Graph structures are ubiquitous throughout the natural sciences. Here we develop an approach that exploits the quantum source's graph structure to improve learning via an arbitrary quantum neural network (QNN) ansatz. In particular, we devise and optimize a self-supervised objective to capture the information-theoretic closeness of the quantum states in the training of a QNN. Numerical simulations show that our approach improves the learning efficiency and the generalization behavior of the base QNN. On a practical note, scalable quantum implementations of the learning procedure described in this paper are likely feasible on the next generation of quantum computing devices.

It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, Rényi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information.

We study a decoherence reduction scheme that involves an intermediate measurement on the qubit in an equal superposition basis, in the general framework of all qubit-environment interactions that lead to qubit pure decoherence. We show under what circumstances the scheme always leads to a gain of coherence on average, regardless of the time at which the measurement is performed, demonstrating its wide range of applicability. Furthermore, we find that observing an average loss of coherence is a highly quantum effect, resulting from noncommutation of different terms in the Hamiltonian. We show the diversity of behavior of coherence as effected by the application of the scheme, which is skewed towards gain rather than loss, on a variant of the spin-boson model that does not fulfill the commutation condition.

Quantum Rényi relative entropies play a significant part in characterizing operational tasks in quantum information theory. In this paper, we first give some fundamental properties of the zero-relative entropy, and we find that the geometric Rényi relative entropy reduces to the zero-relative entropy in the limit case. Then, we define a new mutual information via the zero-relative entropy, and it is the so-called zero-mutual information. In particular, the zero-mutual information is a lower bound of the Petz-Rényi and geometric generalized mutual information. We establish the chain rules for the unsmoothed and smoothed versions of the zero-mutual information. As an application, we discuss generalized mutual information with the Petz-Rényi, sandwiched Rényi, and geometric Rényi types, our result gives a uniform chain rule inequality for quantum generalized mutual information.

The nitrogen-vacancy (NV) center in diamond has been the focus of research efforts because of its suitability for use in applications such as quantum sensing and quantum simulations. Recently, the electron-spin double resonance (ESDR) of NV centers has been exploited for detecting radio-frequency (RF) fields with continuous-wave optically detected magnetic resonance. However, the characteristic phenomenon of ESDR under a strong RF field remains to be fully elucidated. In this study, we theoretically and experimentally analyzed the ESDR spectra under strong RF fields by adopting Floquet theory. Our analytical and numerical calculations could reproduce the ESDR spectra obtained by measuring the spin-dependent photoluminescence under the continuous application of a microwave and a RF field for a DC bias magnetic field perpendicular to the NV axis. We found that anticrossing structures that appear under a strong RF field are induced by the generation of RF-dressed states owing to the two-RF-photon resonances. Moreover, we found that $2n$-RF-photon resonances were allowed by an unintentional DC bias magnetic field parallel to the NV axis. These results should help in the realization of precise MHz-range AC magnetometry with a wide dynamic range beyond the rotating wave approximation regime as well as Floquet engineering in open quantum systems.

We have completed an improved precision measurement of the electron's electric dipole moment using trapped ${\mathrm{HfF}}^{+}$ in rotating bias fields. We report on the accuracy evaluation of this measurement, describing the mechanisms behind our systematic shifts. Our systematic uncertainty is reduced by a factor of 30 compared to the first generation of this measurement [Cairncross et al. Phys. Rev. Lett. 119, 153001 (2017)]. Our combined statistical and systematic accuracy is improved by a factor of 2 relative to any previous measurement [Nature (London) 562, 355 (2018)].

A vibrational wavepacket in ${\mathrm{SF}}_6$ is created by impulsive stimulated Raman scattering with a few-cycle infrared pulse and mapped simultaneously onto five sulfur core-excited states using table-top soft x-ray transient absorption spectroscopy between 170 to 200 eV. The femtosecond vibrations induce real-time energy shifts of the x-ray absorption, whose amplitude depend strongly on the nature of the core-excited state. The pump laser intensity is used to control the number of vibrational states in the superposition, thereby accessing core-excited levels for various extensions of the S-F stretching motion. This enables the determination of the relative core-level potential energy gradients for the symmetric stretching mode, in good agreement with TDDFT calculations. This experiment demonstrates a new means of characterizing core-excited potential energy curves.

The theoretical description of the interplay between coherent evolution and chemical exchange, originally developed for magnetic resonance and later applied to other spectroscopic regimes, was derived under incorrect statistical assumptions. Correcting these assumptions provides access to the exact form of the chemical exchange interaction, which we derive within the Lindblad master equation formalism for generality. The exact form of the interaction is only different from the traditional equation by a scalar correction factor derived from higher-order interactions and regularly improves the radius of convergence of the solution (hence increasing the allowable step size in calculations) by up to an order of magnitude for no additional computational cost.

We theoretically study the frequency shift in atomic clocks caused by the line-shape asymmetry of coherent population trapping (CPT) resonance in a bichromatic laser field. This asymmetry arises due to the inequality of the resonant spectral components and nonzero one-photon detuning. The line-shape-asymmetry-induced shift depends on the intensity of the resonant fields, which leads to a degradation in long-term stability due to fluctuations of the laser field parameters. A frequency stabilization based on the harmonic modulation of two-photon detuning is considered. It is shown that the use of a high-frequency modulation (compared to the CPT resonance width, i.e., the Pound-Drever-Hall regime) makes it possible to significantly suppress this shift (by one to two orders of magnitude).

We discuss the bulk and surface properties of ultradilute self-bound quantum droplets in a heteronuclear Bose-Bose mixture in the presence of higher-order quantum and thermal fluctuations. Within the realm of the Hartree-Fock-Bogoliubov theory, we calculate beyond the Lee-Huang-Yang corrections to the ground-state energy, the droplet equilibrium density, the surface tension, and the critical number of particles. Our predictions are compared with recent diffusion Monte Carlo simulation and density functional theory method and excellent agreement is found. We address in addition the effects of temperature on the formation and on the robustness of the heteronuclear self-bound mixtures.

We investigate the effect of two-body loss due to chemical reactions on quantum magnetism of fermionic polar molecules in an optical lattice. We show that an interplay between dissipation and strong long-range interactions leads to formation of metastable ferromagnetic clusters. The spin states of clusters are controlled by interaction parameters and reflect the symmetry of interactions. The size of clusters strongly depends on the initial configuration of molecules due to Hilbert-space fragmentation during dissipative many-body dynamics. We construct an effective model to show the emergence of metastable states as quasi-dark states. Application to quantum simulation of the spin-$S$ Heisenberg model is discussed.

We investigate families of soliton solutions in a spin-orbit-coupled Bose-Einstein condensate embedded in an optical lattice, which bifurcate from the nearly flat lowest band. Unlike the conventional gap solitons, the obtained solutions have the shape well approximated by a Wannier function (or a few Wannier functions) of the underlying linear Hamiltonian with amplitudes varying along the family and with nearly constant widths. The Wannier solitons sharing all symmetries of the system Hamiltonian are found to be stable. Such solutions allow for the construction of Wannier breathers that can be viewed as nonlinearly coupled one-hump solitons. The breathers are well described by a few-mode model and manifest stable behavior either in an oscillatory regime with balanced average populations or in a self-trapping regime characterized by unbalanced atomic populations of the local potential minima (similarly to the conventional boson Josephson junction), with the frequencies controlled by the interatomic interactions.

In this work we study the evolution of an optical vortex undergoing self-phase modulation inside a nonlinear Kerr medium. The intensity-dependent phase evolution couples the angular and radial degrees of freedom of the input vortex, giving rise to a rich dynamics where new radial modes are created. In the short propagation range, this dynamics is well described by a perturbative approach, predicting the generation of modes with radial numbers between zero and the absolute value of the vortex topological charge. This prediction is confirmed by numerical simulations of the nonlinear propagation equation.

The ultrafast dynamics of disordered systems have recently garnered considerable interest among researchers. However, due to the inherent complexity of such systems, many critical issues require further elucidation through extensive experimental and simulation data. We conduct calculations on high-order harmonic generation in an anisotropic two-dimensional disordered system that is similar to liquid crystals. Our results demonstrate the characteristics of harmonic spectra with different laser polarization angles and reveal a phenomenon of time delay in harmonic polarization perpendicular to the driving field. We show that this time delay arises from the intermolecular scattering of tunneling electrons before they recombine with holes. Thanks to the discovery of this phenomenon, it is hoped that polarization can be utilized to differentiate the quantum trajectories of high-order harmonics within a subcycle. Our discovery offers a different approach for investigating and manipulating ultrafast electron dynamics in condensed matter, while shedding light on the coherent control of ultrashort light sources.

A coordinate space approach to vacuum polarization using Pauli-Villars regularization is used to calculate the Uehling potential as a partial-wave expansion. This is done to develop a method that can be extended to cases of vacuum polarization where there is no simple analytic form to use to carry out the necessary renormalization. The numerical behavior of the partial-wave expansion is examined for the Uehling potential itself, its contribution to the fine structure of muonic hydrogen, and its contribution to electron scattering.

Noise-induced gate errors remain one of the main obstacles to realizing a broad range of quantum information technologies. Dynamical error suppression using carefully designed control schemes is critical for overcoming this challenge. Such schemes must be able to correct against multiple noise sources simultaneously afflicting a qubit to reach error-correction thresholds. Here we present a general framework for designing control fields that simultaneously suppress both noise in the fields themselves as well as transverse dephasing noise. Using the recently developed space curve quantum control formalism, in which robust quantum evolution is mapped to closed geometric curves in a multidimensional Euclidean space, we derive the minimal conditions necessary to guarantee the simultaneous cancellation of both types of noise to leading order. In particular, we find that the cancellation of control field noise requires the derivative of the space curve to have zero-area projections, which is a much more subtle property compared to the closed-curve condition needed to suppress transverse dephasing. We present several techniques for solving both these conditions simultaneously and provide explicit examples of error-resistant control fields. Our work also sheds light on the relation between holonomic evolution and the suppression of control field errors.

We describe a protocol for perfectly transferring a quantum state from one party to another under the dynamics of a fixed, engineered Hamiltonian. Our protocol combines the concepts of fractional revival, dual-rail encoding, and a rare glimpse of the anti-Zeno effect. Remarkably, this nondeterministic transfer can happen on average faster than the speed limit for perfect quantum state transfer.

We theoretically explore the advantages rendered by non-Gaussian operations in phase estimation using a parity-detection-based Mach-Zehnder interferometer, with one input being a coherent state and the other being a non-Gaussian squeezed vacuum state (SVS). We consider a realistic model to perform three different non-Gaussian operations, namely, photon subtraction, photon addition, and photon catalysis on a single-mode SVS. We start by deriving the Wigner function of the non-Gaussian SVSs, which is then utilized to derive the expression for the phase sensitivity. The analysis of the phase sensitivity reveals that all three different non-Gaussian operations can enhance the phase sensitivity under suitable choices of parameters. We also consider the probabilistic nature of these non-Gaussian operations, the results of which reveal the single-photon addition to be the optimal operation. Further, our analysis also enables us to identify the optimal squeezing of the SVS and the transmissivity of the beam splitter involved in the implementation of the non-Gaussian operations.

We demonstrate the storage and on-demand retrieval of single-photon-level telecom pulses in a fiber cavity. The cavity is formed by fiber Bragg gratings at either end of a single-mode fiber. Photons are mapped into and out of the cavity using quantum frequency conversion driven by intense control pulses. In a first spliced-fiber cavity, we demonstrate storage up to $0.55\mu \mathrm{s}$ (11 cavity round trips), with $11.3\%\pm 0.1$% total memory efficiency and a signal-to-noise ratio (SNR) of 12.8 after one round trip. In a second, monolithic cavity, we increase this lifetime to $1.75\mu \mathrm{s}$ (35 round trips) with a memory efficiency of $12.7\%\pm 0.2\%$ (SNR of $7.0\pm 0.2$) after one round trip. Fiber-based cavities for quantum storage at telecom wavelengths offer a promising route to synchronizing spontaneous-photon-generation events and building scalable quantum networks.

We analyze the strengths and limitations of steered discrete-time quantum walks with position-independent coins in generating quantum states of bipartite quantum systems comprising of a qubit coupled to a qudit system. We demonstrate that not all quantum states in the composite space are accessible through such quantum walks, even under the most generalized definition of a quantum step, leading to a bifurcation of the composite Hilbert space into “walk-accessible states” and the “walk-inaccessible states.” We give an algorithm for generating any walk-accessible state from a simple-to-realize product state in a minimal number of walk steps, all of unit step size. We further give a prescription towards constructing minimal quantum walks between any pair of such walk-accessible states. Linear optics has been a popular physical system for implementing coin-based quantum walks, where the composite space is built up of spin and orbital angular momenta of light beams. We establish that in such an implementation, any generalized quantum step can be implemented up to a global phase using a single $q$-plate and a pair of homogeneous wave plates. We then give a quantum walk based scheme for realizing arbitrary vector beams consisting of a finite number of OAM components, using only $q$ plates and wave plates.