Necessary and sufficient conditions for arbitrary multimode (pure or mixed) Gaussian states to be equivalent under incoherent Gaussian operations are derived. We show that two Gaussian states are incoherent equivalence if and only if they are related by incoherent unitaries. This builds the counterpart of the celebrated result that two pure entangled states are equivalent under local operations and classical communication (LOCC) if and only if they are related by local unitaries. Furthermore, incoherent equivalence of Gaussian states is equivalent to frozen coherence [Phys. Rev. Lett. 114, 210401 (2015)]. Basing this as foundation, we find all measures of coherence are frozen for an initial Gaussian state under strongly incoherent Gaussian operations if and only if the relative entropy measure of coherence is frozen for the state. This gives an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.

Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of that state. Most quantum algorithms rely on QST at some point and it is a well-explored topic in the literature, mostly for mixed states. In this paper we focus on the QST of a pure quantum state using parallel unentangled measurements. Pure states are a small but useful subset of all quantum states, and their tomography requires fewer measurements and is essentially a phase recovery problem. Parallel unentangled measurements are easy to implement in practice because they allow the user to measure each qubit individually, e.g., using one-qubit Pauli measurements. We propose two sets of quantum measurements that one can make on a pure state as well as the algorithms that use the measurement outcomes in order to identify the state. We also discuss how those estimates can be fine tuned by finding the state that maximizes the likelihood of the measurements with different variants of the likelihood. The performances of the proposed three types of QST methods are validated by means of detailed numerical tests, including for mixed states that are close to being pure.

Geometric quantum gates are performed by using the geometric phase, making them particularly robust to the pulse amplitude error. However, in many systems, such as the silicon-based spin qubits, the off-resonance error is the dominant noise, which can cause dephasing and is always difficult to deal with for a geometric gate. Thus how to combat with the off-resonance error is very significant for the application of the geometric gates. A recent work [S. Li and Z.-Y. Xue, Phys. Rev. Appl. 16, 044005 (2021).] revealed that by inserting two $\pi$ pulses into the evolution paths, the holonomic quantum gate is effective to suppress the pulse amplitude error, however, it is still useless for combating the off-resonance error. Inspired by this work, we combine using the techniques of dynamical correction and path design. Surprisingly, we find that, by picking up a specific evolution path inserted by only a $\pi$-pulse, the obtained optimized geometric gate is robust to the off-resonance error, assuming the noise is static. Further, by calculating the filter function considering the realistic $1/f$-type noise in silicon, the related results show that the performance of the optimized geometric gate can also surpass both the conventional geometric gate and the naive dynamical gate constructed without using the geometric phase. Our results indicate dynamical correction is a powerful tool to improve the geometric quantum computation to achieve a high-fidelity quantum gate in silicon.

We perform experimental studies of resonantly enhanced sum-frequency mixing (SFM), driven by tunable, spectrally narrowband mid-infrared and fixed-frequency nanosecond laser pulses, aiming at applications in molecular gas detection. The mid-infrared pulses are tuned in the vicinity of two-photon rovibrational transitions in the electronic ground state to provide strong resonance enhancements of the nonlinear susceptibility, while a probe laser at shorter wavelength uses an off-resonant single-photon coupling to excited electronic states. This SFM approach benefits from the advantageous combination of typically small detunings among the mid-infrared, vibrational transitions and the typically large transition dipole moment for couplings of electronic states. Moreover, compared to resonantly enhanced third harmonic generation (THG), a signal wave at much shorter wavelength permits simple and efficient detection. We demonstrate resonantly enhanced SFM via rovibrational states in gaseous hydrogen chloride molecules and compare its features to THG. The SFM spectra offer a large signal-to-noise ratio of 4 orders of magnitude and a detection limit down to a pressure of 0.1 mbar, corresponding to a particle density of $0.35\times {10}^{15}$ per ${\mathrm{cm}}^3$.

We develop a method using relativistic density-functional theory with a self-interaction correction, which is simple and fast yet has reasonable accuracy. A comparison with measured $K\alpha$ lines and their hypersatellites of several atoms, from low $Z$ to high $Z$, reveals that the relativistic local density approximation is suitable for $K\alpha$ lines. In contrast, the relativistic local spin density approximation with a self-interaction correction is better for $K^h\alpha$ hypersatellites. Compared with the nonrelativistic density-functional theory, we found that the relativistic effect is significant (about 100 eV) even for middle-$Z$ atoms, such as Cu. The screening effects, from inner shell to outer shell, and the conduction band, are also discussed. The present paper provides all the transition lines of muonic atoms, which can be used to narrow down the possible transitions by comparing them with the measurements.

Attosecond charge migration (CM) modes in halogenated hydrocarbon chains are investigated from first principles. The initial hole state on the Br site is created by the constrained density functional theory (CDFT) and the following CM dynamics is tracked by the time-dependent density functional theory (TDDFT). We find the attosecond mode is mainly recorded in the spin channel where the electron is initially ionized. By employing approximate functionals at different theory levels, we find the local density approximation gives satisfactory results to reproduce the attosecond mode and more advanced exchange-correlation functionals do not affect the mode significantly. By alleviating the self-interaction error with an average density correction or allowing nuclei to relax, it is shown that the nuclear motion is a key factor to alter the mode. In addition, by a detailed analysis of single-electron orbitals, we find the attosecond mode is attributed to the electronic collective motion in the outermost energy shell. Our results will be useful in understanding the mechanism of molecular modes and motivating the ultrafast CM detection methods for future experiments.

We present a theoretical framework to describe state-resolved ionization dynamics of neon atoms driven by ultraintense x-ray free-electron-laser pulses. In general, x-ray multiphoton ionization dynamics of atoms have been described by time-dependent populations of the electronic configurations visited during the ionization dynamics, neglecting individual state-to-state transition rates and energies. Combining a state-resolved electronic-structure calculation, based on first-order many-body perturbation theory, with a Monte Carlo rate-equation method enables us to study state-resolved dynamics based on time-dependent state populations. Our results demonstrate that configuration-based and state-resolved calculations provide similar charge-state distributions, but the differences are visible when resonant excitations are involved, which are also reflected in calculated time-integrated electron and photon spectra. In addition, time-resolved spectra of ions, electrons, and photons are analyzed for different pulse durations to explore how frustrated absorption manifests itself during the ionization dynamics of neon atoms.

Strong enough intersite interactions may result in lack of ergodicity in disorder-free many-body lattice systems. Ultracold dipolar gases in optical lattices provide an experimentally accessible platform for exploring this physics. Dipolar intersite interactions are usually assumed to decay with a fixed power law. We show that in a one-dimensional polar lattice gas the actual decay depends on the transversal confinement. This affects profoundly the particle dynamics, which mimics rather that of a system with an externally controllable effective power-law interaction. Our results show that the crucial role of the interaction decay on disorder-free localization may be flexibly studied in experiments with polar gases.

Polarization singularities in momentum space, including bound states in the continuum (BICs) and circularly polarized states (CPSs), render great potential in singular and chiral optics. As far-field topological signatures of Bloch modes in photonic crystal slab, the dynamic evolution of the polarization singularities is observed by tuning the geometric parameters of the slab itself. Here, we combine the photonic crystal slab with a reflected multilayer substrate in which interference between the reflected optical field and the upward radiation of the Bloch mode brings us an extra degree of freedom to manipulate the polarization singularities without breaking the structural symmetry. As the polarization singularities evolve with the spacing between the photonic crystal slab and the substrate, the CPSs and extrinsic BICs are both generated from charge reversal of the at-Γ intrinsic BIC and then collide with the off-Γ intrinsic BICs. Importantly, all BICs are topologically protected from splitting throughout the whole dynamic process owing to the preservation of structural symmetry. Our findings suggest an alternative route to pursue ultrahigh-$Q$ CPS resonances and merge diverse BICs, which is potentially applicable in chiral optics, topological photonics, and beam modulation.

Kramers-Kronig (KK) relation between the dispersion and absorption responses of a signal field can be mapped from the frequency domain into the space domain via the dipole-dipole interactions between a sample of homogeneous target atoms and a ring of equally spaced control atoms. This is achieved by establishing an effective two-level configuration for the target atoms in the far-detuned driving regime of both lower and upper transitions while maintaining the maximal Rydberg excitations for the control atoms via an antiblockade driving scheme of the lower and upper transitions. We find, in particular, that it is viable to realize a tunable spatial KK relation supporting asymmetric and even unidirectional reflection for appropriate signal frequencies in a desired range depending on the frequency of a coupling field. Taking a periodic lattice of target atoms instead, the multiple Bragg scattering can be incorporated into the spatial KK relation in order to enhance the nonzero reflectivity yet without breaking the asymmetric or unidirectional reflection.

Different hypotheses about a quantum system such as the logical state of a qubit or the value of physical interaction parameters can be investigated by the interaction with a probe field. Such fields may be prepared in particularly sensitive quantum states and we demonstrate here the use of quantum trajectories to model the stochastic measurement record and conditional evolution of the state of the quantum system subject to its interaction with a traveling pulse of radiation. Our analysis applies to different measurement strategies and to arbitrary input quantum states of the probe field pulse and it thus permits direct comparison of their metrological advantages. A theoretical lower limit to the mean discrimination error can be calculated in a deterministic manner and we verify that it lies below the average inference error in all our examples.

The interaction of a propagating pulse of quantum radiation with a localized quantum system can be described by a cascaded master equation with a distinct initially populated input and a finally populated output field mode [Kiilerich and Mølmer, Phys. Rev. Lett. 123, 123604 (2019)]. By transformation to an appropriate interaction picture, we break the cascaded nature of the master equation and recover an effective time-dependent interaction with a lossless single mode and a supplementary lossy mode. The former closely represents the traveling pulse, while the latter constitutes a non-Markovian component in the exchange of quanta between the scatterer and the quantized field. The transformed master equation offers important insights into the system dynamics, and it permits numerically efficient solutions.

The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this paper, the Pollak–Martinazzo lower-bound theory, in conjunction with correlated Gaussian basis sets, is elaborated and implemented to provide subparts-per-million convergence of the ground- and excited-state energies for the He, Li, and Be atoms. The quality of the lower bounds is comparable to that of the upper bounds obtained from the Ritz method. These results exemplify the power of lower bounds to provide tight estimates of atomic energies.

The developing of (non-Markovian) memory effects strongly depends on the underlying system-environment dynamics. Here we study this problem in multipartite arrangements where all subsystems are coupled to each other by dephasing mechanisms that are taken into account through an underlying Markovian Lindblad dynamics characterized by a nondiagonal rate matrix. Taking as system and environment arbitrary sets of complementary subsystems, it is shown that both operational and nonoperational approaches to quantum non-Markovianity can be characterized in an exact analytical way. Similarly to previous studies about dissipative entanglement generation in this kind of dynamics [Seif, Wang, and Clerk, Phys. Rev. Lett. 128, 070402 (2022)], we found that memory effects can only emerge when a time-reversal symmetry is broken. Nevertheless, it is also found that departures from Markovianity can equivalently be represented through a statistical mixture of Markovian dephasing dynamics, which does not involve any system-environment entanglement. Specific bipartite and multipartite dynamics exemplify the main general results.

We investigate the problem of finding the local analog of the ergotropy, which is the maximum work that can be extracted from a system if we can only apply local unitary transformation acting on a given subsystem. In particular, we provide a closed formula for the local ergotropy in the special case in which the local system has only two levels, and we give analytic lower bounds and semidefinite programming upper bounds for the general case. As nontrivial examples of application, we compute the local ergotropy for an atom in an electromagnetic cavity with Jaynes-Cummings coupling and the local ergotropy for a spin site in an XXZ Heisenberg chain, showing that the amount of work that can be extracted with a unitary operation on the coupled system can be greater than the work obtainable by quenching off the coupling with the environment before the unitary transformation.

Due to the linearity of quantum mechanics, it remains a challenge to design quantum generative machine learning models that embed nonlinear activations into the evolution of the state vector. However, some of the most successful classical generative models, such as those based on neural networks, involve highly nonlinear dynamics for quality training. In this paper we explore the effect of these dynamics in quantum generative modeling by introducing a model that adds nonlinear activations via a neural network structure onto the standard Born machine framework—the quantum neuron Born machine (QNBM). To achieve this, we utilize a previously introduced quantum neuron subroutine, which is a repeat-until-success circuit with midcircuit measurements and classical control. After introducing the QNBM, we investigate how its performance depends on network size, by training a three-layer QNBM with four output neurons and various input and hidden layer sizes. We then compare our nonlinear QNBM to the linear quantum circuit Born machine (QCBM). We allocate similar time and memory resources to each model such that the only major difference is the qubit overhead required by the QNBM. With gradient-based training, we show that while both models can easily learn a trivial uniform probability distribution, on a more challenging class of distributions, the QNBM achieves an almost three-times-smaller error rate than a QCBM with a similar number of tunable parameters. We therefore provide evidence that suggests that nonlinearity is a useful resource in quantum generative models, and we put forth the QNBM as a model with good generative performance and potential for quantum advantage.

Frenkel excitons are of interest for ultrafast switching applications due to the femtosecond timescale at which coherent exciton transfer between chromophores takes place. The Frenkel Hamiltonian, which governs the dynamics of Frenkel excitons, belongs to a class of Hamiltonians that enable universal quantum computation. It is thus of interest to determine how a complete set of exciton-based gates for quantum computing could be constructed as aggregates of chromophores. We demonstrate that a controlled phase shifter can be constructed as a pair of exciton transmission lines that employ two types of chromophores and that are cross coupled by a two-exciton interaction. This element facilitates the construction of controlled basis-change gates, thereby enabling the implementation of a complete set of exciton-based gates for universal quantum computation.

We propose a concise and deterministic protocol to generate NOON states in a hybrid system consisting of a superconducting qubit, a circuit resonator mode, and two magnonic modes, based on Floquet engineering. In particular, we construct a time-reversal-symmetry broken Hamiltonian for chiral state propagation of the three continuous-variable modes depending on qubit state, by the time modulation over qubit-resonator interaction and magnon frequency. Then, an arbitrary magnonic NOON state can be generated by a typical preparing-and-measurement procedure. We analyze the robustness of our protocol against the systematic errors in the qubit-magnon coupling strength, the Floquet-driving intensity, the frequency mismatch of the magnons, and the counterrotating interactions. We can obtain a high-fidelity NOON state in the presence of quantum dissipation on all components.