We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anticommutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\langle W\rangle \le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\langle W\rangle =5$ indicates the degree of confidence in the detection of Majorana fermions.

Encoding a qubit in the continuous degrees of freedom of an oscillator is a promising path to error-corrected quantum computation. One advantageous way to achieve this is through Gottesman-Kitaev-Preskill (GKP) grid states, whose symmetries allow for the correction of any small continuous error on the oscillator. Unfortunately, ideal grid states have infinite energy, so it is important to find finite-energy approximations that are realistic, practical, and useful for applications. In the first half of this work we investigate the impact of imperfect GKP states on computational circuits independently of the physical architecture. To this end, we analyze the behavior of the physical and logical content of normalizable GKP states through several figures of merit, employing a recently developed modular subsystem decomposition. By tracking the errors that enter into the computational circuit due to imperfections in the GKP states, we are able to gauge the utility of these states for noisy intermediate-scale quantum devices. In the second half, we focus on a state preparation approach in the photonic domain wherein photon-number-resolving measurements on some modes of Gaussian states produce non-Gaussian states in others. We produce detailed numerical results for the preparation of GKP states alongside estimating the resource requirements in practical settings and probing the quality of the resulting states with the tools we develop. Our numerical experiments indicate that we can generate any state in the GKP Bloch sphere with nearly equal resources, which has implications for magic state preparation overheads.

Unambiguous state discrimination of two mixed bipartite states via local operations and classical communications (LOCC) is studied and compared with the result of a scheme realized via global measurement. We show that the success probability of a global scheme for mixed-state discrimination can be achieved perfectly by the local scheme. In addition, we simulate this discrimination via a pair of pure entangled bipartite states. This simulation is perfect for local rather than global schemes due to the existence of entanglement and global coherence in the pure states. We also prove that LOCC protocol and the sequential state discrimination (SSD) can be interpreted in a unified view. We then hybridize the LOCC protocol with three protocols (SSD, reproducing, and broadcasting) relying on classical communications. Such hybridizations extend the gaps between the optimal success probability of global and local schemes, which can be eliminated only for the SSD rather than the other two protocols.

Motivated by recent experiments, we explore the kinetics of Bose-Einstein condensation in the upper band of a double-well optical lattice. These experiments engineer a nonequilibrium situation in which the highest energy state in the band is macroscopically occupied. The system subsequently relaxes and the condensate moves to the lowest energy state. We model this process, finding that the kinetics occurs in three phases: The condensate first evaporates, forming a highly nonequilibrium gas with no phase coherence; energy is then redistributed among the noncondensed atoms; finally, the atoms recondense. We calculate the timescales for each of these phases and explain how this scenario can be verified through future experiments.

We study the process of seeded or stimulated third-order parametric down-conversion as an extension of our previous work on spontaneous parametric down-conversion (TOSPDC). We present general expressions for the spectra and throughputs expected for the cases where the seed field or fields overlap either only one or two of the TOSPDC modes and allow for both pump and seed to be either monochromatic or pulsed. We present a numerical study for a particular source design, showing that doubly overlapped seeding can lead to a considerably greater generated flux as compared with singly overlapped seeding. We, furthermore, show that doubly overlapped seeding permits stimulated emission tomography for the reconstruction of the three-photon TOSPDC joint spectral intensity. We hope that our paper will guide future experimental efforts based on the process of third-order parametric down-conversion.

The unique spectral behavior exhibited by a class of nonuniform Bragg periodic structures, namely chirped and apodized fiber-Bragg gratings (FBGs) influenced by parity and time reversal ($\mathcal{PT}$) symmetry, is presented. The interplay between the $\mathcal{PT}$ symmetry and nonuniformities brings exceptional functionalities in the broken $\mathcal{PT}$-symmetric phase such as wavelength selective amplification and single-mode lasing for a wide range of variations in gain-loss. We observe that the device is no more passive and it undergoes a series of transitions from asymmetric reflection to unidirectional invisibility and multimode amplification as a consequence of variation in the imaginary part of the strength of modulation in different apodization profiles, namely Gaussian and raised cosine, at the given value of chirping. The chirping affords bandwidth control as well as control over the magnitude of the reflected (transmitted) light. Likewise, apodization offers additional functionality in the form of suppression of uncontrolled lasing behavior in the broken $\mathcal{PT}$-symmetric regime besides moderating the reflected signals outside the band edges of the spectra.

The Casimir-Lifshitz force $F_{(C-L)}$ between planar objects when one of them is stratified at the nanoscale is herein investigated. Layering results in optical interference effects that give rise to a modification of the optical losses, which, as stated by the fluctuation-dissipation theorem, should affect the Casimir-Lifshitz interaction. On these grounds, we demonstrate that, by nanostructuring the same volume of dielectric materials in diverse multilayer configurations, it is possible to access $F_{(C-L)}$ of attractive or repulsive nature, even getting canceled, at specific separation distances.

Renormalization of the inverse square potential usually breaks its classical conformal invariance. In a strongly attractive potential, the scaling symmetry is broken to a discrete subgroup while, in a strongly repulsive potential, it is preserved at quantum level. In the intermediate, weak-medium range of the coupling, an anomalous length scale appears due to a flow of the renormalization group away from a critical point. We show that potentials with couplings in the strongly repulsive and in the weak-medium ranges can be related by a dynamical supersymmetry. Imposing supersymmetry invariance unifies these two ranges and fixes the anomalous scale to zero, thus restoring the continuous scaling symmetry.

A common way to manipulate a quantum system, for example spins or artificial atoms, is to use properly tailored control pulses. In order to accomplish quantum information tasks before coherence is lost, it is crucial to implement the control in the shortest possible time. Here we report the near time-optimal preparation of a Bell state with fidelity higher than $99\%$ in an NMR experiment, which is feasible by combining the synergistic capabilities of modeling and experiments operating in tandem. The pulses preparing the Bell state are found by experiments that are recursively assisted with a gradient-based optimization algorithm working with a model. Thus, we exploit the interplay between model-based numerical optimal design and experimental-based learning control. Utilizing the balanced synergism between the dual approaches, as dictated by the case specific capabilities of each approach, should have broad applications for accelerating the search for optimal quantum controls.

Gaussian boson samplers (GBSs) have initially been proposed as a near-term demonstration of classically intractable quantum computation. We show here that they have a potential practical application: Samples from these devices can be used to construct a feature vector that embeds a graph in Euclidean space, where similarity measures between graphs—so-called graph kernels—can be naturally defined. This is crucial for machine learning with graph-structured data, and we show that the GBS-induced kernel performs remarkably well in classification benchmark tasks. We provide a theoretical motivation for this success, linking the extracted features to the number of $r$ matchings in subgraphs. Our results contribute to a new way of thinking about kernels as a quantum hardware-efficient feature mapping, and lead to a promising application for near-term quantum computing.

We study the Casimir pressure between two similar plates of finite thickness kept at different temperatures in the case when the dielectric permittivity of the plates depends on temperature. It is suggested to consider the dielectric permittivity at two different temperatures as the permittivities of two dissimilar bodies, thus, allowing to apply the theory of Casimir forces out of thermal equilibrium developed earlier in the literature. Following this approach, we show that, in addition to the equilibrium contribution to the nonequilibrium Casimir pressure, a proper nonequilibrium contribution arises for temperature-dependent dielectric permittivities. Furthermore, the equilibrium contribution in this case does not equal the mean of the equilibrium Casimir pressures at the temperatures of the plates. As an application, the total nonequilibrium Casimir pressure between two gold plates and between two titanium plates is calculated as a function of the plate thickness and their separation using the Drude and the plasma models. For plate separations ranging from 0.5 to $2\mu \mathrm{m}$, the relative difference between the theoretical predictions for these two models reaches 39%. The proper nonequilibrium term may be as large as 4% of the magnitude of the total nonequilibrium pressure.

The dissociation of ${\mathrm{H}}_2{}^{+}$ in a circularly polarized laser pulse is numerically studied by simulating the time-dependent Schrödinger equation. After absorbing one or three photons, the nuclear wave packets carrying the angular momenta $\hslash$ and $3\hslash$ dissociate along the $2p{\sigma }_u$ state. Due to the broad initial kinetic-energy distribution of the superimposed nuclear vibrational states, the one-photon and three-photon dissociation pathways may end with the same kinetic energy. These coexisting dissociation pathways with same parities but different orbital angular momenta interfere with each other, resulting in the spiral nuclear momentum distribution in the laser polarization plane. The interference structure in the nuclear momentum distribution offers another freedom to identify the dissociation pathways of molecules in strong laser fields.

The photodouble ionization of the water molecule is studied at 20 eV excess energy in a combined experimental and theoretical investigation. In the experiments, two photoelectrons of equal kinetic energy are detected in coincidence after energy and angular selection. On the theoretical side, a generalized Sturmian function approach is implemented to describe accurately the correlated two-electron continuum, while separable products of Moccia orbitals [J. Chem. Phys. 40, 2164 (1964)] are used for the initial electronic state of the water molecule. The theoretical triple-differential cross sections (TDCSs) are averaged over all possible molecular orientations in order to be compared with the experiments. The measured TDCSs display rich angular distributions that are in large part well reproduced by the adopted first-order treatment of the interaction with a two-active-electron target.

We propose a scheme to prepare a macroscopic mechanical oscillator in a catlike state, close to a coherent state superposition. The mechanical oscillator, coupled by radiation-pressure interaction to a field in an optical cavity, is first prepared close to a squeezed vacuum state using a reservoir engineering technique. The system is then probed using a short optical pulse tuned to the lower motional sideband of the cavity resonance, realizing a photon-phonon swap interaction. A photon number measurement of the photons emerging from the cavity then conditions a phonon-subtracted catlike state with a negative Wigner distribution exhibiting separated peaks and multiple interference fringes. We show that this scheme is feasible using state-of-the-art photonic crystal optomechanical system.

We study the deflection of photoelectrons in intense elliptically polarized standing light waves, known as the high-intensity Kapitza-Dirac effect. In order to compute the longitudinal momentum transfer to the photoelectron in above-threshold ionization, we utilize a complete description of the quantum dynamics in the spatially dependent field of the standing light wave. We propose experimental conditions under which low-energy photoelectrons can be generated with remarkably high longitudinal momenta that can be controlled via the polarization of the standing wave. We expect that future experimental realizations will provide additional insights into the momentum transfer in intense laser-atom interactions.

We discuss the topological invariant in the ($2+1$)-dimensional quench dynamics of a two-dimensional two-band Chern insulator starting from a topological initial state (i.e., with a nonzero Chern number $c_i$), evolved by a postquench Hamiltonian (with Chern number $c_f$). This process is classified by the torus homotopy group ${\tau }_3\left(S^2\right)$. In contrast to the process with $c_i=0$ studied in previous works, this process cannot be characterized by the Hopf invariant that is described by the sphere homotopy group ${\pi }_3\left(S^2\right)=\mathbb{Z}$. It is possible, however, to calculate a variant of the Chern-Simons integral with a complementary part to cancel the Chern number of the initial spin configuration, which at the same time does not affect the ($2+1$)-dimensional topology. We show that the modified Chern-Simons integral gives rise to a topological invariant of this quench process, i.e., the linking invariant in the ${\mathbb{Z}}_{2c_i}$ class: $\nu =(c_f-c_i)mod\left(2c_i\right)$. We give concrete examples to illustrate this result and also show the detailed deduction to get this linking invariant.

A variational quantum eigensolver (VQE) optimizes parametrized eigenstates of a Hamiltonian on a quantum processor by updating parameters with a classical computer. Such a hybrid quantum-classical optimization serves as a practical way to leverage classical algorithms in exploiting the power of near-term quantum devices. Here, aiming to solve a group of Hamiltonians more efficiently, we develop an extension of the conventional VQE. A snake algorithm is incorporated to couple optimizing processes for VQEs of different Hamiltonians by gradient descent. Such a so-called collective VQE (CVQE) is applied to simulate molecules with varied bond lengths for demonstration. Numeral simulations show that the CVQE exhibits clear collective behavior in the optimization process of updating parameters. Remarkably, the CVQE tends to avoid a single VQE task to be trapped in the local minimum. The collective optimization utilizes intrinsic relations between related tasks and may inspire advanced hybrid quantum-classical algorithms for solving practical problems with current quantum technologies.

Multiplexed quantum memories and high-dimensional entanglement can improve the performance of quantum repeaters by promoting the entanglement generation rate and the quantum communication channel capacity. Here, we experimentally generate a high-dimensional entangled state between a photon and a collective spin-wave excitation stored in the multiplexed atomic quantum memory. We verify the entanglement dimension by the quantum witness and the entanglement of formation. Then we use the high-dimensional entangled state to test the violation of the Bell-type inequality. Our paper provides an effective method to generate multidimensional entanglement between the flying photonic pulses and the atomic quantum interface.

We report on the appearance of a structure at low energies in the photoelectron momentum distribution of the hydrogen atom exposed to two-color counterrotating bicircular laser fields. These structures, which arise due to ac-Stark-shifted resonances, break the threefold symmetry, typical for the $\omega -2\omega$ bicircular fields. We discuss the physical origin of this structure in terms of partial-wave interference between direct ionization channels and a resonant pathway, which passes through the ac-Stark-shifted state, and show how the underlying Rydberg state population depend on the field strength and pulse duration.

Cold-atom interferometers commonly face systematic effects originating from the coupling between the trajectory of the atomic wave packet and the wavefront of the laser beams driving the interferometer. Detrimental for the accuracy and the stability of such inertial sensors, these systematics are particularly enhanced in architectures based on spatially separated laser beams. Here we analyze the effect of a coupling between the relative alignment of two separated laser beams and the trajectory of the atomic wave packet in a four-light-pulse cold-atom gyroscope operated in fountain configuration. We present a method to align the two laser beams at the $0.2\mu \mathrm{rad}$ level and to determine the optimal mean velocity of the atomic wave packet with an accuracy of $0.2\mathrm{mm}{\mathrm{s}}^{-1}$. Such fine tuning constrains the associated gyroscope bias to a level of $1\times {10}^{-10}\mathrm{rad}{\mathrm{s}}^{-1}$. In addition, we reveal this coupling using the point-source interferometry technique by analyzing single-shot time-of-flight fluorescence traces, which allows us to measure large angular misalignments between the interrogation beams. The alignment method which we present here can be employed in other sensor configurations and is particularly relevant to emerging gravitational wave detector concepts based on cold-atom interferometry.