 98.5% probability. The vibrational state is then mapped onto the anti-Stokes sideband of a subsequent pulse, which when subjected to a Hanbury Brown–Twiss intensity correlation measurement reveals the sub-Poisson number statistics of the vibrational mode. By controlling the delay between the two pulses, we are able to witness the decay of the vibrational Fock state over its 3.9-ps lifetime at ambient conditions. Our technique is agnostic to specific selection rules, and should thus be applicable to any Raman-active medium, opening a new general approach to the experimental study of quantum effects related to vibrational degrees of freedom in molecules and solid-state systems.

The turbulence problem at the level of scaling exponents is hard in part because of the multifractal scaling of small scales, which demands that each moment order be treated and understood independently. This conclusion derives from studies of velocity structure functions, energy dissipation, enstrophy density (that is, square of vorticity), etc. However, it is likely that there exist other physically pertinent quantities with less complex statistical structure in the inertial range, potentially resulting in huge simplifications in the turbulence theory. We show that velocity circulation around closed loops is such a quantity. By using a large database of isotropic turbulence, generated from numerical simulations of the Navier-Stokes equations over a wide range of Reynolds numbers, we show that circulation exhibits, to excellent accuracy, a bifractal behavior at the highest Reynolds number considered: space filling for low-order moments, close but not identical to the 1941 paradigm of Kolmogorov, and a monofractal with a dimension of about 2.2 for higher orders. This change in character, occurring around the third moment for the highest Reynolds number considered here, is reminiscent of a “phase transition.” We explore the possibility that the transition point moves to higher-order moments as the Reynolds numbers increases—even though one may continue to regard the structure as bifractal for moments of sufficiently high order. We confirm that the circulation properties depend essentially on the area of the loop, not its shape, and that the relevant contour area in figure-eight loops is the scalar area and not the vector area. These results demonstrate an intrinsic simplicity in the statistical structure of turbulence when considering circulation around closed loops, thus motivating a paradigm shift in turbulence research.

Fault-tolerant quantum computation requires qubit measurements to be both high fidelity and fast to ensure that idling qubits do not generate more errors during the measurement of ancilla qubits than can be corrected. Towards this goal, we demonstrate single-shot readout of semiconductor spin qubits with 97% fidelity in $1.5\mu \mathrm{s}$. In particular, we show that we can engineer donor-based single-electron transistors (SETs) in silicon with atomic precision to measure single spins much faster than the spin decoherence times in isotopically purified silicon ($270\mu \mathrm{s}$). By designing the SET to have a large capacitive coupling between the SET and target charge, we can optimally operate in the “strong-response” regime to ensure maximal signal contrast. We demonstrate single-charge detection with a signal-to-noise ratio (SNR) of 12.7 at 10 MHz bandwidth, corresponding to a SET charge sensitivity (integration time for $\mathrm{SNR}=2$) of 2.5 ns. We present a theory of the shot-noise sensitivity limit for the strong-response regime which predicts that the present sensitivity is about one order of magnitude above the shot-noise limit. By reducing cold amplification noise to reach the shot-noise limit, it should be theoretically possible to achieve high-fidelity, single-shot readout of an electron spin in silicon with a total readout time of approximately 36 ns.

There is growing interest in heat pumps based on materials that show thermal changes when phase transitions are driven by changes of electric, magnetic, or stress field. Importantly, regeneration permits sinks and loads to be thermally separated by many times the changes of temperature that can arise in the materials themselves. However, performance and parameterization are compromised by net heat transfer between caloric working bodies and heat-transfer fluids. Here, we show that this net transfer can be avoided—resulting in true, balanced regeneration—if one varies the applied electric field while an electrocaloric (EC) working body dumps heat on traversing a passive fluid regenerator. Our EC working body is represented by bulk ${\mathrm{PbSc}}_{0.5}{\mathrm{Ta}}_{0.5}{\mathrm{O}}_3$ near its first-order ferroelectric phase transition, where we record directly measured adiabatic temperature changes of up to 2.2 K. Indirectly measured adiabatic temperature changes of similar magnitude are identified, unlike normal, from adiabatic measurements of polarization, at nearby measurement set temperatures, without assuming a constant heat capacity. The resulting high-resolution field-temperature-entropy maps of our material, and a small clamped companion sample, are used to construct cooling cycles that assume the use of an ideal passive regenerator in order to span $\le 20\mathrm{K}$. These cooling cycles possess well-defined coefficients of performance that are bounded by well-defined Carnot limits, resulting in large ($>50\%$) well-defined efficiencies that are not unduly compromised by a small field hysteresis. Our approach permits the limiting performance of any caloric material in a passive regenerator to be established, optimized, and compared; provides a recipe for true regeneration in prototype cooling devices; and could be extended to balance active regeneration.

We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic oscillator modes associated with the tightly confined channel, and hence, the corresponding “lattice sites” are intimately related to the energy of the system. We analyze the quantum-transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension combined with the quasienergy spectrum of the periodically driven channel allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.

We establish an operational characterization of general convex resource theories—describing the resource content of not only states but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs)—in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory. Specifically, we introduce a quantifier of resourcefulness of a measurement in any GPT, the generalized robustness of measurement, and show that it admits an operational interpretation as the maximum advantage that a given measurement provides over resourceless measurements in all state discrimination tasks. In the special case of quantum mechanics, we connect discrimination problems with single-shot information theory by showing that the generalized robustness of any measurement can be alternatively understood as the maximal increase in one-shot accessible information when compared to free measurements. We introduce two different approaches to quantifying the resource content of a physical channel based on the generalized robustness measures and show that they quantify the maximum advantage that a resourceful channel can provide in several classes of state and channel discrimination tasks. Furthermore, we endow another measure of resourcefulness of states, the standard robustness, with an operational meaning in general GPTs as the exact quantifier of the maximum advantage that a state can provide in binary channel discrimination tasks. Finally, we establish that several classes of channel and state discrimination tasks form complete families of monotones fully characterizing the transformations of states and measurements, respectively, under general classes of free operations. Our results establish a fundamental connection between the operational tasks of discrimination and core concepts of resource theories—the geometric quantification of resources and resource manipulation—valid for all physical theories beyond quantum mechanics with no additional assumptions about the structure of the GPT required.

The nitrogen-vacancy (NV) center in diamond exhibits spin-dependent fluorescence and long spin coherence times under ambient conditions, enabling applications in quantum information processing and sensing. NV centers near the surface can have strong interactions with external materials and spins, enabling new forms of nanoscale spectroscopy. However, NV spin coherence degrades within 100 nm of the surface, suggesting that diamond surfaces are plagued with ubiquitous defects. Prior work on characterizing near-surface noise has primarily relied on using NV centers themselves as probes; while this has the advantage of exquisite sensitivity, it provides only indirect information about the origin of the noise. Here we demonstrate that surface spectroscopy methods and single-spin measurements can be used as complementary diagnostics to understand sources of noise. We find that surface morphology is crucial for realizing reproducible chemical termination, and use this insight to achieve a highly ordered, oxygen-terminated surface with suppressed noise. We observe NV centers within 10 nm of the surface with coherence times extended by an order of magnitude.

Active nematics contain topological defects that (under sufficient activity) move, create, and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbulence under the spherical confinement, using numerical modeling. In such spherical droplets, we show the three-dimensional structure of the topological defects, which, because of closed confinement, emerge in the form of closed loops or surface-to-surface spanning line segments. In the turbulent regime, the defects are shown to be strongly spatially and time varying, with ongoing transformations between positive winding, negative winding, and twisted profiles, and with defect loops of zero and nonzero topological charge. The timeline of the active turbulence is characterized by four types of bulk topology-linked events—breakup, annihilation, coalescence, and crossover of the defects—which we note could be used for the analysis of the active turbulence in different three-dimensional geometries. The turbulent regime is separated by a first-order structural transition from a low activity regime of a steady-state vortex structure and an offset single point defect. We also demonstrate coupling of surface and bulk topological defect dynamics by changing from strong perpendicular to in-plane surface alignment. More generally, this work aims to provide insight into three-dimensional active turbulence, distinctly from the perspective of the topology of the emergent three-dimensional topological defects.

With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the bilinear structure of the matrix representation of the generative model, we separate its null eigenspace and reduce the exact description of the generative model to a smaller vector space. After reduction, we group generative models in universality classes according to their rank and metric signature and work out, in a computationally affordable way, their relevant properties (e.g., spectrum). The reduction also provides the environment for a simplified computation of their properties. The proposed scheme works for any generative model admitting a matrix representation and will be very useful in the study of dynamical processes on networks, as well as in the understanding of generative models to come, according to the provided classification.

Understanding the material parameters that control the superconducting transition temperature $T_c$ is a problem of fundamental importance. In many novel superconductors phase fluctuations determine $T_c$, rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension. This in turn leads to an upper bound on $T_c$ in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrow-band systems, where mean-field theory fails. For a simple parabolic band in 2D with Fermi energy $E_F$, we find that $k_B{T}_c\le E_F/8$, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases. Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum $T_c$ to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on $T_c$ in 3D.

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large-$N$ models exhibiting exponential growth of OTOCs and a sharp chaos wave front and other random circuit models showing a diffusively broadened wave front. In this paper, we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large-$N$ limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wave front. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a crossover to a diffusively broadened wave front. At small $N$, we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively broadened wave front.

Magnetic moments arranged at the corners of a honeycomb lattice are predicted to form a novel state of matter, the Kitaev quantum spin liquid, under the influence of frustration effects between bond-dependent Ising interactions. Some layered honeycomb iridates and related materials, such as ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and $\alpha \text{−}{\mathrm{RuCl}}_3$, are proximate to the Kitaev quantum spin liquid, but bosonic spin-wave excitations associated with undesirable antiferromagnetic long-range order mask the inherent properties of the Kitaev Hamiltonian. Here, we use ${}^{63}\mathrm{Cu}$ nuclear quadrupole resonance to uncover the low-energy spin excitations in the nearly ideal honeycomb lattice of effective spin $S=1/2$ at the ${\mathrm{Ir}}^{4+}$ sites in ${\mathrm{Cu}}_2{\mathrm{IrO}}_3$. We demonstrate that, unlike ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, Ir spin fluctuations exhibit no evidence for critical slowing-down toward magnetic long-range order in zero external magnetic field. Moreover, the low-energy spin excitation spectrum is dominated by a mode that has a large excitation gap comparable to the Ising interactions, a signature expected for Majorana fermions of the Kitaev quantum spin liquid.