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Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research. [ABSTRACT FROM AUTHOR]

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as hydrogen, lithium hydride, beryllium hydride, water, and hydrogen fluoride. The errors in the ground state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and finally a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster ansatz for simulations, and the number of qubits varied from two starting from the hydrogen molecule to ten qubits in hydrogen fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient, limited-memory Broyden—Fletcher—Goldfarb—Shanno bound, and sequential least squares programming optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and Powell's conjugate direction algorithm for unconstrained optimization (POWELL) perform most efficiently among the gradient-free methods, in noisy quantum circuit conditions, simultaneous perturbation stochastic approximation, POWELL, and COBYLA are among the best-performing optimizers. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? Atomic spectroscopy for Ar7+, Kr7+, Xe7+, and Rn7+ ions with high accuracy. Plasma screened ionization potential, atomic transition amplitudes and rates. Ionisation potential depression parameters. What is the implication of the main finding? Properties of the astrophysical medium. Properties of laboratory plasma. The growing interest in atomic structures of moderately stripped alkali-like ions in the diagnostic study and modeling of astrophysical and laboratory plasma makes an accurate many-body study of atomic properties inevitable. This work presents transition line parameters in the absence or presence of plasma atmosphere for astrophysically important candidates Ar7+, Kr7+, Xe7+, and Rn7+. We employ relativistic coupled-cluster (RCC) theory, a well-known correlation exhaustive method. In the case of a plasma environment, we use the Debye Model. Our calculations agree with experiments available in the literature for ionization potentials, transition strengths of allowed and forbidden selections, and lifetimes of several low-lying states. The unit ratios of length and velocity forms of transition matrix elements are the critical estimation of the accuracy of the transition data presented here, especially for a few presented for the first time in the literature. We do compare our findings with the available recent theoretical results. Our reported data can be helpful to the astronomer in estimating the density of the plasma environment around the astronomical objects or in the discovery of observational spectra corrected by that environment. The present results should be advantageous in the modeling and diagnostics laboratory plasma, whereas the calculated ionization potential depression parameters reveal important characteristics of atomic structure. [ABSTRACT FROM AUTHOR]

In this work, we present a scheme of a two-photon interaction to calculate magic wavelengths for the 6 2 S 1 2 − 5 2 D 3 2 , 5 2 clock transitions of Ba + ion employing the relativistic coupled-cluster method. These magic wavelengths can be essential inputs to achieve better accuracy in the future ionic clock experiments. In this paper, we further show an application of a two-photon interaction to the spin-mixing processes, | 0 , 0 〉 ↔ | + 1 , − 1 〉 and | 0 , 0 〉 ↔ | − 1 , + 1 〉 , of an ultra-cold spin-1 mixture of 137 Ba + ions and 87 Rb atoms. We determine the protocols for selecting these spin-mixing oscillations by changing the strength and frequencies of the externally applied magnetic field and laser beams, respectively. [ABSTRACT FROM AUTHOR]

We elaborate the two-component Douglas-Kroll reduction of the Dirac-Kohn-Sham problem of relativistic density-functional theory as introduced by Matveev and Rösch [J. Chem. Phys. 118, 3997 (2003)]. That method retains corrections to the Coulomb self-interaction (or Hartree) term of the energy functional that are due to the picture change. Using analytic expressions for the matrix elements, one is able to abandon the resolution of the identity approach for a crucial step of the relativistic transformation. Thus, a major source of uncertainties of the method is eliminated because basis sets no longer have to be extended by functions of higher angular momentum, previously required to ensure kinetic balance. This approach also relies on the electron charge-density fitting scheme via an auxiliary basis set. An efficient approximate implementation results if one restricts the relativistic transformation to the spherically symmetric atom-centered auxiliary functions. It provides accurate results while simplifying greatly the expressions for the matrix elements of the relativistically transformed operators and significantly reducing the computational effort. We demonstrate the performance of the method for the fine structure of one-electron levels of the Hg atom, the g-tensor shifts of NO2, and the properties of the diatomic molecules Bi2, Pb2, PbO, and TlH. [ABSTRACT FROM AUTHOR]

We have applied the highly correlated ab initio effective valence shell Hamiltonian (H[sup v]) method to determine the energy difference between the cyclic and linear isomers of propynlidyne (C[sub 3]H). Calculations are also described for the vertical excitation energies, ionization potentials, electron affinities, dipole moments, oscillator strengths, and some harmonic vibrational frequencies, which are all determined using the third order H[sup v] method. Computations at both the experimental and theoretically optimized geometries are used to illustrate the geometrical dependence of the computed properties. The H[sup v] optimized geometry is obtained using a two-configurational reference function describing the two dominant resonance structures. Our third-order vertical excitation energy to the lowest excited state in the cyclic isomer, dipole moments, and ground state isomer conformational energy difference are all in good agreement with experiment and with other highly correlated many-body calculations. The computations for higher excited states and for ionization potentials, electron affinities, and oscillator strengths represent the first reports of these quantities. An explanation is provided for persistent theoretical difficulties in computing b[sub 1] bending vibrational frequencies of the cyclic isomer. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Here, we report on accurate ab initio calculations to study astrophysically important elec- tromagnetic transition parameters among different low-lying states of Sn IV. Our ab initio calculations are based on the sophisticated relativistic coupled cluster theory, which almost exhausts many important electron correlations. To establish the accuracy of the calculations, we compare our results with the available experiments and estimate the transition amplitudes in length and velocity gauged forms. Most of these allowed and forbidden transition wave- lengths lie in the infrared region, and they can be observed in the different cool stellar and interstellar media. For the improvement of uncertainty, we use experimental energies to the estimations of the above transition parameters. The presented data will be helpful to find the abundances of the ion in different astrophysical and laboratory plasma. [ABSTRACT FROM AUTHOR]

In this paper, we report on weighted oscillator strengths of El transitions and transition probabilities of E2 transitions among different low-lying states of triply ionized germanium using highly correlated relativistic coupled cluster (RCC) method. Due to the abundance of Ge IV in the solar system, planetary nebulae, white dwarf stars, etc., the study of such transitions is important from an astrophysical point of view. The weighted oscillator strengths of El transitions are presented in length and velocity gauge forms to check the accuracy of the calculations. We find excellent agreement between calculated and experimental excitation energies. Oscillator strengths of few transitions, wherever studied in the literature via other theoretical and experimental approaches, are compared with our RCC calculations. [ABSTRACT FROM AUTHOR]

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of 205Pb+. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier. [ABSTRACT FROM AUTHOR]

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of 205Pb+. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier. [ABSTRACT FROM AUTHOR]

We present numerical simulations to unravel the dynamics associated with the creation of a vortex in a Bose–Einstein condensate (BEC), from another nonrotating BEC using two-photon Raman transition with Gaussian (G) and Laguerre–Gaussian (LG) laser pulses. In particular, we consider BEC of Rb atoms at their hyperfine ground states confined in a quasi two dimensional harmonic trap. Optical dipole potentials created by G and LG laser pulses modify the harmonic trap in such a way that density patterns of the condensates during the Raman transition process depend on the sign of the generated vortex. We investigate the role played by the Raman coupling parameter manifested through dimensionless peak Rabi frequency and intercomponent interaction on the dynamics during the population transfer process and on the final population of the rotating condensate. During the Raman transition process, the two BECs tend to have larger overlap with each other for stronger intercomponent interaction strength. [ABSTRACT FROM AUTHOR]

We theoretically investigate the out-of-equilibrium dynamics in binary Bose-Einstein condensate confined within two-dimensional box potentials. One species of the condensate interacts with a pair of oppositely wound, but otherwise identical Laguerre-Gaussian laser pulses, while the other species is influenced only via the interspecies interaction. Depending on the number of helical windings (or the magnitude of topological charge), the species directly participating in the interaction with lasers is dynamically segmented into distinct parts that collide together as the pulses gradually diminish. This collision event generates nonlinear structures in the related species, coupled with the complementary structures produced in the other species, due to the interspecies interaction. The long-time dynamics of the optically perturbed species is found to develop the Kolmogorov-Saffman scaling law in the incompressible kinetic energy spectrum, a characteristic feature of quantum turbulence. This study warrants the usage of Laguerre-Gaussian beams for future experiments on quantum turbulence in Bose-Einstein condensates. • We show the out-of-equilibrium dynamics of a binary Bose-Einstein condensate interacting with two Laguerre-Gaussian (LG) beams. • Condensate is segregated into multiple segments depending on the charge of LG beams. • Collision of the segregated segments results in the generation of vortex and antivortex. • We observe −5/3 and −4 power-law in the incompressible kinetic energy spectra. [ABSTRACT FROM AUTHOR]