We use machine-learning techniques to design three-qubit entangling gates with fidelities of >99.9% and duration of 50 ns for nearest-neighbor coupled flux-tunable transmons in circuit quantum electrodynamics architectures. The gate design procedure enforces realistic constraints and analyzes the robustness of the new gates under decoherence, distortion, and random noise. The controlled-controlled-phase gate in combination with two single-qubit gates realizes a Toffoli gate which is widely used in quantum circuits, logic synthesis, and quantum error correction. We also introduce a three-qubit entangling Parity Checker gate which has applications in quantum arithmetic circuits and quantum error correction schemes. Using these three-qubit gates, we design a circuit for Shor's nine-qubit quantum error correction code and compare its performance to conventional realizations.

Undoing a unitary operation, i.e., reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any specific description, however, it is a hard and challenging task to realize the inverse operation. Recently, a universal quantum circuit has been proposed [Phys. Rev. Lett. 123, 210502 (2019)] to undo an arbitrary unknown $d$-dimensional unitary $U$ by implementing its inverse with a certain probability. In this paper, we report the experimental reversal of three single-qubit unitaries $(d=2)$ by linear optical elements. The experimental results prove the feasibility of the reversing scheme, showing that the average fidelity of inverse unitaries is $F=0.9767\pm 0.0048$, in close agreement with the theoretical prediction.

We propose a scheme for the generation of hybrid states entangling a single-photon time-bin qubit with a coherent-state qubit encoded on phases. Compared to other reported solutions, time-bin encoding makes hybrid entanglement particularly well adapted to applications involving long-distance propagation in optical fibers. This makes our proposal a promising resource for future out-of-the-laboratory quantum communication. In this perspective, we analyze our scheme by taking into account realistic experimental resources and discuss the impact of their imperfections on the quality of the obtained hybrid state.

We present a semianalytical methodology to construct optimal linear-optical circuits for the heralded production of three-photon Greenberger-Horne-Zeilinger (3-GHZ) and two-photon Bell states. We provide a detailed description and analysis of the resulting optical schemes, which deliver success probabilities of 1/54 and 2/27 for dual-rail encoded 3-GHZ and Bell-state generation, respectively. Our results improve the known constructive bounds on the success probabilities for 3-GHZ states and are of particular importance for a ballistic quantum computing model [M. Gimeno-Segovia et al., Phys. Rev. Lett. 115, 020502 (2015)], for which these states provide an essential resource.

The present paper determines the precise values of magic wavelengths corresponding to the clock transitions $5^{2}S\text{–}{4}^{2}D$ of the ${\mathrm{Y}}^{2+}$ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.

We characterized the pulsed Rydberg-positronium production inside the Antimatter Experiment: Gravity, Interferometry, Spectroscopy ($\mathrm{AE}\overline{\text{g}}\mathrm{IS}$) apparatus in view of antihydrogen formation by means of a charge exchange reaction between cold antiprotons and slow Rydberg-positronium atoms. Velocity measurements on the positronium along two axes in a cryogenic environment ($\approx 10\mathrm{K}$) and in $1\mathrm{T}$ magnetic field were performed. The velocimetry was done by microchannel-plate (MCP) imaging of a photoionized positronium previously excited to the $n=3$ state. One direction of velocity was measured via Doppler scan of this $n=3$ line, another direction perpendicular to the former by delaying the exciting laser pulses in a time-of-flight measurement. Self-ionization in the magnetic field due to the motional Stark effect was also quantified by using the same MCP-imaging technique for Rydberg positronium with an effective principal quantum number $n_{\mathrm{eff}}$ ranging between 14 and 22. We conclude with a discussion about the optimization of our experimental parameters for creating Rydberg positronium in preparation for an efficient pulsed production of antihydrogen.

We present a theoretical approach for describing collective x-ray emission processes in extended multilevel targets, based on a combination of propagation equations for the quantum correlation functions and the semiclassical Maxwell-Bloch equations. Such a description overcomes the key deficiencies of the two constituent sets of equations, which have until now been independently used to describe these phenomena. The model developed is employed to study the spectral properties of superfluorescence of $K\alpha$ emission in zinc at $\sim 8630\mathrm{eV}$ after inner-shell photoionization with intense attosecond free-electron laser pulses. At high pump intensities, the numerical simulations predict a splitting of the $K{\alpha }_1$ emission line due to a self-induced Autler-Townes effect, which could readily be observed with standard high-resolution x-ray spectrometers. As short duration of the pump pulse is one of the crucial parameters for the manifestation of this phenomenon in the hard-x-ray regime, experimental verification could be possible due to the most recent developments of free-electron laser sources.

We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer classification, we show that our system hosts a symmetry-protected phase protected by a magnetic group symmetry ($\mathcal{M}$) and characterized by a $Z_2$ topological invariant. In single-particle spectra, we show that the topological nontrivial phase supports two kinds of edge states, which include two (four) zero-energy edge modes in the absence (presence) of two-photon detuning. We further study the bulk-edge correspondence in a non-Hermitian model by taking into account the particle dissipation. It is shown that the non-Hermitian system preserves the bulk-edge correspondence under the $\mathcal{M}$ symmetry but exhibits the non-Hermitian skin effect with breaking the $\mathcal{M}$ symmetry at nonzero magnetic flux. This work provides insights in understanding the exotic topological quantum states of high-spin systems and facilitating their experimental explorations.

We introduce a fidelity-based measure, ${\text{D}}_{\mathrm{QC}}\left(t\right)$, to quantify the differences in the dynamics of classical versus quantum walks over a graph. We provide universal, graph-independent, analytic expressions of this quantum-classical dynamical distance, showing that at short times ${\text{D}}_{\mathrm{QC}}\left(t\right)$ is proportional to the coherence of the walker, i.e., a genuine quantum feature, whereas at long times it depends only on the size of the graph. At intermediate times, ${\text{D}}_{\mathrm{QC}}\left(t\right)$ does depend on the graph topology through its algebraic connectivity. Our results show that the difference in the dynamical behavior of classical and quantum walks is entirely due to the emergence of quantum features at short times. In the long-time limit, quantumness and the different nature of the generators of the dynamics, e.g., the open-system nature of classical walks and the unitary nature of quantum walks, are instead contributing equally.

We explore the role of atomic correlations in a harmonically trapped Bose-Einstein condensate coupled to a dissipative cavity where both the atoms and the cavity are blue-detuned from the external pumping laser. Using a genuine beyond-mean-field many-body approach, we extract density distributions and many-body correlations to unveil a pathway to chaos at large pump power through a hierarchical self-organization of the atoms where the atoms transition from a single-well optical lattice to a double-well optical lattice. Correlated states of the atoms emerge and are characterized by local superfluid correlations in phases which are globally superfluid or Mott insulating. Local superfluid-Mott transitions are precluded by a dynamical instability to chaos which occurs via quasiperiodic attractors. Our results explain the mechanism behind the dynamical instabilities observed in experiments.

Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order ${\alpha }^{7}m$, where $\alpha$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons and the nucleus. The complete calculation of the ${\alpha }^{7}m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and muonic helium atoms and thus provide a stringent test of the standard model of fundamental interactions.

High-order harmonic signals generated in molecules are the consequence of coherent summation of complex laser-induced transition dipoles $d(\theta ,\omega )$ with each fixed-in-space molecule; here $\theta$ is the angle of the molecular axis with respect to the laser polarization axis and $\omega$ is the harmonic energy. In the so-called rotational coherent spectroscopy, it is proposed to extract the fixed-in-space $d(\theta ,\omega )$ in the molecular frame by measuring harmonics generated by a probing laser from the rotational molecular wave packets that have been prepared by a prior pump laser. By varying the time delay between the two lasers, methods have been utilized to extract the $\theta$ dependence of both the amplitude and phase of each individual harmonic, but the relative phase between harmonics cannot be retrieved. Here we report that this limitation can be removed. It requires the additional measurement of harmonic spectra versus the pump-probe angles at one fixed time delay. The two-dimensional input harmonic data (time-delay and pump-probe angle) are then used to retrieve the full complex transition dipole $d(\theta ,\omega )$ using a retrieval method based on machine learning algorithms. We demonstrate this method on ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$ molecules.

We present a quantum thermometry scheme based on a cavity-QED setup, which attains a sensitivity with Heisenberg scaling. A stream of identical two-level systems passes through a thermal bath to be tested. Each system partially thermalizes, carrying information on the temperature of the thermal bath, and it then interacts with a dissipative single-mode cavity. The Heisenberg scaling is attained from the initial coherence of each system. The systems cannot be fully thermalized by the thermal bath. The optimal interaction time between the system and the thermal bath is derived. Direct photon detection is proved to be an optimal measurement when there is no extra thermal bath in the cavity. In the case where there is an extra thermal bath in the cavity independent of the thermal bath to be tested, homodyne detection is the optimal measurement. Moreover, we show that direct photon detection obtains less information in the case where the extra thermal bath in the cavity is in thermal equilibrium with the thermal bath. However, the optimal measurement can utilize the information from the extra thermal bath to improve the estimation precision of the temperature.

We analyze the difference between ex ante and ex post equilibria in classical games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we find a constructive procedure to find two-person Bayesian games with a nonlocal (i.e., no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle, and share the property that their relevant ex ante equilibria are ex post equilibria as well. We introduce here a different type of game, based on the Bell theorem by Vértesi and Bene, which does not have the latter property: The ex ante and ex post equilibria differ.

Quantum walks are important tools for the development of quantum algorithms and carrying out quantum simulations. Recent interest in nonlinear discrete-time quantum walks aims to use it as a shortcut through dynamical regimes hard to obtain using current methods. We introduce a model featuring a modified conditional shift operator to carry dependence on the local occupation probability with a given strength we are able to control. It accounts for a third-order nonlinear contribution which is found in many physical contexts. We find a rich set of dynamical profiles, including solitonlike propagation, self-trapping, and chaos, all these arising from rather simple rules. Our tool set goes beyond unitary transformations, thus broadening the possibilities for controlling quantum dynamics.

Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive potential $\sim -r^{-2}$. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D bosonic gas suppresses the collapse and creates the missing ground state (GS). However, the cubic nonlinearity is not strong enough to suppress the 2D collapse. We demonstrate that the Lee-Hung-Yang (LHY) quartic term, induced by quantum fluctuations around the MF state, is sufficient for the stabilization of the 2D gas against the collapse. By means of numerical solution of the Gross-Pitaevskii equation including the LHY term, as well as with the help of analytical methods, such as expansions of the wave function at small and large distances from the center and the Thomas-Fermi approximation, we construct stable GS, with a singular density $\sim r^{-4/3}$ but convergent integral norm. Counterintuitively, the stable GS exists even if the external potential is repulsive, with the strength falling below a certain critical value. An explanation to this finding is given. Along with the GS, singular vortex states are produced too, and their stability boundary is found analytically. Unstable vortices spontaneously transform into the stable GS, expelling the vorticity to the periphery.

Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space and in a harmonic trapping potential of frequency $\omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $\mathrm{\Delta }{b}_4$ and $\mathrm{\Delta }{b}_5$ as functions of $\mathrm{\Delta }{b}_3$. Additionally, we argue that in the $\omega \to 0$ limit the relationship $b_n^{\text{T}}=n^{-d/2}{b}_n$ holds between the trapped (T) and the homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $\mathrm{\Delta }{b}_3^{\text{T}}$ in one dimension with three-body forces and $\mathrm{\Delta }{b}_2^{\text{T}}$ in two dimensions with two-body forces.

Biphotons of narrow bandwidth and long temporal length play a crucial role in long-distance quantum communication (LDQC) and linear optical quantum computing (LOQC). However, generation of these photons usually requires atomic ensembles with high optical depth or spontaneous parametric down-conversion with sophisticated optical cavity. By manipulating the two-component biphoton wave function generated from a low-optical-depth (low-OD) atomic ensemble, we demonstrate biphotons with subnatural linewidth in the sub-MHz regime. The potential to shape and manipulate the quantum wave packets of these temporally long photons is also demonstrated and discussed. Our work has potential applications in realizing quantum repeaters and large cluster states for LDQC and LOQC, respectively. The possibility to generate and manipulate subnatural-linewidth biphotons with low OD also opens up the opportunity to miniaturize the biphoton source for implementing quantum technologies on chip-scale quantum devices.