We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion of classical (big) data to a quantum superposed state, in contrast to recently developed approaches for quantum machine learning. We performed optical experiments to illustrate a single-bit universal machine, which can be extended to a large-bit circuit for a binary classification task. Our experimental machine exhibits quantum learning speedup of approximately $36\%$, as compared with the fully classical machine. In addition, it features strong robustness against dephasing noise.

Unitarity randomized benchmarking (URB) is an experimental procedure for estimating the coherence of implemented quantum gates independently of state preparation and measurement errors. These estimates of the coherence are measured by the unitarity. A central problem in this experiment is relating the number of data points to rigorous confidence intervals. In this work we provide a bound on the required number of data points for Clifford URB as a function of confidence and experimental parameters. This bound has favorable scaling in the regime of near-unitary noise and is asymptotically independent of the length of the gate sequences used. We also show that, in contrast to standard randomized benchmarking, a nontrivial number of data points is always required to overcome the randomness introduced by state preparation and measurement errors even in the limit of perfect gates. Our bound is sufficiently sharp to benchmark small-dimensional systems in realistic parameter regimes using a modest number of data points. For example, we show that the unitarity of single-qubit Clifford gates can be rigorously estimated using few hundred data points under the assumption of gate-independent noise. This is a reduction of orders of magnitude compared to previously known bounds.

Theoretical and experimental resonance strengths for $KLL$ dielectronic recombination (DR) into He-, Li-, Be-, and B-like mercury ions are presented, based on state-resolved DR x-ray spectra recorded at the Heidelberg electron-beam ion trap. The DR resonance strengths are experimentally extracted by normalizing them to simultaneously recorded radiative recombination signals. The results are compared to state-of-the-art atomic calculations that include relativistic electron correlation and configuration mixing effects. Combining the present data with other existing ones, we derive an improved semiempirical $Z$-scaling law for DR resonance strengths as a function of the atomic number, taking into account higher-order relativistic corrections, which are especially relevant for heavy highly charged ions.

The effect of Coulomb interaction screening on nonrelativistic free-free absorption is investigated by integrating the numerical continuum wave functions. The screened potential is taken to be in Debye-Hückel (Yukawa) form with a screening length $D$. It is found that the values of the free-free Gaunt factors for different Debye screening lengths $D$ for a given initial electron energy ${\varepsilon }_i$ and absorbing photon energy $\omega$ generally lie between those of the pure Coulomb field and field-free case. However, for initial electron energies below 0.1 Ry and fixed photon energy, the Gaunt factors show dramatic enhancements (broad and narrow resonances) in the vicinities of the critical screening lengths, $D_{nl}$, at which the energies of $nl$ bound states in the potential merge into the continuum. These enhancements of the Gaunt factors can be significantly higher than their values in the unscreened (Coulomb) case over a broad range of ${\varepsilon }_i$. The observed broad and narrow resonances in the Gaunt factors are related to the temporary formation of weakly bound (virtual) and resonant (quasibound) states of the low-energy initial electron on the Debye-Hückel potential when the screening length is in the vicinity of $D_{nl}$.

Effective range is a quantity to characterize the energy dependence in two-body scattering strength and is widely used in cold atomic systems, especially across narrow resonances. Here we show that the effective range can significantly modify the magnetic property of one-dimensional (1D) spin-$1/2$ fermions in the strongly repulsive regime. In particular, the effective range breaks the large spin degeneracy in the hard-core limit and induces a Heisenberg exchange term in the spin chain that is much more sensitive to the local density than that induced by the bare coupling. With an external harmonic trap, this leads to a very rich magnetic pattern where the antiferromagnetic and ferromagnetic correlations can coexist and distribute in highly tunable regions across the trap. Finally, we propose to detect the range-induced magnetic order in the tunneling experiment. Our results can be directly tested in 1D Fermi gases across narrow resonance and suggest a convenient route toward the local manipulation of quantum magnetism in cold atoms.

We study nonreciprocal microwave transmission based on the Gebhard-Ruckenstein hopping. We consider a superconducting device that consists of microwave resonators and a coupler. The Gebhard-Ruckenstein hopping between the resonators gives rise to a linear energy dispersion which manifests chiral propagation of microwaves in the device. This device functions as an on-chip circulator with a wide bandwidth when transmission lines are attached.

By employing the angular spectrum representation, we successfully derive the partial-wave expansion coefficients of the circular Airy beams (CABs) with different polarizations, based on which the scattering of a spherical particle in the CABs is solved exactly. Special attention is focused on exploring the potential applications of the CABs in the abruptly autofocusing (AAF) property and optical manipulation of microparticle by optical force. It is found that both the linear and circular polarizations are the best candidates to implement the AAF property robustly against strong disturbance by a large-sized particle. In addition, although the CABs can be intensively focused to a small region, resulting in an abrupt increase of light intensity by two orders of magnitude at the focal point and enabling three-dimensional stable trapping of a Rayleigh particle near the focal point, the usual CABs fail to generate an optical force outweighing the Brownian force to achieve a stable transverse trapping in the region before the focal point. On the other hand, a Mie particle can be confined transversely in the primary ring and accelerated along the curved trajectory of CABs to the focal point, then pushed further all the way through the focal point rather than being trapped therein, and eventually accelerated further along a straight trajectory in the direction of light propagation over 100 wavelengths, due to the weak diffraction characteristic of a morphed Bessel-like beam of CABs. The exotic curved-straight trajectory transport of particles by the CABs may find applications in the case where the transport path is partly blocked.

We present an accurate and efficient method for calculating the image of a mesoscopic particle that is captured using a high-numerical-aperture objective lens. We test various scattering models of silica, plastic, and birefringent vaterite spheres in water. We show that the calculated images accurately replicate experimental observations. This method uses the idea that the optical system can be represented as a product of matrices acting on the electromagnetic field in a truncated Hilbert space representation. A general reusable matrix encapsulating the polarization, limited capture angle, or beam shaping in the microscope can be applied to find the image and not be limited to a particular particle shape or medium. We show that the image obtained from this method can be used to determine and match particle properties. We also use incoherent averaging on multiple $T$-matrices to produce polychromatic images. Data obtained using this method could be used as an input to track the general behavior of particles in suspension or within an optical trap.

Employing a procedure called monitoring—via a completely positive trace preserving map that is able to interpolate between weak and projective measurements—we investigate the resilience of the recently proposed realism-based nonlocality to local and bilocal weak measurements. This analysis indicates realism-based nonlocality as the most ubiquitous and persistent form of quantumness within a wide class of quantum-correlation quantifiers. In particular, we show that the set of states possessing this type of quantumness forms a strict superset of symmetrically discordant states and, therefore, of discordant, entangled, steerable, and Bell-nonlocal states. Moreover, we find that, under monitoring, realism-based nonlocality is not susceptible to sudden death.

Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demonstrate that this is not the case in the presence of finite pulse-durations, where a detuning can drastically alter the coherence response of the probe qubit, with important implications for sensing applications. Using the electronic spin associated with a nitrogen-vacancy center in diamond as a test qubit system, we analytically and experimentally study the qubit coherence response under CPMG and XY8 dynamical decoupling control schemes in the presence of finite pulse-durations and static detunings. Most striking is the splitting of the NMR resonance under CPMG, whereas under XY8 the amplitude of the NMR signal is modulated. Our work shows that the detuning error must not be neglected when extracting data from quantum sensor coherence traces.

We present a general framework encompassing a number of continuous-variable quantum key distribution protocols, including standard one-way protocols, measurement-device-independent protocols, as well as some two-way protocols, or any other continuous-variable protocol involving only a Gaussian modulation of coherent states and heterodyne detection. The main interest of this framework is that the corresponding protocols are all covariant with respect to the action of the unitary group $\text{U}\left(n\right)$, implying that their security can be established thanks to a Gaussian de Finetti reduction. In particular, we give a composable security proof of two-way continuous-variable quantum key distribution against general attacks. We also prove that no active symmetrization procedure is required for these protocols, which would otherwise make them prohibitively costly to implement.

Bond rearrangement, namely the dissociation of water ions into ${{\mathrm{H}}_2}^{+}+{\mathrm{O}}^{(q-1)+}$ ($q=1$–4) following fast ion-impact ionization, unexpectedly occurs following multiple ionization of water in spite of the presumably fast “Coulomb explosion” of the transient molecular ion. Furthermore, the branching ratio of bond rearrangement is found to be nearly equal for each level of ionization, $q$. In addition, formation of ${{\mathrm{H}}_2}^{+}$ is more than twice as likely to occur from the lighter water isotopologue ${\mathrm{H}}_2{\mathrm{O}}^{+}$ than ${{\mathrm{D}}_2}^{+}$ from ${\mathrm{D}}_2{\mathrm{O}}^{+}$. These findings are consistent with the ground state dissociation mechanism in which a fast projection of the ground state nuclear wave function onto the vibrational continuum of the cation potential energy surface is sometimes followed by ${{\mathrm{H}}_2}^{+}$ formation.

The absolute generalized cross sections and angular distribution parameters of photoelectrons for the two-photon above-threshold $3p$ ionization of Ar were calculated in the exciting photon energy range from 15.76 to 36 eV. The correlation function technique developed earlier was extended for the case when an intermediate-state function is of a continuum-type. We show that two-photon ionization of Ar near the $3p^4$ threshold to a large extent is determined by the ${(3p⤍\varepsilon d)}^2$ two-photon absorption via the giant resonance. This many-electron correlation causes (i) an increase of the photoionization cross sections by more than a factor of 3; and (ii) the appearance of resonances in the exciting-photon energy range of the doubly excited states. The predictions are supported by a good agreement between length and velocity results obtained after taking into account the higher-order perturbation theory corrections.

We apply the Monte Carlo wave-packet approach to study the interatomic Coulombic decay (ICD) dynamics of neon dimers after removing a $2s$ electron from one of the Ne atoms by one-photon absorption from an XUV pulse. This method reproduces well both the lifetime for the $2s$ inner-valence vacancy in $\mathrm{Ne}{}_2{}^{+}\left(2s^{-1}\right)$ and the kinetic energy release (KER) spectra for the coincident ${\mathrm{Ne}}^{+}$ and ${\mathrm{Ne}}^{2+}$ fragments following triple ionization, i.e., two photoionizations and one ionization via ICD, of ${\mathrm{Ne}}_2$ measured in an XUV-pump–XUV-probe experiment [K. Schnorr et al., Phys. Rev. Lett. 111, 093402 (2013)]. Comparisons between the calculated and measured nuclear KER spectra give physical insights in the considered process. For example, an analysis of the ratios between the low- and high-energy peaks in the nuclear KER spectra for large delays provides an estimate of the photoionization cross sections for removing a $2p$ electron from the excited states in $\mathrm{Ne}{}_2{}^{+}\left(2s^{-1}\right)$. Such comparisons also allow an estimate for the ICD rates for the $2s$ inner-valence vacancy in the single-site two hole state in $\mathrm{Ne}{{}_2}^{2+}\left(2s^{-1}2p^{-1}\right)$. Finally, the influence of photon statistics of the free electron laser pulses on the nuclear KER spectra is considered.

The recoil momentum and energy of ultracold atoms is studied for situations where collective scattering or emission of photons is important. Effects due to the dipole-dipole interaction are emphasized. For two and many atoms confined in optical traps, calculations of the energy and momentum with respect to atomic separation are performed. When the atomic separation is comparable to or larger than the transition wavelength, the ultracold atoms' recoil energy depends mainly on collective spontaneous decay rather than forces from the cooperative frequency shift. Calculations for a laser pulse reflecting from an atomic array suggest that the recoil energy of atoms can be substantially larger than might be expected from an independent atom picture.

Quantum memories can be used not only for storage of quantum information but also for a substantial manipulation of ensembles of quantum states. Therefore, the speed of such manipulation and the ability to write and retrieve signals of relatively short duration become important. One approach towards enhancing the performance of a quantum memory is to combine an active medium with an optical cavity. Previous works investigating cavity-enhanced memories concentrated on noise processes in the bad cavity limit, that is, for signals that are much longer than the cavity field lifetime. In this work we investigate four-wave mixing noise that arises from the retrieval of relatively short signals from cavity-assisted memories, thus complementing recent works by other authors. We propose an approach that allows one to account for noise sources of different frequencies and different physical origin by using two-band spectral filtering of the noise sources in the Heisenberg-Langevin picture. We demonstrate that in these spectrally selective memories the sideband atomic noise sources contribute to the four-wave mixing noise on par with the sideband quantized field entering the cavity.

We employ a polaron picture to investigate the properties of the two-photon quantum Rabi model (QRM), which describes a two-level or spin-half system coupled with a single bosonic mode by a two-photon process. In the polaron picture, the coupling in the two-photon process leads to spin-related asymmetry so that the original single bosonic mode splits into two separated frequency modes for the opposite spins, which correspond to two bare polarons. Importantly, the tunneling causes these two bare polarons to exchange their components with each other, thus leading to additional induced polarons. According to this picture, the variational ground-state wave function of the two-photon QRM can be correctly constructed, with the ground-state energy and other physical observables in good agreement with the exact numerics in all the coupling regimes. Furthermore, generalization to multiple induced polarons involving higher orders in the tunneling effect provides a systematic way to yield a rapid convergence in accuracy even around the difficult spectral collapse point. In addition, the polaron picture provides a distinctive understanding of an incomplete spectral collapse behavior that is about the existence of discrete energy levels apart from the collapsed spectrum at the spectral collapse point. This work illustrates that the polaron picture is helpful to capture the key physics in this nonlinear light-matter interaction model and indicates that this method can be applicable to more complicated QRM-related models.

We study the limitations on coherence evolutions under the constraints of thermodynamic laws, and focus on the optimal thermal operations (TO) reaching the bounds. For the qubit case, we prove that the TO that preserves maximal coherence can be reproduced by thermal operations involving only a single-mode reservoir, which we call single-mode thermal operations (STO). For higher dimensional systems, we derive tight limitations on coherence merging which are allowed by TO, and find that these bounds can also be reached by STO. By applying the coherence merging bounds to a two-qubit system, we observe that for some states, it is impossible to erase correlations while preserving the marginal states by TO. Our results reveal the strong ability of STO in coherence processing. Because interactions between quantum systems and single-mode reservoirs are realizable under recent techniques, our theoretical results are helpful to experimentally demonstrate the limitations of thermodynamic laws.

The uncertainty principle is one of the central concepts in quantum theory. Different forms of this principle have been discussed in various foundational and information theoretic topics. Whereas in the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by the fine-grained uncertainty relation, in the continuous-variable paradigm the Robertson-Schrödinger (RS) uncertainty relation has been used to detect multimode entanglement. Here we show that the RS uncertainty relation plays an important role in discriminating between quantum and postquantum nonlocal correlations in the multimode continuous outcome scenario. We provide a class of $m$-mode postquantum nonlocal correlations with a continuous outcome spectrum. While nonlocality of the introduced class of correlations is established through the Calvalcanti-Foster-Reid-Drummond class of Bell inequalities, the RS uncertainty relation detects their postquantum nature. Our result suggests a wider role of the uncertainty principle in the study of nonlocality in continuous-variable multimode systems.