Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto, in spite of various theoretical proposals. Here, we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice. By implementing the ground states of the toric-code model with twists through quantum circuits, we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons, i.e., the Ising anyons. In particular, we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type, and can be explored to encode topological logical qubits. Furthermore, we demonstrate how to implement both single- and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits. Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons, offering a new lens into the study of such peculiar quasiparticles.

The new dimensional deformation approach is proposed to generate higher-dimensional analogues of integrable systems. An arbitrary ($K$+1)-dimensional integrable Korteweg–de Vries (KdV) system, as an example, exhibiting symmetry, is illustrated to arise from a reconstructed deformation procedure, starting with a general symmetry integrable (1+1)-dimensional dark KdV system and its conservation laws. Physically, the dark equation systems may be related to dark matter physics. To describe nonlinear physics, both linear and nonlinear dispersions should be considered. In the original lower-dimensional integrable systems, only liner or nonlinear dispersion is included. The deformation algorithm naturally makes the model also include the linear dispersion and nonlinear dispersion.

Random numbers are one of the key foundations of cryptography. This work implements a discrete quantum random number generator (QRNG) based on the tunneling effect of electrons in an avalanche photo diode. Without any post-processing and conditioning, this QRNG can output raw sequences at a rate of 100 Mbps. Remarkably, the statistical min-entropy of the 8,000,000 bits sequence reaches 0.9944 bits/bit, and the min-entropy validated by NIST SP 800-90B reaches 0.9872 bits/bit. This metric is currently the highest value we have investigated for QRNG raw sequences. Moreover, this QRNG can continuously and stably output raw sequences with high randomness over extended periods. The system produced a continuous output of 1,174 Gbits raw sequence for a duration of 11,744 s, with every 8 Mbits forming a unit to obtain a statistical min-entropy distribution with an average value of 0.9892 bits/bit. The statistical min-entropy of all data (1,174 Gbits) achieves the value of 0.9951 bits/bit. This QRNG can produce high-quality raw sequences with good randomness and stability. It has the potential to meet the high demand in cryptography for random numbers with high quality.

Thermal-electric conversion is crucial for smart energy control and harvesting, such as thermal sensing and waste heat recovering. So far, researchers are aware of two main ways of direct thermal-electric conversion, Seebeck and pyroelectric effects, each with different working mechanisms, conditions and limitations. Here, we report the concept of Geometric Thermoelectric Pump (GTEP), as the third way of thermal-electric conversion beyond Seebeck and pyroelectric effects. In contrast to Seebeck effect that requires spatial temperature difference, GTEP converts the time-dependent ambient temperature fluctuation into electricity. Moreover, GTEP does not require polar materials but applies to general conducting systems, and thus is also distinct from pyroelectric effect. We demonstrate that GTEP results from the temperature-fluctuation-induced charge redistribution, which has a deep connection to the topological geometric phase in non-Hermitian dynamics, as a consequence of the fundamental nonequilibrium thermodynamic geometry. The findings advance our understanding of geometric phase induced multiple-physics-coupled pump effect and provide new means of thermal-electric energy harvesting.

The implementation of scalable quantum networks requires photons at the telecom band and long-lived spin coherence. The single Er$^{3+}$ in solid-state hosts is an important candidate that fulfills these critical requirements simultaneously. However, to entangle distant Er$^{3+}$ ions through photonic connections, the emission frequency of individual Er$^{3+}$ in solid-state matrix must be the same, which is challenging because the emission frequency of Er$^{3+}$ depends on its local environment. Herein, we propose and experimentally demonstrate the Stark tuning of the emission frequency of a single Er$^{3+}$ in a Y$_2$SiO$_5$ crystal by employing electrodes interfaced with a silicon photonic crystal cavity. We obtain a Stark shift of 182.9$\pm 0.8$ MHz, which is approximately 27 times of the optical emission linewidth, demonstrating promising applications in tuning the emission frequency of independent Er$^{3+}$ into the same spectral channels. Our results provide a useful solution for construction of scalable quantum networks based on single Er$^{3+}$ and a universal tool for tuning emission of individual rare-earth ions.

Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks, has attracted continuing research interests for the theoretical principles behind its success. A recent work reported an anomaly (inverse) relation between the variance of neural weights and the landscape flatness of the loss function driven under SGD [Feng Y and Tu Y Proc. Natl. Acad. Sci. USA 118 e2015617118 (2021)}]. To investigate this seeming violation of statistical physics principle, the properties of SGD near fixed points are analyzed with a dynamic decomposition method. Our approach recovers the true “energy” function under which the universal Boltzmann distribution holds. It differs from the cost function in general and resolves the paradox raised by the anomaly. The study bridges the gap between the classical statistical mechanics and the emerging discipline of artificial intelligence, with potential for better algorithms to the latter.

We present a scheme for dissipatively preparing bipartite Knill–Laflamme–Milburn (KLM) entangled state in a neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the coherent population trapping, is actively exploited to engineer a steady KLM state from an arbitrary initial state. Instead of commonly used antiblockade dynamics of two Rydberg atoms, we particularly utilize the Rydberg–Rydberg interaction as the pumping source to drive the undesired states so that it is unnecessary to satisfy a certain relation with laser detuning. The numerical simulation of the master equation signifies that both the fidelity and the purity above 98$\%$ is available with the current feasible parameters, and the corresponding steady-state fidelity is robust to the variations of the dynamical parameters.

We introduce a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free energy estimation based on targeted free energy perturbation by performing calculations on samples from both ends of the mapping. We demonstrate applications of the present method by estimating the free energy of a classical Coulomb gas in a harmonic trap.

The recent progress of the Majorana experiments paves a way for the future tests of non-Abelian braiding statistics and topologically protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary so as to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-Abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity.

Quantum Fisher information (QFI) plays an important role in quantum metrology, placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract. We observe that both the wave and particle properties within a Mach–Zehnder interferometer can naturally be quantified by QFI. Firstly, the particle property can be quantified by how well one can estimate the a priori probability of the path taken by the particle within the interferometer. Secondly, as the interference pattern is always related to some phase difference, the wave property can be quantified by how well one can estimate the phase parameter of the original state. With QFI as the unified figure of merit for both properties, we propose a more general and stronger wave-particle duality relation than the original one derived by Englert.

Recent studies have identified plasma as a topological material. Yet, these researches often depict plasma as a fluid governed by electromagnetic fields, i.e., a classical wave system. Indeed, plasma transport can be characterized by a unique diffusion process distinguished by its collective behaviors. We adopt a simplified diffusion-migration method to elucidate the topological plasma transport. Drawing parallels to the thermal conduction-convection system, we introduce a double-ring model to investigate the plasma density behaviors in the anti-parity-time reversal (APT) unbroken and broken phases. Subsequently, by augmenting the number of rings, we have established a coupled ring chain structure. This structure serves as a medium for realizing the APT symmetric one-dimensional (1D) reciprocal model, representing the simplest tight-binding model with a trivial topology. To develop a model featuring topological properties, we should modify the APT symmetric 1D reciprocal model from the following two aspects: hopping amplitude and onsite potential. From the hopping amplitude, we incorporate the non-reciprocity to facilitate the non-Hermitian skin effect, an intrinsic non-Hermitian topology. Meanwhile, from the onsite potential, the quasiperiodic modulation has been adopted onto the APT symmetric 1D reciprocal model. This APT symmetric 1D Aubry–André–Harper model is of topological nature. Additionally, we suggest the potential applications for these diffusive plasma topological states. This study establishes a diffusion-based approach to realize topological states in plasma, potentially inspiring further advancements in plasma physics.

Superconducting transmon qubits with fixed frequencies are widely used in many applications due to their advantages of better coherence and less control lines compared to the frequency tunable qubits. However, any uncontrolled interactions with the qubits such as the two-level systems could lead to adverse impacts, degrading the qubit coherence and inducing crosstalk. To mitigate the detrimental effect from uncontrolled interactions between qubits and defect modes in fixed-frequency transmon qubits, we propose and demonstrate an active approach using an off-resonance microwave drive to dress the qubit and to induce the ac-Stark shift on the qubit frequency. We show experimentally that the qubit frequency can be tuned well away from the defect mode so that the impact on qubit coherence is greatly reduced while maintaining the universal controls of the qubit initialization, readout, and single-qubit gate operations. Our approach provides an effective way for tuning the qubit frequency and suppressing the detrimental effect from the defect modes that happen to be located close to the qubit frequency.

We propose a general approach based on the gradient descent method to study the inverse problem, making it possible to reversely engineer the microscopic configurations of materials that exhibit desired macroscopic properties. Particularly, we demonstrate its application by identifying the microscopic configurations within any given frequency range to achieve transparent phonon transport through one-dimensional harmonic lattices. Furthermore, we obtain the phonon transmission in terms of normal modes and find that the key to achieving phonon transparency or phonon blocking state lies in the ratio of the mode amplitudes at ends.

We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schrödinger equation under considered parity-time symmetric potentials and for obtaining multifarious soliton solutions. Neural networks to found principally physical information are adopted to figure out the solution to the examined nonlinear partial differential equation and to generate six different types of soliton solutions, which are basic, dipole, tripole, quadruple, pentapole, and sextupole solitons we consider. We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution to the partial differential equation described before. We may assess whether physics-informed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results. Moreover, we scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works. Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate the nonlinear Schrödinger equation under consideration and to predict the dynamics of soliton solution.

We propose a scheme to generate and control supersonic shock waves in a non-resonantly incoherent pumped exciton-polariton condensate, and different types of shock waves can be generated. Under conditions of different initial step waves, the ranges of parameters about various shock waves are determined by the initial incidence function and the cross-interaction between the polariton condensate and the reservoir. In addition, shock waves are successfully found by regulating the incoherent pump. In the case of low condensation rate from polariton to condensate, these results are similar to the classical nonlinear Schrödinger equation, and the effect of saturated nonlinearity resulted from cross interaction is equivalent to the self-interaction between polariton condensates. At high condensation rates, profiles of shock waves become symmetrical due to the saturated nonlinearity. Compared to the previous studies in which the shock wave can only be found in the system with repulsive self-interaction (defocusing nonlinearity), we not only discuss the shock wave in the exciton-polariton condensate system with the repulsive self-interaction, but also find the shock wave in the condensates system with attractive self-interaction. Our proposal may provide a simple way to generate and control shock waves in non-resonantly pumped exciton-polariton systems.

Stochastic resonance is a counterintuitive phenomenon amplifying the weak periodic signal by application of external noise. We demonstrate the enhancement of a weak periodic signal by stochastic resonance in a trapped-ion oscillator when the oscillator is excited to the nonlinear regime and subject to an appropriate noise. Under the full control of the radio-frequency drive voltage, this amplification originates from the nonlinearity due to asymmetry of the trapping potential, which can be described by a forced Duffing oscillator model. Our scheme and results provide an interesting possibility to make use of controllable nonlinearity in the trapped ion, and pave the way toward a practical atomic sensor for sensitively detecting weak periodic signals from real noisy environment.

The dark energy concept in the standard cosmological model can explain the expansion of the universe. However, the mysteries surrounding dark energy remain, such as its source, its unusual negative pressure, its long-range force, and its unchanged density as the universe expands. We propose a graviton momentum hypothesis, develop a semiclassical model of gravitons, and explain the pervasive dark matter and accelerating universe. The graviton momentum hypothesis is incorporated into the standard model and explains well the mysteries related to dark energy.

This concise review summarizes recent advancements in theoretical studies of vortex quantum droplets (VQDs) in matter-wave fields. These are robust self-trapped vortical states in two- and three-dimensional (2D and 3D) Bose–Einstein condensates (BECs) with intrinsic nonlinearity. Stability of VQDs is provided by additional nonlinearities resulting from quantum fluctuations around mean-field states, often referred to as the Lee–Huang–Yang (LHY) corrections. The basic models are presented, with emphasis on the interplay between the mean-field nonlinearity, LHY correction, and spatial dimension, which determines the structure and stability of VQDs. We embark by delineating fundamental properties of VQDs in the 3D free space, followed by consideration of their counterparts in the 2D setting. Additionally, we address stabilization of matter-wave VQDs by optical potentials. Finally, we summarize results for the study of VQDs in the single-component BEC of atoms carrying magnetic moments. In that case, the anisotropy of the long-range dipole-dipole interactions endows the VQDs with unique characteristics. The results produced by the theoretical studies in this area directly propose experiments for the observation of novel physical effects in the realm of quantum matter, and suggest potential applications to the design of new schemes for processing classical and quantum information.

In practical optical communication systems, there are some factors that can affect transmission quality of optical solitons. The constant coefficient nonlinear Schrödinger (NLS) equation has been unable to meet the actual research needs. We need to use the variable coefficient NLS equation to simulate an actual system, so as to explore its potential application value. Based on the variable coefficient NLS equation, six dispersion decreasing fibers (DDFs) with different dispersion curve functions are used as transmission media to study generation and interaction of two solitons in an optical communication system. The two soliton interaction phenomena, such as the bound state solitons, are theoretically obtained. Moreover, the output characteristics of bound state solitons in different DDFs are discussed, which enriches the transmission phenomenon of two solitons in the optical communication system. This study has great application value in fields such as optical information processing devices, condensed matter physics, and plasma, and provides an indispensable theoretical basis for development of new optical devices.

A thermodynamic formalism describing the efficiency of information learning is proposed, which is applicable to stochastic thermodynamic systems with multiple internal degrees of freedom. The learning rate, entropy production rate and entropy flow from the system to the environment under coarse-grained dynamics are derived. The Cauchy–Schwarz inequality is applied to demonstrate the lower bound on the entropy production rate of an internal state. The inequality of the entropy production rate is tighter than the Clausius inequality, leading to a derivative of the upper bound on the efficiency of learning. The results are verified in cellular networks with information processes.

We theoretically demonstrate a rich and significant new families of exact spatially localized and periodic wave solutions for a modified Korteweg–de Vries equation. The model applies for the description of different nonlinear structures which include breathers, interacting solitons and interacting periodic wave solutions. A joint parameter which can take both positive and negative values of unity appeared in the functional forms of those closed form solutions, thus implying that every solution is determined for each value of this parameter. The results indicate that the existence of newly derived structures depend on whether the type of nonlinearity of the medium should be considered self-focusing or defocusing. The obtained nonlinear waveforms show interesting properties that may find practical applications.

We investigate the quantum squeezing of matter-wave solitons in atomic Bose–Einstein condensates. By calculating quantum fluctuations of the solitons via solving the Bogoliubov–de Gennes equations, we show that significant quantum squeezing can be realized for both bright and dark solitons. We also show that the squeezing efficiency of the solitons can be enhanced and manipulated by atom–atom interaction and soliton blackness. The results reported here are beneficial not only for understanding quantum property of matter-wave solitons, but also for promising applications of Bose-condensed quantum gases.

As an essential concept to understand the world, whether the real values (or physical realities) of observables are suitable to physical systems beyond the classic has been debated for many decades. Although standard no-go results based on Bell inequalities have ruled out the joint reality of incompatible quantum observables, the possibility of giving simple yet strong arguments to rule out joint reality in any physical system (not necessarily quantum) with weaker assumptions and less observables has been explored and proposed recently. Here, we perform a device-independent experiment on a two-qubit superconducting system to show that the joint reality of two observables is incompatible with locality under the weaker assumption of the reality of observables in a single space-time region (or single qubit). Our results clearly show the violation of certain inequalities derived from both linear and nonlinear criteria. In addition, we study the robustness of the linear and nonlinear criterion against the effect of systematic decoherence. Our demonstration opens up the possibility of delineating classical and non-classical boundaries with simpler nontrivial quantum system.

A certain class of exact solutions of Einstein Maxwell spacetime in general relativity is discussed to demonstrate that at the level of theory, when certain parametric resonance condition is met, the interaction of electromagnetic field with a gravitational wave will display certain Lyapunov instability and lead to exponential amplification of a gravitational wave train described by certain Newman–Penrose component of the Weyl curvature. In some way akin to a free electron laser in electromagnetic theory, by the conversion of electromagnetic energy into gravitational energy in a coherent way, the feasibility of generating a pulsed-laser-like intense beam of gravitational wave is displayed.

We first confirm an idea obtained from first-principles calculations, which is in line with symmetry theory: Although superatomic molecular orbitals (SAMOs) can be classified according to their angular momentum similar to atomic orbitals, SAMOs with the same angular momentum split due to the point group symmetry of superatoms. Based on this idea, we develop a method to quantitatively modulate the splitting spacing of molecular orbitals in a superatom by changing its structural symmetry or by altering geometric parameters with the same symmetry through expansion and compression processes. Moreover, the modulation of the position crossover is achieved between the lowest unoccupied molecular orbital and the highest occupied molecular orbital originating from the splitting of different angular momenta, leading to an effective reduction in system energy. This phenomenon is in line with the implication of the Jahn–Teller effect. This work provides insights into understanding and regulating the electronic structures of superatoms.

We consider a quantum Brayton refrigeration cycle consisting of two isobaric and two adiabatic processes, using an ideal Bose gas of finite particles confined in a harmonic trap as its working substance. Quite generally, such a machine falls into three different cases, classified as the condensed region, non-condensed phase, and regime across the critical point. When the refrigerator works near the critical region, both figure of merit and cooling load are significantly improved due to the singular behavior of the specific heat, and the coefficient of performance at maximum figure of merit is much larger than the Curzon–Ahlborn value. With the machine in the non-condensed regime, the coefficient of performance for maximum figure of merit agrees well with the Curzon–Ahlborn value.

We take the higher-order nonlinear Schrödinger equation as a mathematical model and employ the bilinear method to analytically study the evolution characteristics of femtosecond solitons in optical fibers under higher-order nonlinear effects and higher-order dispersion effects. The results show that the effects have a significant impact on the amplitude and interaction characteristics of optical solitons. The larger the higher-order nonlinear coefficient, the more intense the interaction between optical solitons, and the more unstable the transmission. At the same time, we discuss the influence of other free parameters on third-order soliton interactions. Effectively regulate the interaction of three optical solitons by controlling relevant parameters. These studies will lay a theoretical foundation for experiments and further practicality of optical soliton communications.

Inspired by the problem of biofilm growth, we numerically investigate clustering in a two-dimensional suspension of active (Janus) particles of finite size confined in a circular cavity. Their dynamics is regulated by a non-reciprocal mechanism that causes them to switch from active to passive above a certain threshold of the perceived near-neighbor density (quorum sensing). A variety of cluster phases, i.e., glassy, solid (hexatic) and liquid, are observed, depending on the particle dynamics at the boundary, the quorum sensing range, and the level of noise.