In the traditional random-conformational-search model, various hypotheses with a series of meta-stable intermediate states were proposed to resolve the Levinthal paradox in protein-folding time. Here we introduce a quantum strategy to formulate protein folding as a quantum walk on a definite graph, which provides us a general framework without making hypotheses. Evaluating it by the mean of first passage time, we find that the folding time via our quantum approach is much shorter than the one obtained via classical random walks. This idea is expected to evoke more insights for future studies.

We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine $k$ precisely, if it is unknown. The time complexity of our counting algorithm is $O(\sqrt{N})$, similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.

Based on velocity resonance and Darboux transformation, soliton molecules and hybrid solutions consisting of soliton molecules and smooth positons are derived. Two new interesting results are obtained: the first is that the relationship between soliton molecules and smooth positons is clearly pointed out, and the second is that we find two different interactions between smooth positons called strong interaction and weak interaction, respectively. The strong interaction will only disappear when $t \to \infty$. This strong interaction can also excite some periodic phenomena.

Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates. However, it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size. Here, we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond. We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment. Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms, and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.

Building blocks of quantum computers have been demonstrated in small to intermediate-scale systems. As one of the leading platforms, the trapped ion system has attracted wide attention. A significant challenge in this system is to combine fast high-fidelity gates with scalability and convenience in ion trap fabrication. Here we propose an architecture for large-scale quantum computing with a two-dimensional array of atomic ions trapped at such large distance which is convenient for ion-trap fabrication but usually believed to be unsuitable for quantum computing as the conventional gates would be too slow. Using gate operations far outside of the Lamb–Dicke region, we show that fast and robust entangling gates can be realized in any large ion arrays. The gate operations are intrinsically parallel and robust to thermal noise, which, together with their high speed and scalability of the proposed architecture, makes this approach an attractive one for large-scale quantum computing.

We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point. Motivated by the conformal mapping, we find that the dynamical entanglement spectra demonstrate distinct finite-size scaling behaviors from the static case. As a prototypical example, we compute real-time dynamics of the entanglement spectra of a one-dimensional transverse-field Ising chain. Numerical simulation confirms that the entanglement spectra scale with the subsystem size $l$ as $\sim$$l^{-1}$ for the dynamical equilibrium state, much faster than $\propto$ $\ln^{-1} l$ for the critical ground state. In particular, as a byproduct, the entanglement spectra at the long time limit faithfully gives universal tower structure of underlying Ising criticality, which shows the emergence of operator-state correspondence in the quantum dynamics.

The spin qubit in quantum dots is one of the leading platforms for quantum computation. A crucial requirement for scalable quantum information processing is the high efficient measurement. Here we analyze the measurement process of a quantum-dot spin qubit coupled to a superconducting transmission line resonator. Especially, the phase shift of the resonator is sensitive to the spin states and the gate operations. The response of the resonator can be used to measure the spin qubit efficiently, which can be extend to read out the multiple spin qubits in a scalable solid-state quantum processor.

Solitonic characteristics are revealed in the diffusion process of a hump or a notch wave packet in a one-dimensional Bose–Einstein condensate. By numerically solving the time-dependent Gross–Pitaevskii equation, we find completely different spreading behavior for attractive or repulsive condensates. For the attractive condensate, a series of bright solitons are continuously generated one after another at the wave front and they nearly stay at the positions where they are generated in the whole diffusion process. In contrast, for the repulsive condensate, the initial wave packet splits at the beginning into a series of grey solitons that travel at different velocities. The moving velocity of the grey soliton depends on nonlinear interaction strength, as well as the shape of a particular grey soliton.

We demonstrate a long-coherent-time coupling between microwave and optical fields through cold atomic ensembles. The phase information of the microwave field is stored in a coherent superposition state of a cold atomic ensemble and is then read out by two optical fields after 12 ms. A similar operation of mapping the phase of optical fields into a cold atomic ensemble and then retrieving by microwave is also demonstrated. These studies demonstrate that long-coherent-time cold atomic ensembles could resonantly couple with microwave and optical fields simultaneously, which paves the way for realizing high-efficiency, high-bandwidth, and noiseless atomic quantum converters.

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the (2+1)-dimensional fifth-order KdV system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the $N$-soliton solution, we obtain hybrid solutions consisting of soliton molecules, lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules, and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order KdV equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.

We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop (PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator (OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer (DDS) which is also referenced to the 100 MHZ OCXO to generate the final 6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are $-$47 dBc/Hz, $-$77 dBc/Hz, $-$104 dBc/Hz and $-$121 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than $5.0 \times 10^{-14}\tau^{1/2}$ when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.

We report the realization of quantum logic spectroscopy on the $^1\!S_0\rightarrow {}^3\!P_0$ clock transition of a single $^{27}$Al$^+$ ion. This ion is trapped together with a $^{40}$Ca$^+$ ion in a linear Paul trap, coupled by Coulomb repulsion, which provides sympathetic Doppler laser cooling and also the means for internal state detection of the clock state of the $^{27}$Al$^+$ ion. A repetitive quantum nondemolition measurement is performed to improve the fidelity of state detection. These techniques are applied to obtain clock spectroscopy at approximately 45 Hz. We also perform the preliminary locking on the $^1\!S_0\rightarrow {}^3\!P_0$ clock transition. Our work is a fundamental step that is necessary toward obtaining an ultra-precision quantum logic clock based on $^{40}$Ca$^+$-$^{27}$Al$^+$ ions.

Temperature is a fundamental thermodynamic variable for matter. Physical observables are often found to either increase or decrease with it, or show a non-monotonic dependence with peaks signaling underlying phase transitions or anomalies. Statistical field theory has established connection between temperature and time: a quantum ensemble with inverse temperature $\beta$ is formally equivalent to a dynamic system evolving along an imaginary time from 0 to $i\beta$ in the space one dimension higher. Here we report that a gas of hard-core bosons interacting with a thermal bath manifests an unexpected temperature-periodic oscillation of its macroscopic observables, arising from the microscopic origin of space-time locked translational symmetry breaking and crystalline ordering. Such a temperature crystal, supported by quantum Monte Carlo simulation, generalizes the concept of purely spatial density-wave order to the imaginary time axis for Euclidean action.

Measurement-device-independent quantum key distribution (MDI-QKD) offers a practical way to realize a star-type quantum network. Previous experiments on MDI-QKD networks can only support the point-to-point communication. We experimentally demonstrate a plug-and-play MDI-QKD network which can support the point-to-multipoint communication among three users. Benefiting from the plug-and-play MDI-QKD architecture, the whole network is automatically stabilized in spectrum, polarization, arrival time, and phase reference. The users only need the encoding devices, which means that the hardware requirements are greatly reduced. Our experiment shows that it is feasible to establish a point-to-multipoint MDI-QKD network.

High-dimensional quantum states key distribution (HD-QKD) can enable more than one bit per photon and tolerate more noise. Recently, a practical HD-QKD system based on time-phase states has provided a secret key at Mbps over metropolitan distances. For the purposes of further improving the secret key rate of a practical HD-QKD system, we make two main contributions in this work. Firstly, we present an improved parameter estimation for this system in the finite-key scenario based on the Chernoff bound and the improved Chernoff bound. Secondly, we analyze how the dimension $d$ affects the performance of the practical HD-QKD system. We present numerical simulations about the secret key rate of the practical HD-QKD system based on different parameter estimation methods. It is found that using the improved Chernoff bound can improve the secret key rate and maximum channel loss of the practical HD-QKD system. In addition, a mixture of the 4-level and 8-level practical HD-QKD system can provide better performance in terms of the key generation rate over metropolitan distances.

The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Three Alice–Bob Boussinesq (ABB) nonlocal systems with shifted parity ($\hat{P}_{\rm s}$), delayed time reversal ($\hat{T}_{\rm d}$) and $\hat{P}_{\rm s}\hat{T}_{\rm d}$ nonlocalities are investigated. The multi-soliton solutions of these models are systematically found from the $\hat{P}_{\rm s}$, $\hat{T}_{\rm d}$ and $\hat{P}_{\rm s}\hat{T}_{\rm d}$ symmetry reductions of a coupled local Boussinesq system. The result shows that for ABB equations with $\hat{P}_{\rm s}$ and/or $\hat{T}_{\rm d}$ nonlocality, an odd number of solitons is prohibited. The solitons of the $\hat{P}_{\rm s}$ nonlocal ABB and $\hat{T}_{\rm d}$ nonlocal ABB equations must be paired, while any number of solitons is allowed for the $\hat{P}_{\rm s}\hat{T}_{\rm d}$ nonlocal ABB system. $t$-breathers, $x$-breathers and rogue waves exist for all three types of nonlocal ABB system. In particular, different from classical local cases, the first-order rogue wave can have not only four leaves but also five and six leaves.

Considering the influences of collective dephasing, multilocal qutrit-flip, local qutrit-flip, and the combination of global mixed noise, we study the dynamics of entanglement and the phenomenon of distillability of sudden death (DSD) in a qutrit-qutrit system under various decoherent noises. It is shown that the system always undergoes DSD when it interacts with multilocal and local qutrit-flip noise, and the time-determined bound entangled state is more dependent on different noises. Comparing with the cases of global mixed and collective dephasing noise, we conclude that the qutrit-flip noise is responsible for the DSD.

We study a homogeneous two-component dipolar Fermi gas with 1D spin-orbit coupling (SOC) at zero temperature and find that the system undergoes a transition from the paramagnetic phase to the ferromagnetic phase under suitable dipolar interaction constant $\lambda_{\rm d}$, SOC constant $\lambda_{\rm SOC}$ and contact interaction constant $\lambda_{\rm s}$. This phase transition can be of either 1st order or 2nd order, depending on the parameters. Near the 2nd-order phase transition, the system is partially magnetized in the ferromagnetic phase. With SOC, the ferromagnetic phase can even exist in the absence of the contact interaction. The increase in dipolar interaction, SOC strength, and contact interaction are all helpful to stabilize the ferromagnetic state. The critical dipolar interaction strength at the phase transition can be reduced by the increase in SOC strength or contact interaction. Phase diagrams of these systems are obtained.

Quantum sensing, using quantum properties of sensors, can enhance resolution, precision, and sensitivity of imaging, spectroscopy, and detection. An intriguing question is: Can the quantum nature (quantumness) of sensors and targets be exploited to enable schemes that are not possible for classical probes or classical targets? Here we show that measurement of the quantum correlations of a quantum target indeed allows for sensing schemes that have no classical counterparts. As a concrete example, in the case that the second-order classical correlation of a quantum target could be totally concealed by non-stationary classical noise, the higher-order quantum correlations can single out a quantum target from the classical noise background, regardless of the spectrum, statistics, or intensity of the noise. Hence a classical-noise-free sensing scheme is proposed. This finding suggests that the quantumness of sensors and targets is still to be explored to realize the full potential of quantum sensing. New opportunities include sensitivity beyond classical approaches, non-classical correlations as a new approach to quantum many-body physics, loophole-free tests of the quantum foundation, et cetera.

The first digit law, also known as Benford's law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form $\log(1+{1}/{d})$, where $d=1, 2,\ldots, 9$. Such a law has been elusive for over 100 years because it has been obscure whether this law is due to the logical consequence of the number system or some mysterious mechanism of nature. We provide a simple and elegant proof of this law from the application of the Laplace transform, which is an important tool of mathematical methods in physics. It is revealed that the first digit law originates from the basic property of the number system, thus it should be attributed as a basic mathematical knowledge for wide applications.

We study the asymmetric decompositions of bound-state (BS) soliton solutions to the nonlinear Schrödinger equation. Assuming that the BS solitons are split into multiple solitons with different displacements, we obtain more accurate decompositions compared to the symmetric decompositions. Through graphical techniques, the asymmetric decompositions are shown to overlap very well with the real trajectories of the BS soliton solutions.

Using the single-mode approximation, we study entanglement measures including two independent quantities; i.e., negativity and von Neumann entropy for a tripartite generalized Greenberger–Horne–Zeilinger (GHZ) state in noninertial frames. Based on the calculated negativity, we study the whole entanglement measures named as the algebraic average $\pi_{3}$-tangle and geometric average ${\it \Pi}_{3}$-tangle. We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits. The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers. The results show that there will always exist entanglement, even if acceleration $r$ arrives to infinity. The degree of entanglement for all 1–1 tangles are always equal to zero, but 1–2 tangles always decrease with the acceleration parameter $r$. We notice that the von Neumann entropy increases with the number of the accelerated observers and $S_{\kappa_{\rm I}\zeta_{\rm I}}$ ($\kappa, \zeta\in ({\rm A, B, C})$) first increases and then decreases with the acceleration parameter $r$. This implies that the subsystem $\rho_{\kappa_{\rm I}\zeta_{\rm I}}$ is first more disorder and then the disorder will be reduced as the acceleration parameter $r$ increases. Moreover, it is found that the von Neumann entropies $S_{\rm ABCI}$, $S_{\rm ABICI}$ and $S_{\rm AIBICI}$ always decrease with the controllable angle $\theta$, while the entropies of the bipartite subsystems $S_{2-2_{\rm non}}$ (two accelerated qubits), $S_{2-1_{\rm non}}$ (one accelerated qubit) and $S_{2-0_{\rm non}}$ (without accelerated qubit) first increase with the angle $\theta$ and then decrease with it.

With the development of quantum information processing, multipartite entanglement measures are needed in many cases. However, there are still no complete orthogonal genuine multipartite entanglement (GME) bases available as Bell states to bipartite systems. To achieve this goal, we find a method to construct complete orthogonal GME states, and we exclude many equivalent states by leveraging the group theory. We also provide the case of a $3$-order $3$-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application. Moreover, we discuss some open questions and believe that this work will enlighten extensive studies in this field.

The Weyl semimetal has emerged as a new topologically nontrivial phase of matter, hosting low-energy excitations of massless Weyl fermions. Here, we present a comprehensive study of a type-II Weyl semimetal WP$_{2}$. Transport studies show a butterfly-like magnetoresistance at low temperature, reflecting the anisotropy of the electron Fermi surfaces. This four-lobed feature gradually evolves into a two-lobed variant with an increase in temperature, mainly due to the reduced relative contribution of electron Fermi surfaces compared to hole Fermi surfaces for magnetoresistance. Moreover, an angle-dependent Berry phase is also discovered, based on quantum oscillations, which is ascribed to the effective manipulation of extremal Fermi orbits by the magnetic field to feel nearby topological singularities in the momentum space. The revealed topological character and anisotropic Fermi surfaces of the WP$_{2}$ substantially enrich the physical properties of Weyl semimetals, and show great promises in terms of potential topological electronic and Fermitronic device applications.

We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation. An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values. As an example, we apply our method to the derivation of three-mode symmetric continuous variable entangled state. Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.

Using the adiabatic invariant action and applying the Bohr–Sommerfeld quantization rule and first law of black hole thermodynamics, a study of the quantization of the entropy and horizon area of a Kerr–Newman–de Sitter black hole is carried out. The same entropy spectrum is obtained in two different coordinate systems. It is also observed that the spacing of the entropy spectrum is independent of the black hole parameters. Also, the corresponding quantum of horizon area is in agreement with the results of Bekenstein.

Pressure generation to a higher pressure range in a large-volume press (LVP) denotes our ability to explore more functional materials and deeper Earth's interior. Pressure generated by normal tungsten carbide (WC) anvils in a commercial way is mostly limited to 25 GPa in LVPs due to the limitation of their hardness and design of cell assemblies. We adopt three newly developed WC anvils for ultrahigh pressure generation in a Walker-type LVP with a maximum press load of 1000 ton. The hardest ZK01F WC anvils exhibit the highest efficiency of pressure generation than ZK10F and ZK20F WC anvils, which is related to their performances of plastic deformations. Pressure up to 35 GPa at room temperature is achieved at a relatively low press load of 4.5 MN by adopting the hardest ZK01F WC anvils with three tapering surfaces in conjunction with an optimized cell assembly, while pressure above 35 GPa at 1700 K is achieved at a higher press load of 7.5 MN. Temperature above 2000 K can be generated by our cell assemblies at pressure below 30 GPa. We adopt such high-pressure and high-temperature techniques to fabricate several high-quality and well-sintered polycrystalline minerals for practical use. The present development of high-pressure techniques expands the pressure and temperature ranges in Walker-type LVPs and has wide applications in physics, materials, chemistry, and Earth science.