Optical continuous-variable cluster states (CVCSs) in combination with Gottesman-Kitaev-Preskill (GKP) qubits enable fault-tolerant quantum computation so long as these resources are of high enough quality. Previous studies concluded that a particular CVCS, the quad rail lattice (QRL), exhibits a lower GKP gate-error rate than others do. We show in this work that many other experimentally accessible CVCSs also achieve this level of performance by identifying operational equivalences to the QRL. Under this equivalence, the GKP Clifford gate set for each CVCS maps straightforwardly from that of the QRL, inheriting its noise properties. Furthermore, each cluster state has at its heart a balanced four-splitter—the four-mode extension to a balanced beam splitter. We classify all four-splitters, show they form a single equivalence class under SWAP and parity operators, and give a construction of any four-splitter with linear optics, thus extending the toolbox for theoretical and experimental cluster-state design and analysis.

In this paper we investigate higher-order corrections to the energies of bound states in hydrogen subjected to the external blackbody radiation field. In particular, within the framework of thermal quantum electrodynamics and the $S$-matrix approach we analyze the combined type of two-loop self-energy corrections, including one zero-vacuum and one loop at finite temperature. By utilizing the method of dimensional regularization, we derive closed analytical expressions for the energy shifts of atomic levels. Our numerical calculations demonstrate that even at room temperature these corrections can be significant for excited states, reaching the magnitude of the thermally induced Stark contribution.

The nondipole effect in strong-field sequential double ionization of an Ar atom is investigated with the Heisenberg-core potential classical ensemble model, in which the magnetic component of the laser field is included. We show that the magnetic field induces a nonzero displacement of the electron along the laser propagation direction when the electron is driven back by the linearly polarized laser field. This displacement significantly affects the electron-ion rescattering, manifesting as a pronounced linear momentum transfer against the radiation pressure for the low-energy photoelectron. Such phenomenon depends on the laser intensity and traveling time of the photoelectrons. Particularly, a larger negative linear momentum transfer for low-energy electrons is obtained in a more intense laser field with longer pulse duration, in which case it would be beneficial to observe the nondipole effect in experiment.

Using only linearly polarized light, we study the possibility of generating spin-polarized photoelectrons from xenon atoms. No net spin polarization is possible, since the xenon ground state is spinless, but when the photoelectrons are measured in coincidence with the residual ion, spin polarization emerges. Furthermore, we show that ultrafast dynamics of the recolliding photoelectrons contribute to an apparent flipping of the spin of the photoelectron, a process that has been completely neglected so far in all analyses of recollision-based processes. We link this phenomenon to the “spin-orbit clock” of the remaining ion. These effects arise already in dipole approximation.

We focus on the influence of multiphoton effect on the fluorescence spectrum and photon statistics of the bichromatically driven two-level atomic system. The influence of the multiphoton effect of the weaker driving field on the system and spontaneous emission are revealed by Schrieffer-Wolff perturbation theory, respectively. The physical origin of the multiphoton process affecting the fluorescence spectral asymmetry characteristics is fully investigated by studying the population distribution and the dressed atomic transition weight. Further, the suppression condition of the central peak of the central band is investigated. The photon statistical properties of the system are revealed by studying the frequency-resolved correlations between different sidepeaks and the central peak and sidepeak, respectively. In particular, the physical picture of the asymmetry of the two-photon correlation signal that is affected by the multiphoton process of the weaker driving field affecting the timing detection is fully revealed by the two methods of correlation moment and conditional quantum state, respectively. These results of ours provide a theoretical approach for studying multiphoton processes in multichromatically driven quantum systems, as well as for developing quantum simulation techniques such as spin locking.

We study attosecond pulses synthesized from high-order harmonic generation (HHG) under different circular-elliptical bichromatic laser fields by numerically solving the time-dependent Schrödinger equation. For $\omega -3\omega$ bichromatic laser fields, the ellipticity of parts of the elliptically polarized attosecond pulse train (APT) in each optical cycle will first approach unity and then decrease as the ellipticity of the $3\omega$ field decreases. However, for the $\omega -2\omega$ bichromatic laser field, the ellipticity of the APT remains small when the ellipticity of the $2\omega$ field decreases. Our result is well reproduced in terms of quantum-orbit theory. By analyzing the quantum orbits, the underlying physics for the generation of the nearly circularly polarized attosecond pulse with the $\omega -3\omega$ circular-elliptical bichromatic laser field is revealed. Our work provides a simple method to obtain highly elliptically polarized attosecond pulses from HHG.

We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing noninvertible Pauli maps and quantify the fraction of the same. The memory kernel perspective appears to be less transparent on the issue of invertibility than the approaches based on maps or master equations. Here we consider a related and potentially helpful issue: the identification of criteria of parameterized families of maps leading to the existence of a well-defined semigroup limit.

Quantum generative modeling (QGM) relies on preparing quantum states and generating samples from these states as hidden—or known—probability distributions. As distributions from some classes of quantum states (circuits) are inherently hard to sample classically, QGM represents an excellent test bed for quantum supremacy experiments. Furthermore, generative tasks are increasingly relevant for industrial machine learning applications, and thus QGM is a strong candidate for demonstrating a practical quantum advantage. However, this requires that quantum circuits are trained to represent industrially relevant distributions, and the corresponding training stage has an extensive training cost for current quantum hardware in practice. In this work, we propose protocols for classical training of QGMs based on circuits of the specific type that admit an efficient gradient computation, while remaining hard to sample. In particular, we consider instantaneous quantum polynomial (IQP) circuits and their extensions. Showing their classical simulability in terms of the time complexity, sparsity, and anticoncentration properties, we develop a classically tractable way of simulating their output probability distributions, allowing classical training to a target probability distribution. The corresponding quantum sampling from IQPs can be performed efficiently, unlike when using classical sampling. We numerically demonstrate the end-to-end training of IQP circuits using probability distributions for up to 30 qubits on a regular desktop computer. When applied to industrially relevant distributions this combination of classical training with quantum sampling represents an avenue for reaching advantage in the noisy intermediate-scale quantum (NISQ) era.

Natively, atomic and molecular processes develop on a subfemtosecond timescale. In order to, for instance, track and capture the electron motion in that scale we need suitable “probes.” Attosecond pulses configure the most appropriate tools for such a purpose. These ultrashort bursts of light are generated when a strong laser field interacts with matter and high-order harmonics of the driving source are produced. In this work, we propose a way to twist attosecond pulse trains. In our scheme, each of the attosecond pulses in the train has a well-defined linear polarization, but with a different polarization angle between them. To achieve this goal, we consider an infrared pulse with a particular polarization state, called amplitude polarization. This kind of pulse was experimentally synthesized in previous works. Our twisted attosecond pulse train is then obtained by nonlinear driving an atomic system with that laser source, through the phenomenon of high-order harmonics generation. We achieve a considerable level of control over the modulation of the linear polarization state between two consecutive ultrashort bursts of extreme ultraviolet (XUV) radiation. Through quantum-mechanical simulations, supplemented with signal processing tools, we are able to dissect the underlying physics of the generation process. We are confident these polarized-sculpted XUV sources will play an instrumental role in future pump-probe-based experiments.

The two-color-laser-field scheme for broadband terahertz (THz) radiation from air has been intensively and broadly investigated due to the simplicity of technology and relatively high yield efficiency. Experiments showed that the detected THz angular distribution is usually conical, with a dip in the laser propagation axis which is unfavorable for its application, and the formation of an oscillating tail in the THz waveform has not yet been well understood. Here, we develop an electric-field-element interference model in which each local current source has a phase velocity determined by the laser pulse and a Gaussian temporal profile, rather than an ideal point source, and the current oscillation caused by the plasma dynamics is considered. By introducing the temporal interference, the effects of the phase velocity and the Gaussian profile of the current can correct the THz angular distribution. Therefore, by adjusting the laser pulse duration and the group velocity, the THz angular distribution can be controlled, and the dip can even be eliminated. In addition, the plasma dynamics can result in the formation of an oscillating tail in the THz waveform and sunken spikes in the corresponding spectrum. This is similar to the experimental results, which are usually explained by water-vapor absorption. In turn, the spikes in the spectrum could provide a way to measure the plasma filament density.

The distribution of primes over the set of natural numbers is a fascinating subject closely related to topics that range from the fundamental problem of factorization to applications in cryptography. Despite numerous efforts, efficient methods to locate huge primes are still under investigation. Here, we present an alternative approach to identifying prime numbers that is based on the evolution of the linear entanglement entropy. Specifically, we show that a singular behavior in the amplitudes of the Fourier series of this entropy is associated with prime numbers. We also discuss how this intriguing connection between primes and entanglement could be experimentally implemented using existing optical devices, and examine a possible relationship between our results and the zeros of the Riemann zeta function.

Multipartite entangled states involving nonlocality are one of the most fascinating characteristics of quantum mechanics. In this work we propose a thermal-dephasing-tolerant generation of mesoscopic entangled states with Rydberg dressed atoms. We encode a logical state on dressed states rather than Rydberg states. Such treatment can increase the lifetime of multipartite entanglement coherence to around three times compared to the Rydberg-state-coding one at the same system size and therefore induce solid fidelities of mesoscopic superposition states generation. The current work theoretically verifies the advantages of using Rydberg dressed states in many-body quantum entanglement, which is helpful for large-scale quantum computation and many-body Rydberg quantum simulation.

We study the quantum transduction of a superconducting qubit to an optical photon in electro-optomechanical and electro-optomagnonical systems. The electro-optomechanical system comprises a flux-tunable transmon qubit coupled to a suspended mechanical beam, which then couples to an optical cavity. Similarly, in an electro-optomagnonical system, a flux-tunable transmon qubit is coupled to an optical whispering gallery mode via a magnon excitation in a yttrium iron garnet ferromagnetic sphere. In both systems, the transduction process is done in sequence. In the first sequence, the qubit states are encoded in coherent excitations of phonon (magnon) modes through the phonon-qubit (magnon-qubit) interaction, which is nondemolition in the qubit part. We then measure the phonon (magnon) excitations, which reveal the qubit states, by counting the average number of photons in the optical cavities. The measurement of the phonon (magnon) excitations can be performed at regular intervals of time.

We study how to achieve, manipulate, and switch classical or quantum nonreciprocal effects of light with a spinning Kerr resonator. In particular, we show that even when there is no classical nonreciprocity (i.e., with the same mean number of photons for both clockwise and counterclockwise propagating modes), it is still possible to realize nonreciprocity of quantum correlations of photons in such a device. Also, by tuning the angular velocity and the optical backscattering strength, purely higher-order quantum nonreciprocity can appear, featuring qualitatively different third-order optical correlations, even in the absence of any nonreciprocity for both the mean photon number and its second-order correlations. The possibility to switch a single device between a classical isolator and a purely quantum directional system can provide more functions for nonreciprocal materials and new opportunities to realize novel quantum effects and applications, such as nonreciprocal multiphoton blockade, one-way photon bundles, and back-action-immune quantum communications.

We study the heat transfer between $N$ coupled quantum resonators with applied synthetic electric and magnetic fields realized by changing the resonator parameters by external drivings. To this end we develop two general methods, based on the quantum optical master equation and on the Langevin equation for $N$ coupled oscillators where all quantum oscillators can have their own heat baths. The synthetic electric and magnetic fields are generated by a dynamical modulation of the oscillator resonance with a given phase. Using Floquet theory, we solve the dynamical equations with both methods, which allow us to determine the heat flux spectra and the transferred power. We apply these methods to study the specific case of a linear tight-binding chain of four quantum coupled resonators. We find that, in that case, in addition to a nonreciprocal heat flux spectrum already predicted in previous investigations, the synthetic fields induce here nonreciprocity in the total heat flux, hence realizing a net heat flux rectification.

Quantum decoherence tends to bring about the emergence of the classical from the quantum world through the interaction of a quantum system with the environment, which is the main impediment to the realization of quantum information processing. Counterintuitively, we propose that the decoherence enables the creation of a bright source of strongly sub-Poissonian nonlocality. The absence of the decoherence makes such a source impossible. Decoherence is devised to be adjustable and manipulable on the basis of the dressed-atom approach and combination mode technique. The strong sub-Poissonianity and robust Bell violation are originated from the large squeezing parameter of the reservoir pertaining to the controllable decoherence within the framework of the reservoir theory.