Adiabatic quantum computation requires keeping a system in a particular eigenstate. However, unwanted transitions can occur due to the interaction of the system with a noisy environment. The adiabatic evolution of the system will then be ruined. To reduce the effect of the environment, quantum control methods can be used. This allows one to speed up the adiabatic process. Here we present an effective control scheme to allow for a speedup of the adiabatic process by using a sequence of pulses on the system. Using the hierarchical functional derivative (HFD) approach, we calculate the fidelity evolution, which is a measure of the adiabaticity in an open system. By carefully choosing the pulse intensity and duration, an accelerated adiabatic path can be obtained for both a weak-coupling and a strong non-Markovian environment.

Given a parametrized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We studied several constrained variations of this problem and answered this question in the affirmative, with some caveats. Grover's quantum search algorithm is optimal up to a constant. The success probability of Grover's algorithm goes from unity for two qubits, decreases for three and four qubits, and returns near unity for five qubits, then oscillates ever so close to unity, reaching unity in the infinite qubit limit. The variationally approach employed here found an experimentally discernible improvement of $5.77\%$ and $3.95\%$ for three and four qubits, respectively. Our findings are interesting as an extreme example of variational search, and they illustrate the promise of using hybrid quantum classical approaches to improve quantum algorithms. This paper further demonstrates that to find optimal parameters, one does not need to vary over a family of quantum circuits to find an optimal solution. This result looks promising and points out that there is a set of variational quantum problems with parameters that can be efficiently found on a classical computer for an arbitrary number of qubits.

In network science, graphs obtained by taking the Kronecker or tensor power of the adjacency matrix of an initiator graph are used to construct complex networks. In this paper, we analytically prove sufficient conditions under which such Kronecker graphs can be searched by a continuous-time quantum walk in optimal $\mathrm{\Theta }\left(\sqrt{N}\right)$ time. First, if the initiator is regular and its adjacency matrix has a dominant principal eigenvalue, meaning its unique largest eigenvalue asymptotically dominates the other eigenvalues in magnitude, then the Kronecker graphs generated by this initiator can be quantum searched with probability 1 in $\pi \sqrt{N}/2$ time, asymptotically, and we give the critical jumping rate of the walk that enables this. Second, for any fixed initiator that is regular, nonbipartite, and connected, the Kronecker graphs generated by it are quantum searched in $\mathrm{\Theta }\left(\sqrt{N}\right)$ time. This greatly extends the number of Kronecker graphs on which quantum walks are known to optimally search. If the fixed, regular, connected initiator is bipartite, however, then search on its Kronecker powers is not optimal, but is still better than a classical computer's $O\left(N\right)$ runtime if the initiator has more than two vertices.

When some of the parties of a multipartite entangled pure state are lost, the question arises whether the residual mixed state is also entangled, in which case the initial entangled pure state is said to be robust against particle loss. In this paper, we investigate this entanglement robustness for $N$-qubit pure states. We identify exhaustively all entangled states that are fragile, i.e., not robust, with respect to the loss of any single qubit of the system. We also study the entanglement robustness properties of symmetric states and put these properties in the perspective of the classification of states with respect to stochastic local operations assisted with classic communication (SLOCC classification).

The nuclear-recoil effect on the $g$ factor of the ground state of highly charged B-like ions is studied to first order in the electron-to-nucleus mass ratio $m/M$. The leading one-electron and two-electron recoil contributions are calculated nonperturbatively in the parameter $\alpha Z$ within the rigorous QED formalism. The interelectronic-interaction correction to the nuclear-recoil effect is evaluated in the Breit approximation by means of perturbation theory to the first order in $1/Z$. The higher-order interelectronic-interaction corrections are taken into account partially by performing the calculations with the effective screening potential. The results obtained represent an up-to-date treatment of the nuclear-recoil effect on the $g$ factor of highly charged B-like ions in the range $Z=20–92$.

Using time-resolved measurements, we demonstrate coherent collective Rydberg excitation crossing over into Rydberg blockade in a dense and ultracold gas trapped at a distance of 100 $\mu \mathrm{m}$ from a room-temperature atom chip. We perform Ramsey-type measurements to characterize the coherence. The experimental data are in good agreement with numerical results from a master equation using a mean-field approximation and with results from a super-atom-based Hamiltonian. This represents significant progress in exploring a strongly interacting driven Rydberg gas on an atom chip.

An atom can be excited through tunneling when it is exposed to a strong laser field. This excitation process is known as frustrated tunneling ionization (FTI). Recently it has been reported that coherent extreme-ultraviolet emission can be achieved through FTI. In the present work we extend the strong-field-approximation (SFA) model developed by Lewenstein et al. to derive a quantum mechanical description of the FTI emission. An analytic expression is derived to describe FTI emission as four steps: tunneling of an electron from the ground state of an atom, acceleration of the electron in the continuum, recombination into the exited state of the parent atom, and free induction decay. The coherence property of FTI emission is studied using the attosecond lighthouse method, in which a spatially chirped laser beam generates FTI emissions in different directions. The spatial distribution of the FTI emission in the far field is analyzed using both the extended SFA model and the time-dependent Schrödinger equation model. The results obtained from the two models agree well, thereby confirming the validity of our extended SFA model.

Electric-field noise from ion-trap electrode surfaces can limit the fidelity of multiqubit entangling operations in trapped-ion quantum information processors and can give rise to systematic errors in trapped-ion optical clocks. The underlying mechanism for this noise is unknown, but it has been shown that the noise amplitude can be reduced by energetic ion bombardment, or “ion milling,” of the trap electrode surfaces. Using a single trapped ${}^{88}\mathrm{Sr}^{+}$ ion as a sensor, we investigate the temperature dependence of this noise both before and after ex situ ion milling of the trap electrodes. Making measurements over a trap electrode temperature range of 4 K to 295 K in both sputtered niobium and electroplated gold traps, we see a marked change in the temperature scaling of the electric-field noise after ion milling: power-law behavior in untreated surfaces is transformed to Arrhenius behavior after treatment. The temperature scaling becomes material-dependent after treatment as well, strongly suggesting that different noise mechanisms are at work before and after ion milling. To constrain potential noise mechanisms, we measure the frequency dependence of the electric-field noise, as well as its dependence on ion-electrode distance, for niobium traps at room temperature both before and after ion milling. These scalings are unchanged by ion milling.

Non-Born-Oppenheimer quantum dynamics of ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{HD}}^{+}$ excited by single one-cycle laser pulses linearly polarized along the molecular ($z$) axis have been studied within a three-dimensional model, including the internuclear distance $R$ and electron coordinates $z$ and $\rho$, by means of the numerical solution of the time-dependent Schrödinger equation on the timescale of about 200 fs. Laser carrier frequencies corresponding to the wavelengths of ${\lambda }_l=400$ and 50 nm have been used and the amplitudes of the pulses have been chosen such that the energies of ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{HD}}^{+}$ are above the dissociation threshold after the ends of the laser pulses. It is shown that excitation of ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{HD}}^{+}$ above the dissociation threshold is accompanied by formation of vibrationally “hot” and “cold” ensembles of molecules. Dissociation of vibrationally “hot” molecules does not prevent the appearance of post-laser-pulse electronic oscillations, parallel $z$ oscillations, and transversal $\rho$ oscillations. Moreover, dissociation of “hot” molecules does not influence characteristic frequencies of electronic $z$ and $\rho$ oscillations. The main difference between the laser-induced quantum dynamics of homonuclear ${\mathrm{H}}_2{}^{+}$ and its heteronuclear isotope ${\mathrm{HD}}^{+}$ is that fast post-laser-pulse electronic $z$ oscillations in ${\mathrm{H}}_2{}^{+}$ are regularly shaped with the period of ${\tau }_{\mathrm{shp}}\approx 30$ fs corresponding to nuclear oscillations in ${\mathrm{H}}_2{}^{+}$, while electronic $z$ oscillations in ${\mathrm{HD}}^{+}$ arise as “echo pulses” of its initial excitation and appear with the period of ${\tau }_{\mathrm{echo}}\approx 80$ fs corresponding to nuclear motion in ${\mathrm{HD}}^{+}$. Accordingly, corresponding power spectra of nuclear motion contain strong low-frequency harmonics at ${\omega }_{\mathrm{shp}}=2\pi /{\tau }_{\mathrm{shp}}$ in ${\mathrm{H}}_2{}^{+}$ and ${\omega }_{\mathrm{echo}}=2\pi /{\tau }_{\mathrm{echo}}$ in ${\mathrm{HD}}^{+}$. Power spectra related to both electronic and nuclear motion have been calculated in the acceleration form. Both higher- and lower-order harmonics are generated at the laser wavelength ${\lambda }_l=400$ nm, while only lower-order harmonics are well pronounced at ${\lambda }_l=50$ nm. It is also shown that a rationalized harmonic order, defined in terms of the frequency of the laser-induced electronic $z$ oscillations, agrees with the concept of inversion symmetry for electronic motion in diatomic molecules.

We study the possibility to enhance the phase-space density of noninteracting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semiclassical description, which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase-space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase-space density can only increase by a factor $M$ for $M$-level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.

One of the major challenges in realizing a strongly interacting lattice gas using Rydberg states is the occurrence of avalanche loss processes. As these are directly proportional to the total Rydberg fraction, the commonly suggested solution is using far off-resonantly excited Rydberg states. We instead propose the realization of a correlated bosonic lattice gas at near-resonant excitation, where the total Rydberg fraction in the bulk is low due to the strong, interaction-driven effective detuning. Using real-space dynamical mean-field theory we show that its reduced effect at the boundary of a system can easily be compensated by considering a tailored beam waist of the driving Rabi laser. In this geometry we discuss the spectral properties at the crossover between the supersolid and the superfluid state and present the momentum-resolved spectral properties of the supersolid bulk. The latter results are obtained within an extended quasiparticle method which also yields a correction of the mean-field phase transition.

We propose a scheme for producing the phase squeezing of the output light in a dissipative optomechanical coupling system. This is achieved by applying a degenerate parametric drive on the mechanical oscillator. We also show that this scheme is capable of generating the stationary entanglement between an optical cavity field and a macroscopic mechanical oscillator. The effects of the strength of the mechanical parametric drive, the power of the input laser, the temperature of the environment on the output phase squeezing, and the optomechanical entanglement are investigated. For a temperature of 20 mK, we find that up to 9 dB of the output phase squeezing and the large optomechanical entanglement can be achieved.

Frequency-angular characteristics of signal and idler photons generated under spontaneous parametric down-conversion are studied in a strongly frequency nondegenerate regime, without paraxial approximation, accounting for possible inherent absorption of idler waves in a nonlinear crystal, classical thermal field fluctuations, and the multimode character of parametric interaction induced by transverse spatial limitation of the pump beam. Spatial limitation is shown to lead to a huge increase in angular divergence of the idler photons generated at terahertz frequencies. General expressions are obtained for the frequency-angular sensitivity function of the nonlinear-optical terahertz wave detector and for power densities of the signal and idler photon fluxes. The absorption-induced difference in the parametric conversion coefficients for the noise and externally incident radiation of the idler frequency is shown to be described by approximately the same loss factor for all active spatial idler modes. Two different parametric contributions of the internal thermal noise to the number of output idler photons were revealed with different dependence on the idler-wave absorption. Expressions for the loss factors, which describe absorption-induced effects in signal and idler channels, are obtained and shown to be turning into one another by changing the sign of the absorption coefficient. Relative contribution of thermal and quantum field fluctuations into the intrinsic radiation of a nonlinear crystal at signal and idler frequencies is analyzed accounting for the crystal absorption properties.

We propose to create optical nonreciprocity in a three-mode optomechanical system comprising one mechanical and two optical modes, where the mechanical mode is coupled with only one of the optical modes. The optical nonreciprocal response of the system is based on the nonlinearity induced by the optomechanical interaction. However, nonlinearity is a necessary but not a sufficient condition for observing nonreciprocity. Another necessary condition for nonreciprocal response of the system to a classical driving field is demonstrated analytically. The effects of the parameters on the nonreciprocal response of the system are discussed numerically. The three-mode optomechanical system provides a platform to realize nonreciprocity for strong optical signal fields.

The wave function for a quantum mechanical particle in a circular box can be prepared in shape-preserving wave packets that rotate at constant angular speed around the center of the box. Some of these rotating wave packets correspond to classical trajectories undergoing uniform circular motion through the force-free interior of the box. This apparent violation of Ehrenfest's theorem is resolved by considering the force exerted on the particle's wave packet by the enclosing wall. Remarkably, the wave packet continues to rotate even after the wall potential is removed. We show that this force-free finite-energy rotating state actually corresponds to classical motion with constant velocity, again in agreement with Ehrenfest's theorem. Even so, the classical angular momentum carried by the rotating states poses a conceptual challenge because it differs from its quantum mechanical angular momentum, and indeed can have the opposite sign.

We experimentally observed the violation of Kujula–Dzhafarov noncontextuality inequalities by nonseparable spin-orbit laser modes. Qubits are encoded on polarization and transverse modes of an intense laser beam. A spin-orbit nonseparable mode was produced by means of a radial polarization converter ($S$ plate). Our results show that the quantum contextuality can be emulated by nonseparable spin-orbit modes in an intense laser beam. Additionally, an improvement in the nonseparable mode preparation allowed us to observe a greater violation of the Clauser–Horne–Shimony–Holt inequality for such system. The results are in very good agreement with the theoretical predictions of quantum mechanics.

Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure steady states. Nonequilibrium dynamics featuring a dark state recently gained a lot of attraction since their implementation in the context of driven-open quantum systems represents a viable possibility to engineer unique, pure states. Inspired by recent experimental progress with ultracold Rydberg ensembles, we analyze a driven many-body spin system, which displays a mean-field bistability between a dark steady state and a mixed steady state. As a function of the driving strength one observes a discontinuous phase transition that connects the zero entropy (dark) state with a finite entropy (mixed) state. The transition is characterized by a jump of the von Neumann entropy from zero to a finite value, which is of genuine nonequilibrium character. We analyze the relevant long wavelength fluctuations driving this transition by means of the renormalization group. This allows us to approach the nonequilibrium dark-state transition and identify similarities and clear differences to common, equilibrium phase transitions, to establish the phenomenology for a first-order dark-state phase transition, and to relate it to the dynamics in driven dissipative Rydberg ensembles.

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement—the translation from circuit diagrams to machine qubits—on quantum systems whose connectivity is described by hierarchies.

The size of quantum information—or entanglement—transfer rates between subsystems is a generic question in problems ranging from decoherence in quantum computation and sensing, to quantum underpinnings of thermodynamics, to the behavior of quantum black holes. We investigate such rates for given couplings between subsystems, for sufficiently random subsystem evolution, and find evidence of a conjectured relation of these rates to the size of the couplings. This provides a direct connection between entanglement transfer and the microphysical couplings in the Hamiltonian that are responsible for it.

Quantum communication with structured photons is topical, owing to the multidimensional state space of spatial modes. However, spatial modes are fragile and their quality degrades when perturbed in traditional communication media such as free-space and optical fibers. Here, we illustrate the effects of atmospheric turbulence on a six-state quantum-key-distribution protocol with orbital angular momentum (OAM) modes. We experimentally characterize the fidelity decay as a function of turbulence strength, showing a concomitant decrease with increasing perturbation, and consider the influence of both mode order and mode size, showing that OAM modes with higher helicity are more resilient to turbulence for this protocol. We outline two approaches to mitigate the photon information loss. In the first, we show that by postselecting on a high-dimensional subspace at the detection side, we can recover information contained in the scattered modes. In the second, we measure the channel operator by means of classically entangled light and mitigate errors on the quantum state through entanglement concentration by means of one-party Procrustean filtering. The tools we provide here will be beneficial for realizing more robust quantum communication with OAM modes of light.