We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.

Human experts cannot efficiently access physical information of a quantum many-body states by simply “reading” its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. We demonstrate that convolutional neural network (CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.

Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering (EPR steering) [C. Y. Chiu et al., npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.

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 development of high-fidelity two-qubit quantum gates is essential for digital quantum computing. Here, we propose and realize an all-microwave parametric controlled-Z (CZ) gates by coupling strength modulation in a superconducting Transmon qubit system with tunable couplers. After optimizing the design of the tunable coupler together with the control pulse numerically, we experimentally realized a 100 ns CZ gate with high fidelity of 99.38%$ \pm 0.34$% and the control error being 0.1%. We note that our CZ gates are not affected by pulse distortion and do not need pulse correction, providing a solution for the real-time pulse generation in a dynamic quantum feedback circuit. With the expectation of utilizing our all-microwave control scheme to reduce the number of control lines through frequency multiplexing in the future, our scheme draws a blueprint for the high-integrable quantum hardware design.

The upper critical dimension of the Ising model is known to be $d_{\rm c}=4$, above which critical behavior is regarded to be trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model simultaneously exhibits two upper critical dimensions at $(d_{\rm c}=4,~d_{\rm p}=6)$, and critical clusters for $d \geq d_{\rm p}$, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs. Our findings significantly advance the understanding of the Ising model, which is a fundamental system in many branches of physics.

We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation from which only short Markov chains are needed before making measurements for physical observables, irrespective of the system locating at the classical critical point, fermionic Mott insulator, Dirac semimetal, or quantum critical point. We further propose a network-initialized Monte Carlo scheme based on such neural networks, which provides independent samplings and can accelerate the Monte Carlo simulations by significantly reducing the thermalization process. We demonstrate the performance of our approach on the two-dimensional Ising and fermion Hubbard models, expect that it can systematically speed up the Monte Carlo simulations especially for the very challenging many-electron problems.

Non-Hermitian materials can exhibit not only exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is unclear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functions can only affect the Hall conductivity. However, we are surprised to find a non-Hermitian anomalous Berry connection induced anomalous linear longitudinal conductivity independent of the scattering time. We also show the emergence of a second-order nonlinear longitudinal conductivity induced by non-Hermitian anomalous Berry connection, violating a well-known fact of its absence in a Hermitian system with symmetric energy spectra. These anomalous phenomena are illustrated in a pseudo-Hermitian system with large non-Hermitian anomalous Berry connection. Finally, we propose a practical scheme to realize the anomalous oscillations in an optical system.

Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal interesting topological properties but have not been measured in non-Abelian systems. Here, we use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. By manipulating the Hamiltonian with periodic drivings, we simulate the Bernevig–Hughes–Zhang model and obtain the quantum geometric tensor from interference oscillation. In addition, we reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.

High-fidelity two-qubit gates are essential for the realization of large-scale quantum computation and simulation. Tunable coupler design is used to reduce the problem of parasitic coupling and frequency crowding in many-qubit systems and thus thought to be advantageous. Here we design an extensible 5-qubit system in which center transmon qubit can couple to every four near-neighboring qubits via a capacitive tunable coupler and experimentally demonstrate high-fidelity controlled-phase (CZ) gate by manipulating central qubit and one near-neighboring qubit. Speckle purity benchmarking and cross entropy benchmarking are used to assess the purity fidelity and the fidelity of the CZ gate. The average purity fidelity of the CZ gate is 99.69$\pm 0.04$% and the average fidelity of the CZ gate is 99.65$\pm 0.04$%, which means that the control error is about 0.04%. Our work is helpful for resolving many challenges in implementation of large-scale quantum systems.

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.

We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations. A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues. Under the renormalization of a factor $b$, the largest eigenvalue $\sigma_1$ has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation $\sigma_1^b = b^{\beta/\nu} \sigma_1$, where $\beta$ and $\nu$ are the critical exponents of order parameter and correlation length, respectively. With the Ising model in different dimensions, it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class. Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian, which is the foundation of Wilson's RG theory and is absent for most complex systems.

Memory is a ubiquitous characteristic of complex systems, and critical phenomena are one of the most intriguing phenomena in nature. Here, we propose an Ising model with memory, develop a corresponding theory of critical phenomena with memory for complex systems, and discover a series of surprising novel results. We show that a naive theory of a usual Hamiltonian with a direct inclusion of a power-law decaying long-range temporal interaction violates radically a hyperscaling law for all spatial dimensions even at and below the upper critical dimension. This entails both indispensable consideration of the Hamiltonian for dynamics, rather than the usual practice of just focusing on the corresponding dynamic Lagrangian alone, and transformations that result in a correct theory in which space and time are inextricably interwoven, leading to an effective spatial dimension that repairs the hyperscaling law. The theory gives rise to a set of novel mean-field critical exponents, which are different from the usual Landau ones, as well as new universality classes. These exponents are verified by numerical simulations of the Ising model with memory in two and three spatial dimensions.

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.

Utilizing some conservation laws of the (1+1)-dimensional Camassa–Holm (CH) equation and/or its reciprocal forms, some (n+1)-dimensional CH equations for $n\geq 1$ are constructed by a modified deformation algorithm. The Lax integrability can be proven by applying the same deformation algorithm to the Lax pair of the (1+1)-dimensional CH equation. A novel type of peakon solution is implicitly given and expressed by the LambertW function.

An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang–Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models.

Starting from a general sixth-order nonlinear wave equation, we present its multiple kink solutions, which are related to the famous Hirota form. We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures. By introducing the velocity resonance mechanism to the multiple kink solutions, we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients. The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited. After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada–Kotera–Caudrey–Dodd–Gibbons (SKCDG) equation, the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.

We apply supervised machine learning to study the topological states of one-dimensional non-Hermitian systems. Unlike Hermitian systems, the winding number of such non-Hermitian systems can take half integers. We focus on a non-Hermitian model, an extension of the Su–Schrieffer–Heeger model. The non-Hermitian model maintains the chiral symmetry. We find that trained neuron networks can reproduce the topological phase diagram of our model with high accuracy. This successful reproduction goes beyond the parameter space used in the training process. Through analyzing the intermediate output of the networks, we attribute the success of the networks to their mastery of computation of the winding number. Our work may motivate further investigation on the machine learning of non-Hermitian systems.

A random quantum circuit is a minimally structured model to study entanglement dynamics of many-body quantum systems. We consider a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we find that, as the physical error rate is decreased below a critical value $p_{\rm c} \approx 0.056$, the logarithmic entanglement negativity changes from the area law to the volume law, giving rise to an entanglement transition. The critical exponent of the correlation length can be determined from the finite-size scaling analysis, revealing the universal dynamic property of the noisy intermediate-scale quantum devices.

Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources in both quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average phonon number of the oscillation mode is used as the order parameter to provide evidence for the DPT. Our work highlights the suitability of trapped ions for simulating open quantum systems and shall facilitate further investigations of DPT with various dissipation terms.

Stabilized by quantum fluctuations, dipolar Bose–Einstein condensates can form self-bound liquid-like droplets. However in the Bogoliubov theory, there are imaginary phonon energies in the long-wavelength limit, implying dynamical instability of this system. A similar instability appears in the Bogoliubov theory of a binary quantum droplet, and is removed due to higher-order quantum fluctuations as shown recently [Gu Q and Yin L 2020 Phys. Rev. B 102 220503(R)]. We study the excitation energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations significantly enhance the phonon stability. We adopt a self-consistent approach without the problem of complex excitation energy in the Bogoliubov theory, and obtain a stable anisotropic sound velocity which is consistent with the superfluid hydrodynamic theory, but slightly different from the result of the extended Gross–Pitaevskii equation due to quantum depletion. A modified Gross–Pitaevskii equation in agreement with the Beliaev theory is proposed, which takes the effect of quantum fluctuations into account more completely.

We study the quantum-droplet state in a three-dimensional (3D) Bose gas in the presence of 1D spin-orbit coupling and Raman coupling, especially the stripe phase with density modulation, by numerically computing the ground state energy including the mean-field energy and Lee–Huang–Yang correction. In this droplet state, the stripe can exist in a wider range of Raman coupling, compared with the BEC-gas state. More intriguingly, both spin-orbit coupling and Raman coupling strengths can be used to tune the droplet density.

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 interaction between optical solitons is of great significance for studying interaction between light and matter and development of all-optical devices, and is conducive to the design of integrated optical path. Optical soliton interactions for the nonlinear Schrödinger equation are investigated to improve the communication quality and system integration. Solutions of the equation are derived and used to analyze the interaction of two solitons. Some suggestions are put forward to weaken their interactions.

Exploring quantum phenomena beyond predictions of any classical model has fundamental importance to understand the boundary of classical and quantum descriptions of nature. As a typical property that a quantum system behaves distinctively from a classical counterpart, contextuality has been studied extensively and verified experimentally in systems composed of at least three levels (qutrit). Here we extend the scope of experimental test of contextuality to a minimal quantum system of only two states (qubit) by implementing the minimum error state discrimination on a single $^{171}$Yb$^+$ ion. We observe a substantial violation of a no-go inequality derived by assuming non-contextuality, and firmly conclude that the measured results of state discrimination cannot be reconciled with any non-contextual description. We also quantify the contextual advantage of state discrimination and the tolerance against quantum noises.

High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. We demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined with other qubit readout methods based on the discrimination of cavity photon states to further improve the qubit state readout.

The fractional second- and third-order nonlinear Schrödinger equation is studied, symmetric and antisymmetric soliton solutions are derived, and the influence of the Lévy index on different solitons is analyzed. The stability and stability interval of solitons are discussed. The anti-interference ability of stable solitons to the small disturbance shows a good robustness.

The solutions of the problems related to open quantum systems have attracted considerable interest. We propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. We then optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels. The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.

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.

We experimentally demonstrate a low-noise phase-sensitive amplifier (PSA) scheme that is able to amplify bright entangled beams at a high level intensity gain of up to 4.4. Moreover, we demonstrate that the PSA scheme introduces much less uncorrelated extra noise to the entangled state than the phase-insensitive amplifier scheme with the same intensity gain. This PSA scheme has potential applications for quantum communication in continuous variable regimes.