The Poisson equation has wide applications in many areas of science and engineering. Although there are some quantum algorithms that can efficiently solve the Poisson equation, they generally require a fault-tolerant quantum computer, which is beyond the current technology. We propose a variational quantum algorithm (VQA) to solve the Poisson equation, which can be executed on noisy intermediate-scale quantum devices. In detail, we first adopt the finite-difference method to transform the Poisson equation into a linear system. Then, according to the special structure of the linear system, we find an explicit tensor product decomposition, with only $(2{log}_{2}n+1)$ items, of its coefficient matrix under a specific set of simple operators, where $n$ is the dimension of the coefficient matrix. This implies that the proposed VQA needs fewer quantum measurements, which dramatically reduces the required quantum resources. Additionally, we design observables to efficiently evaluate the expectation values of the simple operators on a quantum computer. Numerical experiments demonstrate that our algorithm can solve the Poisson equation.

Quantum phase transitions, being in charge of the property of matter, are normally induced by varying the Hamiltonian and are characterized by an avoided level crossing between the ground and an excited state. Recently, a quantum phase anomaly induced by a boundary is predicted theoretically as the number of sites $N$ goes to infinity in a one-dimensional Heisenberg spin $XY$ model without an external magnetic field. The infinite-size lattice apparently is inaccessible in experiment, which prevents the experimental observation of the theoretical prediction. In this paper, we find that the finite-size odd-sited lattice can also give the infinite-size lattice's ground-state behavior, and successfully observe such a critical anomaly between two phases having topologically different boundary conditions for the Mott insulator in a finite-size photonic lattice.

We study realistic 3D laser cooling of positronium (Ps) in the presence of a magnetic field. Triplet and singlet states mixing due to the magnetic field, and dynamical Stark effect, generally produce higher annihilation rates than in the zero-field case. 3D cooling is efficient only at very low field $B\lesssim 50\mathrm{mT}$ and at high field values $B⪆0.7\mathrm{T}$. Near $100\mathrm{ns}$ long laser pulses, spectrally broad enough to cover most of the Ps Doppler profile and with energy in the $\mathrm{mJ}$ range, are required to cool Ps. Simulations based on full diagonalization of the Stark and Zeeman Hamiltonian and a kinetic Monte Carlo algorithm exactly solving the rate equations indicate that an efficient cooling (typically from $300\mathrm{K}$ down to below $50\mathrm{K}$) is possible even in a magnetic field. We also propose 3D moving molasses cooling that can produce a well-defined monochromatic Ps beam useful for applications.

We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called the vector space-fractional Bessel beam (SFBB), has been established from the Lorenz gauge condition and Hertz vector transformations. We perform scalar and vector wave analysis focusing on electromagnetics applications, especially in cases where the dimensions of the beam are comparable to its wavelength $(k_r\approx k)$. The propagation characteristics such as the diffraction and self-healing properties have been explored with particular emphasis on the polarization states and transverse propagation modes. Due to continuous order orbital angular momentum dependence, this beam can serve as a bridge between the ordinary integer Bessel beam and the fractional Bessel beam and, thus, can be considered as a generalized solution of the space-fractional wave equation that is applicable in both integer and fractional dimensional spaces. The proposed SFBBs provide better control over the beam characteristics and can be readily generated using digital micromirror devices, spatial light modulators, metasurfaces, or spiral phase plates. Our findings offer insights on electromagnetic wave propagation, thus paving a route towards applications in optical tweezers, refractive index sensing, optical trapping, and optical communications.

We investigate the ultrafast nonlinear dynamics in a silica ringresonator composed of a silver-nanoparticle-doped core that exhibits rapidly varying frequency-dependent Kerr nonlinearity that even changes sign across a specific frequency, defined as zero-nonlinearity frequency. We model optical propagation in such a resonator through a modified Lugiato-Lefever equation, revealing that the formation of bright cavity solitons can be possible in both positive and negative nonlinearity domains. The intrapulse Raman scattering along with the frequency-dependent Kerr nonlinearity modify the stability and the dynamics of cavity solitons, which we analyze using a bistability analysis, intracavity modulation-instability analysis, and semianalytical variational approach. Our derived analytical results agree well with the direct numerical solutions of the Lugiato-Lefever equation. The generation of a dispersive wave from a cavity soliton encountering higher-order dispersion is also influenced by the location of the zero-nonlinearity frequency, which we describe by providing a modified phase matching equation. Our results and analysis provide a framework for better understanding the dynamics of cavity solitons and their interactions in two different bright-solitonic domains with possible applications in dual-pump spectroscopy, formation of soliton molecules, and counterpropagating solitons to other fields.

When the photoionization is described beyond the dipole approximation, the electron in atoms and molecules will experience a spatially dependent light phase. As demonstrated in a recent experiment on one-photon double ionization of ${\mathrm{H}}_2$ [S. Grundmann et al., Science 370, 339 (2020)], the resulting phase difference modifies the electron interference pattern. By solving the full-dimensional time-dependent Schrödinger equation beyond the dipole approximation, the present work provides corresponding ab initio calculations that have been missing so far, to the best of our knowledge. Due to the two-electron nature of this process, one may wonder about the roles played by the electron-electron correlation in the shifting of the interference fringes. Indeed, we show that the modification of the interference pattern occurs at the two-electron level, which is independent of the energy partition between the two electrons. Our numerical results agree excellently with the prediction of a simple model, in which the entangled electron pair is launched by light with a spatially dependent phase.

Vacuum-one-photon entanglement can serve as an alternative to many protocols implemented by two-photon states, and also exhibits its own practical advantages. Quantum swapping plays a central role in both constructing photonic quantum computers and quantum networks. However, the phase-sensitivity in free space makes it very challenging to scale quantum swapping of vacuum-one-photon entanglement up to multistage, especially to large-scale quantum networks. Here, we implement multistage quantum swapping of vacuum-one-photon entanglement on a three-dimensional reconfigurable photonic chip. We also propose and experimentally demonstrate a prototype of a fully connected multipartite network based on multistage quantum swapping. Our results provide an integrated, scalable, and portable solution of multistage quantum swapping, showing the potential as a crucial element of the all-photonic quantum information processing.

In single-particle entanglement (SPE) two degrees of freedom of a single particle are entangled. SPE is a resource that can be exploited both in quantum communication protocols and in experimental tests of noncontextuality based on the Kochen-Specker theorem. SPE can be certified via a test of quantum contextuality based on Bell inequalities. Experiments of Bell-type inequality violation by single-particle entangled systems may be affected by an analog of the locality loophole in this context, due to the presence of unavoidable nonidealities in the experimental devices which actually produce unwanted correlations between the two observables that are simultaneously measured. This issue is tackled here by quantitatively analyzing the behavior of realistic devices in SPE experiments with photons. In particular, we show how it is possible to provide a semi-device-independent randomness certification of realistic quantum random-number generators based on Bell-inequality violation by SPE states of photons. The analysis is further enlarged to encompass, with a Markovian model, memory effects due to dead time, dark counts, and afterpulsing affecting single-photon detectors, in particular when not dealing with coincidence measurements. An unbiased estimator is also proposed for quantum transition probabilities out of the collection of experimental data.

Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly interacting systems and black holes. The utility of random quantum circuits in these settings stems from their ability to rapidly generate quantum pseudorandomness. In a seminal paper by Brandão, Harrow, and Horodecki [Commun. Math. Phys. 346, 397 (2016)] it was proven that the $t\mathrm{th}$ moment operator of local random quantum circuits on $n$ qudits with local dimension $q$ has a spectral gap of at least $\mathrm{\Omega }\left(n^{-1}{t}^{-5-3.1/ln\left(q\right)}\right)$, which implies that they are efficient constructions of approximate unitary designs. As a first result, we use Knabe bounds for the spectral gaps of frustration-free Hamiltonians to show that one-dimensional random quantum circuits have a spectral gap scaling as $\mathrm{\Omega }\left(n^{-1}\right)$, provided that $t$ is small compared to the local dimension: $t^2\le O\left(q\right)$. This implies a (nearly) linear scaling of the circuit depth in the design order $t$. Our second result is an unconditional spectral gap bounded below by $\mathrm{\Omega }\left[n^{-1}{ln}^{-1}\left(n\right)t^{-\alpha \left(q\right)}\right]$ for random quantum circuits with all-to-all interactions. This improves both the $n$ and $t$ scaling in design depth for the nonlocal model. We show this by proving a recursion relation for the spectral gaps involving an auxiliary random walk. Lastly, we solve the smallest nontrivial case exactly and combine with numerics and Knabe bounds to improve the constants involved in the spectral gap for small values of $t$.

In this work, we extend a multiqubit benchmarking technique known as the binned output generation (BOG) in order to discriminate between coherent and incoherent noise sources in the multiqubit regime. While methods exist to discriminate coherent from incoherent noise at the single and few-qubit level, these methods scale poorly beyond a few qubits or must make assumptions about the form of the noise. On the other end of the spectrum, system-level benchmarking techniques exist, but they fail to discriminate between coherent and incoherent noise sources. We experimentally verify the BOG against randomized benchmarking (RB) (the industry standard benchmarking technique) in the two-qubit regime, then apply this technique to a six-qubit linear chain, a regime currently inaccessible to RB. In this experiment, we inject an instantaneous coherent $Z$-type noise on each qubit and demonstrate that the measured coherent noise scales correctly with the magnitude of the injected noise, while the measured incoherent noise remains unchanged as expected. This demonstrates a robust technique to measure coherent errors in a variety of hardware.

The relativistic spin operator cannot be uniquely defined within relativistic quantum mechanics. Searching for relativistic equations that describe both the evolution of the spin and its influence on the motion of particles with spin represents a problem with almost centenary history. We develop a self-consistent module for modeling relativistic particles with spin motion into three-dimensional particle-in-cell simulations, where the expression of the spin-induced force can be chosen by various semiclassical models, such as the Frenkel and noncovariant Derbenev-Kondratenko models. Through simulations, we propose a potential experimental scheme for observing and testing theoretical descriptions on relativistic spin dynamics, where ultraintense lasers are used to collide with relativistic electron beams. The basis for the scheme is that different models predict different transverse polarization distributions of the scattered electrons after interactions, which can be measured in experiments.

We experimentally study the Rb-Xe spin-exchange optical pumping process. The dependence of the spin-exchange rate on the intensity of the pumping light is measured at different temperatures under low magnetic fields. We demonstrate that the spin-exchange rate will decrease as the Rb spin polarization increases, which agrees well with the theoretical prediction. In our measurement, three spin exchange and spin relaxation mechanisms, namely, the spin exchange rates between Rb and Xe atoms caused by van der Waals molecule (${\mathrm{\Gamma }}_{\mathrm{vdW}}$) and binary collision (${\mathrm{\Gamma }}_{\mathrm{bin}}$) processes, and the spin relaxation rate due to the wall collision of Xe atoms (${\mathrm{\Gamma }}_{\mathrm{w}}$), have comparable magnitudes. These rates are extracted separately from the measured data with different Rb spin polarization at various temperatures. Our work provides a comprehensive confirmation of the physical picture of the spin-exchange optical pumping process.

The experimental success achieved in recent decades in the coherent manipulation of several Rabi cycles has led to a new stage in the physics of radiation-matter interaction. Motivated by this perspective, we propose here the engineering of coherent many-body Rabi oscillations (CMBROs) induced from the interactions of a moderately dense atomic sample with the environment and a high-finesse cavity mode. The CMBRO follows from the interplay between superradiance and superabsorption: the collective decay and absorption of the atomic sample inside the cavity. The equations we have derived for this interplay, based on the mean-field approximation, describe a two-level superradiant laser in an appropriate parameter regime, and its properties are also discussed. The control of quantum coherence according to the method presented here can be adapted to the implementation of quantum information processes as well as for the investigation of the fundamentals of quantum mechanics.

The variational quantum eigensolver is a promising algorithm for noisy intermediate scale quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. We consider the exactly diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe Ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $O\left(N\right)$ and $O\left({log}_{2}N\right)$ that can prepare any trigonometric LMG eigenstate of $N$ particles. The number of gates required for both circuits is $O\left(N\right)$. The energies of the eigenstates can then be measured and compared to the exactly known answers.

We explore the dual problem of the convex roof construction by identifying it as a linear semi-infinite programming (LSIP) problem. Using the LSIP theory, we show the absence of a duality gap between primal and dual problems, even if the entanglement quantifier is not continuous, and prove that the set of optimal solutions is nonempty and bounded. In addition, we implement a central cutting-plane algorithm for LSIP to quantify entanglement between three qubits. The algorithm has global convergence property and gives lower bounds on the entanglement measure for nonoptimal feasible points. As an application, we use the algorithm for calculating the convex roof of the three-tangle and $\pi$-tangle measures for families of states with low and high ranks. Since the $\pi$-tangle measure quantifies the entanglement of W states, we apply the values of the two quantifiers to distinguish between the two different types of genuine three-qubit entanglement.

For quantum matter, eigenstate entanglement entropies obey an area law or log-area law at low energies and small subsystem sizes and cross over to volume laws for high energies and large subsystems. This transition is captured by crossover functions, which assume a universal scaling form in quantum critical regimes. We demonstrate this for the harmonic lattice model, which describes quantized lattice vibrations and is a regularization for free scalar field theories, modeling, e.g., spin-0 bosonic particles. In one dimension, the ground-state entanglement obeys a log-area law. For dimensions $d\ge 2$, it displays area laws, even at criticality. The distribution of excited-state entanglement entropies is found to be sharply peaked around subsystem entropies of corresponding thermodynamic ensembles in accordance with the eigenstate thermalization hypothesis. Numerically, we determine crossover scaling functions for the quantum critical regime of the model and do a large-deviation analysis. We show how infrared singularities of the system can be handled and how to access the thermodynamic limit using a perturbative trick for the covariance matrix. Eigenstates for quasi-free bosonic systems are not Gaussian. We resolve this problem by considering appropriate squeezed states instead. For these, entanglement entropies can be evaluated efficiently.

We propose a carrier synchronization scheme for continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) with a real local oscillator (LO). The middle node Charlie evaluates carrier frequency offsets and phase drift values based on the pilot signal sent by the legal parties Alice and Bob and a part of their public data. Alice and Bob then calibrate their modulation data according to the evaluation parameters to achieve carrier synchronization. We simulate the entire CV-MDI-QKD protocol and verify the feasibility of this scheme. The influences of pilot segment size and public data size on the excess noise are also analyzed. Besides, we experiment to measure the actual frequency offsets and phase drifts in the channel, which gives guidance on the actual implementation. This solution can ensure the implementation of CV-MDI-QKD with a real LO, paving the way for the practical application of this high-rate QKD protocol.

Simulated quantum annealing based on the path-integral Monte Carlo is one of the most common tools to simulate quantum annealing on classical hardware. Nevertheless, it is in principle highly nontrivial whether or not this classical algorithm can correctly reproduce the quantum dynamics of quantum annealing, particularly in the diabatic regime. We study this problem numerically through the generalized Kibble-Zurek mechanism of defect distribution in the simplest ferromagnetic one-dimensional transverse-field Ising model with and without coupling to the environment. We find that, in the absence of coupling to the environment, simulated quantum annealing correctly describes the annealing-time dependence of the average number of defects, but a detailed analysis of the defect distribution shows clear deviations from the theoretical prediction. When the system is open (coupled to the environment), the average number of defects does not follow the theoretical prediction but is qualitatively compatible with the numerical result by the infinite-time-evolving block decimation combined with the quasiadiabatic propagator path integral, which is valid in a very-short-time region. The distribution of defects in the open system turns out to be not far from the theoretical prediction. It is surprising that the classical stochastic dynamics of simulated quantum annealing ostensibly reproduces some aspects of the quantum dynamics. However, a serious problem is that it is hard to predict for which physical quantities in which system it is reliable. Those results suggest the necessity to exert a good amount of caution in using simulated quantum annealing to study the detailed quantitative aspects of the dynamics of quantum annealing.

Quantum network is the key to enable distributed quantum information processing. As the single-link communication rate decays exponentially with the distance, to enable reliable end-to-end quantum communication, the number of nodes needs to grow with the network scale. For highly connected networks, we identify a threshold transition in the capacity as the density of network nodes increases: below a critical density the rate is almost zero, while above the threshold the rate increases linearly with the density. Surprisingly, above the threshold the typical communication capacity between two nodes is independent of the distance between them, due to multipath routing enabled by the quantum network. In contrast, for less connected networks such as scale-free networks, the end-to-end capacity saturates to constants as the number of nodes increases, and always decays with the distance. Our results are based on capacity evaluations, therefore the minimum density requirement for an appreciable capacity applies to any general protocols of quantum networks.