In this article, we propose an interactive protocol for one party (the verifier) holding a quantum computer to verify the quantum computation power of another party's (the prover) device via a one-way quantum channel. This protocol is referred to as the dihedral coset problem (DCP) challenge. The verifier needs to prepare quantum states encoding secrets (DCP samples) and send them to the prover. The prover is then tasked with recovering those secrets with a certain accuracy. Numerical simulation demonstrates that this accuracy is sensitive to errors in quantum hardware. Additionally, the DCP challenge serves as a benchmarking protocol for locally fully connected quantum architecture and aims to be performed on current and near-future quantum resources. We conduct a 4-qubit experiment on one of the IBM Q devices.

Cavity magnon-polaritons have recently attracted intensive attention as a promising platform for exploring quantum phenomena. In this paper, we propose a Floquet engineering strategy to realize the non-Hermitian shortcut to adiabaticity in cavity magnon-polaritons. The nonadiabatic loss is restrained and the fast population transfer from the microwave photon to the magnon is realized. This model has potentially important applications in quantum information processing.

We report theoretical investigation of the twisted-electron-impact single-ionization dynamics of an ${\mathrm{H}}_2\mathrm{O}$ molecule. The triple-differential cross sections for $1b_1$, $3a_1$, $1b_2$, and $2a_1$ orbitals are obtained by a twisted-electron-impact multicenter distorted-wave method. The coplanar asymmetric kinematic condition is adopted at incident electron energy $E_i=250$ eV and ejected electron energy $E_e=10$ eV. By integrating the impact parameter, all possible rotation angles ${\phi }_k$ of the projectile are averaged for the triple-differential cross section, which is independent of the orbital angular momentum and varies as a function of opening angle ${\theta }_k$. The results show that the ionization by a plane-wave projectile is more likely than by a twisted-electron projectile if the scattering angle is smaller than a critical value. However, when the scattering angle exceeds the critical point, the twisted-electron projectile can possess higher ionization probability, which will reach a maximum when the opening angle numerically approaches the scattering angle.

Motivated by recent advances in quantum dynamics, we investigate the dynamics of the system with $\text{SU}(1,1)$ symmetry. Instead of performing the time-ordered integral for the evolution operator of the time-dependent Hamiltonian, we show that the time evolution operator can be expressed as an $\text{SU}(1,1)$ group element. Since the $\text{SU}(1,1)$ group describes the “rotation” on a hyperbolic surface, the dynamics can be visualized on a Poincaré disk, a stereographic projection of the upper hyperboloid. As an example, we present the trajectory of the revival of Bose-Einstein condensation and that of the scale-invariant Fermi gas on the Poincaré disk. Further considering quantum gases in an oscillating lattice, we also study the dynamics of the system with time-dependent single-particle dispersion.

We study the postquench dynamics of unitary Bose gases using a two-channel model, focusing on the effect of variations in the width of the Feshbach resonance due to density changes. We generally find that increasing the density leads to a corresponding increase in the production of closed-channel molecules, a decrease in the buildup of quantum depletion and a transition from linear to quadratic early-time growth of the two-body contact as well as the condensed pair fraction. Motivated by the presence of closed-channel molecules in the unitary regime, we study the embedded two-body problem, finding a transition from open- to closed-channel-dominated dimers due to many-body effects.

Strongly correlated quantum many-body states provide invaluable resources for state-of-the-art quantum information science, ranging from quantum simulation to quantum metrology. In this work, we propose a supervised machine learning algorithm for optimal control of quantum many-body atomic states in optical lattices by numerical simulations based on the Bayesian method of Gaussian process regression (GPR). We combine this method with the time evolving block decimation (TEBD) algorithm for the preparation of the Heisenberg antiferromagnetic state in a system of bosonic atoms confined with a one-dimensional optical lattice. The quantum many-body ground state of 80 atoms is efficiently optimized within a few hundred machine learning iterations, reaching a state fidelity above $96\%$. With a multistep learning strategy, we find the machine-learning-based optimal control method is scalable to large systems owing to its transferability. Its robustness against noise is demonstrated by considering imperfections that are typically present in optical lattice experiments. In the application of the GPR method to the preparation of the two-dimensional (2D) antiferromagnetic state, a state fidelity of $94\%$ is reached for a 2D array of $6\times 6$ spins through the time dependent variational principle (TDVP) algorithm, confirming the generalizability of our method. We further optimize the Hamiltonian ramping sequence crossing a quantum phase transition of the quantum $XXZ$ spin chain with the exact diagonalization method, from which a control protocol for generating the long-sought atomic Greenberger-Horne-Zeilinger state is obtained. We believe the proposed optimal control method for quantum Hamiltonian ground-state preparation would benefit present ultracold-atom experiments in the study of strongly correlated many-body physics.

In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as self-organized quantum processors. We develop a computational approach that uses a neural network as a variational ansatz for quantum solitons in an array of waveguides. By training the resulting phase space quantum machine-slearning model, we find different soliton solutions, varying the number of particles and interaction strength. We consider Gaussian states that enable measuring the degree of entanglement and sampling the probability distribution of many-particle events. We also determine the probability of generating particle pairs and unveil that soliton bound states emit correlated pairs. These results may have a role in boson sampling with nonlinear systems and in quantum processors for entangled nonlinear waves.

Optical vortex beams with fractional orbital angular momentum (OAM) can greatly enhance the channel capacity in free-space optical communication. However, high precision measurement of fractional OAM modes is always difficult, especially under the influence of atmospheric turbulence (AT). In this work, we identify the high-resolution OAM modes down to 0.01 using an improved residual neural network (ResNet) architecture based convolutional neural network (CNN). Experimentally, using a single cylindrical lens, the light intensity distribution can be readily converted into a diffraction pattern containing significant features trained into a CNN model. For the fractional OAM modes from 5.0 to 5.9 over a long propagation distance of 1500 m, at 0.1 resolution, our model's predicting accuracy is up to 99.07% under strong AT, $C_{\mathrm{n}}^2=1\times {10}^{-15}{\mathrm{m}}^{-2/3}$. At 0.01 resolution, the accuracy is as high as 86.98% under intermediate AT, $C_{\mathrm{n}}^2=1\times {10}^{-16}{\mathrm{m}}^{-2/3}$, and exceeds 73.78% under strong AT, $C_{\mathrm{n}}^2=1\times {10}^{-15}{\mathrm{m}}^{-2/3}$. So, these results may have great implications in free-space optical communication.

We investigate the thermodynamic limit of Dicke superradiance. We find an expression for the system's density matrix that we can prove is exact in the limit of large atom numbers $N$. This is in contrast to previously known solutions whose accuracy has only been established numerically and that are valid only for a range of times. We also introduce an asymptotically exact solution when the system is subject to additional incoherent decay of excitations as this is a common occurrence in experiments.

The Schrödinger-Newton equation has frequently been studied as a nonlinear modification of the Schrödinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schrödinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.

The generalized notion of noncontextuality provides an avenue to explore the fundamental departure of quantum theory from a classical explanation. Recently, extracting different forms of quantum advantages in various information processing tasks has received an upsurge of attention. In a recent work [Schmid and Spekkens, Phys. Rev. X 8, 011015 (2018)] it has been demonstrated that minimum error discrimination of two nonorthogonal pure quantum states entails contextual advantage when the states are supplied with equal prior probabilities. We generalize their work for arbitrary prior probabilities and extend the investigation for three arbitrary mirror-symmetric states. We show that the contextual advantage can be obtained for any value of prior probability when only two quantum states are present in the task. But surprisingly, for the case of three mirror-symmetric states, the contextual advantage can be revealed only for a restrictive range of prior probabilities with which the states are supplied. Further, we extend our study to examine the contextual advantage for maximum confidence state discrimination. We demonstrate that the prior probabilities of state preparation play a similar role in exploiting the quantum advantage in maximum confidence discrimination.

In strongly interacting systems with a separation of energy scales, low-energy effective Hamiltonians help provide insights into the relevant physics at low temperatures. The emergent interactions in the effective model are mediated by virtual excitations of high-energy states: For example, virtual doublon-hole excitations in the Fermi-Hubbard model mediate antiferromagnetic spin-exchange interactions in the derived effective model, known as the $t-J-3s$ model. Formally this procedure is described by performing a unitary Schrieffer-Wolff basis transformation. In the context of quantum simulation, it can be advantageous to consider the effective model to interpret experimental results. However, virtual excitations such as doublon-hole pairs can obfuscate the measurement of physical observables. Here we show that quantum simulators allow one to access the effective model even more directly by performing measurements in a rotated basis. We propose a protocol to perform a Schrieffer-Wolff transformation on Fermi-Hubbard low-energy eigenstates (or thermal states) to dynamically prepare approximate $t-J-3s$ model states using fermionic atoms in an optical lattice. Our protocol involves performing a linear ramp of the optical lattice depth, which is slow enough to eliminate the virtual doublon-hole fluctuations but fast enough to freeze out the dynamics in the effective model. We perform a numerical study using exact diagonalization and find an optimal ramp speed for which the state after the lattice ramp has maximal overlap with the $t-J-3s$ model state. We compare our numerics to experimental data from our Lithium-6 fermionic quantum gas microscope and show a proof-of-principle demonstration of this protocol. More generally, this protocol can be beneficial to studies of effective models by enabling the suppression of virtual excitations in a wide range of quantum simulation experiments.

Quantum algorithms can be realized in the form of a quantum circuit. To map a quantum circuit for a specific quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the qubit topology. Due to the neighborhood constraint of qubit topology, the implementation of the quantum algorithm rightly, is essential for moving information around in a quantum computer. Swapping of qubits using a swap gate moves the quantum state between two qubits and solves the neighborhood constraint of qubit topology. Although, one needs to decompose the swap gate into three controlled-not gates to implement the swap gate efficiently, but unwillingly quantum cost with respect to the gate count and depth increases. In this paper, a formalism of moving quantum states without using swap operation is introduced. Moving quantum states through qubits have been attained with the adoption of temporary intermediate qudit states. This introduction of intermediate qudit states has exhibited a three times reduction in quantum cost with respect to the gate count and approximately two times reduction with respect to circuit depth compared to the state-of-the-art approach of the swap gate insertion. We also exhibit that the adoption of the intermediate qudit makes the approach sublimer than the existing works by obtaining a better fidelity. Furthermore, the proposed approach is generalized to any finite-dimensional quantum system.

As known, electron vacuum polarization by nuclear Coulomb field produces a Uehling potential with the range $\hslash /2m_{e}c$. Similarly, neutrino vacuum polarization by $Z$ boson field produces long-range potential $\sim G^2/r^5$ with the large range $\hslash /2m_{\nu }c$. Attempts to measure the parity-conserving part of this potential produced only limits on this potential which are several orders of magnitude higher than the standard model predictions. We show that the parity nonconserving (PNC) part of the neutrino exchange potential $W_L\left(r\right)$ gives a significant fraction of the observed PNC effects. Mixed $Z-\gamma$ electron vacuum polarization produces a PNC potential with range $\hslash /2m_{e}c$, which exceeds the range of the weak interaction by five orders of magnitude. We calculate the contribution of the long-range PNC potentials to the nuclear spin-independent and nuclear spin-dependent PNC effects. The cases of the single-isotope PNC effects and the ratio of PNC effects in different isotopes are considered for Ca, Cs, Ba, Sm, Dy, Yb, Hg, Tl, Pb, Bi, Fr, Ra atoms and ions. Contributions of the long-range PNC potentials ($\sim 1\%$) significantly exceed the experimental error (0.35%) for PNC effect in Cs. The difference between potentials produced by Dirac neutrino and Majorana neutrino may, in principle, help to determine what kind of neutrino is realized in nature.

We study the coherent single-photon scattering in a one-dimensional waveguide coupled to a giant artificial molecule consisting of two coupled giant atoms. Since each giant atom couples to the waveguide via two coupling points, the couplings of the molecule with the waveguide have three different coupling configurations: the separated-, braided-, and nested-coupling cases. We obtain the exact expressions of the single-photon transmission and reflection amplitudes with the real-space approach. It is found that the behavior of the scattering spectra depends on the phase shift between two neighboring coupling points, the coupling configuration, and the coupling between the two giant atoms. Concretely, we study the photon scattering in both the Markovian and non-Markovian regimes, in which the photon propagating time between two neighboring coupling points is neglected and considered, respectively. Under the Markovian limit, the asymmetric Fano line shapes in different coupling configurations of the giant-molecule waveguide-QED system can be obtained by choosing proper phase shift, and the transmission window can be adjusted by the coupling strength between the two giant atoms in these three coupling configurations. In particular, multiple reflection peaks and dips in these configurations are revived in the non-Markovian regime. This paper will pave the way for the study of controllable single-photon devices based on the giant-molecule waveguide-QED systems.

In this study, we determine a violation of the Leggett-Garg inequalities due to gravitational interaction in a hybrid system consisting of a harmonic oscillator and a spatially localized superposed particle. The violation of the Leggett-Garg inequalities is discussed using the two-time quasiprobability in connection with the entanglement negativity generated by gravitational interaction. It is demonstrated that the entanglement suppresses the violation of the Leggett-Garg inequalities when one of the two times of the quasiprobability $t_1$ is chosen as the initial time. Further, it is shown that the Leggett-Garg inequalities are generally violated due to gravitational interaction by properly choosing the configuration of the parameters, including $t_1$ and $t_2$, which are the times of the two-time quasiprobability. The feasibility of detecting violations of the Leggett-Garg inequalities in hybrid systems is also discussed.

The relation between genuine multipartite entanglement in the pure state of a collection of $N$ qubits and the nonclassical correlations in its two-qubit subsystems is studied. Quantum discord is used as the quantifier of nonclassical correlations in the subsystem while the generalized geometric measure [A. Sen(De) and U. Sen, Phys. Rev. A 81, 012308 (2010)] is used to quantify global entanglement in the $N$-qubit state. While no definite discernible dependence between the two can be found for randomly generated global states, for those with additional structure like weighted graph states we find that local discord is indicative of global multipartite entanglement. Global states that admit efficient classical descriptions like stabilizer states furnish an exception in which, despite multipartite entanglement, nonclassical correlation is absent in two-qubit subsystems. We discuss these results in the context of mixed state quantum computation where nonclassical correlation is considered a candidate resource that enables exponential speedup over classical computers.

High-sensitivity metrology plays an important role in parameter estimation, and weak-value amplification is a significant tool used to enhance sensitivity. However, the efficiency of weak-value amplification is always affected by the postselection probability and meter loss. In this article we report on the realization of a device for weak interaction that realizes the nonunitary evolution based on a spatial light modulator and applies the weak-value amplification of nonunitary evolution. The weak-value amplification of nonunitary evolution can achieve efficiency nearly ninefold that of unitary evolution experimentally under specific settings, because of the quadratic relation between the meter shift and the norm of the weak value $|A_w|$. This work demonstrates the superiority of nonunitary evolution in weak-value amplification, provides an experimental scheme of weak interaction for other forms of nonunitary evolution, and possesses the potential to be combined with other techniques for higher efficiency.

We carry out a direct iterative Foldy-Wouthuysen transformation of a general Dirac Hamiltonian coupled to an electromagnetic field, including the anomalous magnetic moment. The transformation is carried out through an iterative disentangling of the particle and antiparticle Hamiltonians in the expansion for higher orders of the momenta. The time-derivative term from the unitary transformation is found to be crucial in supplementing the transverse component of the electric field in higher orders. Final expressions are obtained for general combined electric and magnetic fields, including strong magnetic fields. The time derivative of the electric field is shown to enter only in the seventh order of the fine-structure constant if the transformation is carried out in the standard fashion. We put special emphasis on the case of strong fields, which are important for a number of applications, such as electrons bound in Penning traps.