A Jastrow-Gutzwiller operator adds many-body correlations to a quantum state. However, the operator is nonunitary, making it difficult to implement directly on a quantum computer. We present an implementation of the Jastrow-Gutzwiller operator using the cascaded variational quantum eigensolver algorithm. We demonstrate the method on IBM Q Lagos for a Hubbard model.

Quantum mechanics is sensitive to the geometry of the underlying space. Here we present a framework for quantum scattering of a nonrelativistic particle confined to a two-dimensional space. When the motion manifold hosts localized curvature modulations, scattering occurs from an emergent geometric potential and the metric tensor field. Analytical and full numerical simulations identify the geometric potential as the primary source for low-energy scattering, while the metric tensor field of the curved space governs high-energy diffraction. Compared to flat spaces, important differences in the validity range of perturbation approaches are found and demonstrated by full numerical simulations using combined finite element and boundary element methods. As an illustration, we consider a Gaussian-shaped dent leading to effects known as gravitational lensing. Experimentally, the considered setup is realizable based on geometrically engineered two-dimensional materials.

We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.

We show how both the ellipticity $\eta$ and degree of polarization $P$ influence the extraordinary optical chirality properties of nonparaxial vortex beams. We find that, in stark contrast to paraxial optics and nonvortex modes, extremely rich and tunable spatial distributions of optical chirality density can be produced by an optical vortex beam under tight focusing. We develop a theoretical description of how the optical chirality can be tailored for purpose by altering both the state $\eta$ and degree of polarization $P$ of the input vortex mode, along with the magnitude and sign of optical orbital angular momentum via the pseudoscalar topological charge $\ell$. We expect that the results will have a significant role in both producing alternative techniques and improving existing methods in chiral nano-optics and structured light photonics.

Quantum illumination utilizes an entanglement-enhanced sensing system to outperform classical illumination in detecting a suspected target, despite the entanglement-breaking loss and noise. However, practical and optimal receiver design to fulfill the quantum advantage has been a long open problem. Recently, Shi et al. [arXiv:2207.06609 (2022)] proposed the correlation-to-displacement $(`\mathrm{C}{}_{{\displaystyle \stackrel{⃗}{}}}\mathrm{D}\text{'})$ conversion module to enable an optimal receiver design that greatly reduces the complexity of the previous known optimal receiver [Q. Zhuang, Z. Zhang, and J. H. Shapiro, Phys. Rev. Lett. 118, 040801 (2017)]. There, the analyses of the conversion module assume an ideal target with a known reflectivity and a fixed return phase. In practical applications, however, targets often induce a random return phase; moreover, their reflectivities can have fluctuations obeying a Rayleigh distribution. In this paper, we extend the analyses of the $\mathrm{C}{}_{{\displaystyle \stackrel{⃗}{}}}\mathrm{D}$ module to realistic targets and show that the entanglement advantage is maintained albeit reduced. In particular, the conversion module allows exact and efficient performance evaluation despite the non-Gaussian nature of the quantum channel involved.

Many-qubit Mølmer-Sørensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parametrizes these errors from simple experimental measurements, without free parameters. We validate the model in comparison with experiments that implement sequences of MS interactions on two ${}^{171}\mathrm{Yb}^{+}$ ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic ${\chi }_{\mathrm{red}}^2\approx 2$. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are $91\%$ and $83\%$ of the optimal theoretical values. Our model predicts $0.{93}_{-0.02}^{+0.03}$ and $0.{95}_{-0.03}^{+0.04}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations, the model achieves approximation ratios that are $99\%$ of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

Quantum entanglement assisted with measurements provides various pathways to communicate information to parties within a network. In this work, we generalize a previous broadcasting protocol and present schemes to broadcast product and multipartite entangled quantum states, where in the latter case the sender can remotely add phase gates or abort distributing the states. We first focus on the broadcasting of product quantum states in a network, and generalize the basic protocol to include an arbitrary basis rotation and allow for multiple receivers and senders. We show how to add and delete senders from the network. The generalization also includes the case where a phase to be applied to the broadcast states is not known in advance but is provided to a sender encoded in another quantum state. Applications of broadcasting product states include authentication and three-state quantum cryptography. In the second part, we study the distribution of a single multiqubit state shared among several receivers entangled with multiqubit phase gates, which includes the graph states as an example. We show that by coordinating with the sender, the receivers can assist in performing remote, distributed measurement-based quantum computation with the Pauli-$X$ basis measurement alone. As another application of this, we discuss the distribution of the multiqubit Greenberger-Horne-Zeilinger state.

The Coulomb interaction between the active electron and the parent ion is inherent in high-order harmonic generation from laser-driven atoms, but it is often neglected in modeling the electron dynamics. For this reason, the pioneering measurement scheme based on orthogonally polarized two-color fields [reported in Nature (London) 485, 343 (2012)], which is able to measure ionization and return times for the electron trajectories, does not reflect the time shifts caused by the Coulomb interaction. We introduce a simple Coulomb correction to the electron motion in the two-color scheme, leading to modified retrieval equations for the extraction of time information from the observables. We apply the modified equations to data calculated from simulations of the time-dependent Schrödinger equation and we show that the scheme effectively reveals the Coulomb shift of the ionization time.

Inspired by the covering-space method in path integrals on multiply connected spaces, we here present a universal formula of time-evolution kernels for continuous- and discrete-time quantum walks on orbit spaces. In this note, we focus on the case in which walkers' configuration space is the orbit space $\mathrm{\Lambda }/\mathrm{\Gamma }$, where $\mathrm{\Lambda }$ is an arbitrary lattice and $\mathrm{\Gamma }$ is a discrete group whose action on $\mathrm{\Lambda }$ has no fixed points. We show that the time-evolution kernel on $\mathrm{\Lambda }/\mathrm{\Gamma }$ can be written as a weighted sum of time-evolution kernels on $\mathrm{\Lambda }$, where the summation is over the orbit of initial point in $\mathrm{\Lambda }$ and weight factors are given by a one-dimensional unitary representation of $\mathrm{\Gamma }$. Focusing on one dimension, we present a number of examples of the formula. We also present universal formulas of resolvent kernels, canonical density matrices, and unitary representations of arbitrary groups in quantum walks on $\mathrm{\Lambda }/\mathrm{\Gamma }$, all of which are constructed in exactly the same way as for the time-evolution kernel.

Hilbert space fragmentation is a novel type of ergodicity breaking in closed quantum systems. Recently, an algebraic approach was utilized to provide a definition of Hilbert space fragmentation characterizing families of Hamiltonian systems based on their (generalized) symmetries. In this paper we reveal a simple connection between the aforementioned classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP). The maximum CGP (in the basis associated with the algebra of each family of Hamiltonians) is exactly related to the number of independent Krylov subspaces $K$, which is precisely the characteristic used in the classification of the system. In order to gain further insight, we numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension. More generally, allowing the time evolution to be any unitary channel in a specified algebra, we show analytically that the scaling of the Haar averaged value of the CGP depends only on $K$. These results illustrate the intuitive relationship between coherence generation and symmetry algebras.

We propose a few-body quantum phenomenon, which manifests itself through stochastic state preparations and measurements followed by a conditioned postprocessing procedure. We show two experimental protocols to implement these phenomena with existing quantum computers, and examine their feasibility by using simulations. Our simulation results suggest that the experimental demonstration is feasible if we repeat the state preparations and measurements about thirty thousand times to three-qubit systems.

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of $p$ layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization, the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic initializations exist, an analytical understanding and performance guarantees for large $p$ remain evasive. We introduce a greedy initialization of QAOA which guarantees improving performance with an increasing number of layers. Our main result is an analytic construction of $2p+1$ transition states—saddle points with a unique negative curvature direction—for QAOA with $p+1$ layers that use the local minimum of QAOA with $p$ layers. Transition states connect to new local minima, which are guaranteed to lower the energy compared to the minimum found for $p$ layers. We use the Greedy procedure to navigate the exponentially increasing with $p$ number of local minima resulting from the recursive application of our analytic construction. The performance of the Greedy procedure matches available initialization strategies while providing a guarantee for the minimal energy to decrease with an increasing number of layers $p$.

Continuous-variable (CV) teleportation is a fundamental protocol in quantum information science. A number of experiments have been designed to simulate ideal teleportation under realistic conditions. In this paper, we detail an analytical approach for determining optimal input states for quantifying the performance of CV unidirectional and bidirectional teleportation. The metric that we consider for quantifying performance is the energy-constrained channel fidelity between ideal teleportation and its experimental implementation, and along with this, our focus is on determining optimal input states for distinguishing the ideal process from the experimental one. We prove that, under certain energy constraints, the optimal input state in unidirectional as well as bidirectional teleportation is a finite entangled superposition of twin-Fock states saturating the energy constraint. Moreover, we also prove that, under the same constraints, the optimal states are unique; that is, there is no other optimal finite entangled superposition of twin-Fock states.

The simulation of quantum systems is one of the most promising applications of quantum computers. In this paper, we present a quantum algorithm to perform digital quantum simulations of the (reduced) Bardeen-Cooper-Schrieffer (BCS) model on a quantum register with a star-shaped connectivity map, as it is, e.g., featured by color centers in diamond. We show how to effectively translate the problem onto the quantum hardware and implement the algorithm using only the native interactions between the qubits. Furthermore, we discuss the complexity of the circuit. We use the algorithm to simulate the dynamics of the BCS model by subjecting its mean-field ground state to a time-dependent perturbation. The quantum simulation algorithm is studied using a classical simulation.

Inverse Compton scattering of polarized laser photons by energetic electrons is an excellent method to generate polarized gamma rays. A 100% polarized laser can generate 100% polarized gamma rays, but polarization varies depending on the scattering angle of the gamma rays. In this study, we experimentally measure the spatial polarization distribution of circularly polarized gamma rays using a magnetized iron that can measure the circular polarization of MeV gamma rays. Measurements of the asymmetry of gamma-ray transmission relative to the magnetized iron at each scattering angle clearly show that gamma rays are circularly polarized near the central axis, and they change from circular to linear polarization as the scattering angle increases. A simple way to obtain highly polarized gamma rays is to use a collimator that transmits only the central axis of the gamma rays with such polarization characteristics. Polarized gamma rays are, indeed, generated by ${90}^{\circ }$ collisional inverse Compton scattering between an electron beam and a circularly polarized laser.

We propose a scheme to achieve nonreciprocal conventional photon blockades simultaneously in two independent optical modes, which are connected by a two-level system. In the case that only one optical mode is weakly driven, we find that strong nonreciprocal photon blockades of both optical modes can be observed. We show that, for both optical modes, the single-photon blockades happens by driving the nonlinear device from one side, while photon-induced tunneling appears when driving the system from the other side, which is attributed to the anharmonic eigenenergy spectrum constructed by resonantly coupling to a two-level system. According to photon resonance transition processes under different driving directions, the four optimal Fizeau-Sagnac shifts can be obtained to generate perfect nonreciprocal conventional photon blockades of both optical modes. Our study opens an avenue to simultaneously manipulate multiple nonreciprocal single-photon devices and may have potential applications in chiral quantum information processing.