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The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the Partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from $O(\frac{N^4}{\epsilon^2})$ to $O(\frac{1}{\epsilon^2})$ for a system of $N$ qubits and accuracy $\epsilon$, while the overall cost of VQE can be reduced from $O(\frac{N^7}{\epsilon^2})$ to $O(\frac{N^3}{\epsilon^2})$. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20-40% to 5-10% without any additional error correction or mitigation technique. Additionally, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem.

Motivated by the recent realization of space-borne Bose-Einstein Condensate (BEC) under micro-gravity conditions, we extend the understanding of ultracold dipolar bosonic gases by exploring their behavior in a novel trapping configuration known as the ``bubble trap" topology. Utilizing the three-dimensional numerical simulations within the extended Gross-Pitaevskii framework, we unveil diverse ground state phases in such a static curved topology. Subsequently, we investigate the influence of rotation on a dipolar BEC confined to the surface of a spherical bubble. Our findings reveal that the rotation of a bubble trap with certain rotation frequencies can modify the effective local dipole-dipole interaction strength, leading to the induction of supersolidity and the formation of quantum droplets. In addition, we demonstrate that a bubble trap can sustain high circulation and the flow also persists for a longer time. Significantly, adjusting the rf detuning parameter allows the condensate to achieve hypersonic velocity. Finally, we explore the impact of drastic change in the topological nature of the trap on the rotating dipolar BEC, transitioning from a filled shell trap to a bubble trap and vice versa., Comment: 9 pages, 10 figures

We present a theoretical study of a spin-orbit coupled spin-1 Bose-Einstein condensate under the influence of sinusoidally varying magnetic fields. In the ground state of the ferromagnetic spin-1 condensate, we investigate topological excitations in the system arising due to the combined effect of Rashba spin-orbit coupling and an in-plane sinusoidally varying magnetic field. In this work, we offer a comparative study for various choices of magnetic fields in the $x\rm{-}y$ plane. For a fixed field strength, the spin-orbit coupled system sustains a rich variety of exotic vortex structures ranging from vortex-antivortex lattices to vortex clusters as we increase the coupling strength., Comment: 23 pages, 14 figures

H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated {\pi}-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 direct mapping and allows quantum simulation of the HMO model for systems with up to 2^N conjugated centers in N qubits. The transformation of the H\"uckel Hamiltonian to qubit space is achieved by two different strategies: a machine-learning-assisted transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated {\pi}-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. The higher excited states of large systems, however, 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 C_{60} fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are system-agnostic and hence are easily adaptable to similar problems of different complexity in other fields of research.

Recent experimental realization of the heteronuclear dipolar mixture of Dy and Er atoms opens fascinating prospects for creating intriguing novel phases in dipolar quantum gases. The experimentally measured value of intra-species $s$-wave scattering length of $^{166}$Er condensate in a $^{164}$Dy-$^{166}$Er mixture is larger than its intra-species dipolar length, implies that the $^{166}$Er condensate itself will not be in a regime of dominated dipole-dipole interaction (DDI). However, we find that the presence of $^{164}$Dy atoms with high magnetic moment induces droplet nucleation and supersolidity in $^{166}$Er condensate via the long-range and anisotropic inter-species DDI. Remarkably, we find that the imbalance in the magnetic dipole moment combined with its strong anisotropic coupling led to the emergence of unique ground state phases. The emerging phases include doubly superfluid states, a mixture of insulating droplets and supersolid states, binary supersolids with uniform and alternating domains and a combination of supersolid-superfluid mixed states. We delineate the properties of all these ground state phases and construct a phase diagram. We also explore the dynamical evolution across these phase boundaries via a linear quench of inter-species scattering length. Although we have demonstrated the result for the $^{164}$Dy-$^{166}$Er mixture, our results are generally valid for other dipolar bosonic mixtures of different Dy-Er isotope combinations and may become an important benchmark for future experimental scenarios., Comment: 11 pages, 8 figures

Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the fermionic space to the qubit space provides us with a series of Pauli strings and the energy calculation involves the evaluation of the expectation values of all these individual strings. This introduces a major bottleneck for applications of VQEs in quantum chemistry. Unlike the fermionic Hamiltonian, the terms in a qubit Hamiltonian are additive and the present paper exploits this property to describe a new approach for extracting information from the partial qubit Hamiltonian of simple molecules to design more efficient variational quantum eigensolvers. In the partial (qubit) Hamiltonian approach (PHA), the qubit Hamiltonian is studied term-by-term to understand their relative contributions to the overall energy and a partial Hamiltonian is constructed with fewer Pauli strings that can resolve the entire Hamiltonian. With PHA, we can simulate molecules at a much lower computational cost with a truncated Hamiltonian. Additionally, the outcomes of the measurements with PHA quench the error due to noise introduced by the quantum circuits. We have also demonstrated the application of PHA as an initialization technique, where the simple partial Hamiltonian can be used to find a suitable initial state for a more complex system. The results of this study have the potential to demonstrate the potential advancement in the field of quantum computing and its implementation in quantum chemistry.

The growing interest in atomic structures of moderately-stripped alkali-like ions in 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, Ar$^{7+}$, Kr$^{7+}$, Xe$^{7+}$, and Rn$^{7+}$. We employ relativistic coupled-cluster (RCC) theory, a well-known correlation exhaustive method. In the case of a plasma environment, we use 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 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 ionisation potential depression parameters reveal important characteristics of atomic structure.

We examine the quench dynamics of an extended Su-Schrieffer-Heeger(SSH) model involving long-range hopping that can hold multiple topological phases. Using winding number diagrams to characterize the system's topological phases geometrically, it is shown that there can be multiple winding number transition paths for a quench between two topological phases. The dependence of the quench dynamics is studied in terms of the survival probability of the fermionic edge modes and post-quench transport. For two quench paths between two topological regimes with the same initial and final topological phase, the survival probability of edge states is shown to be strongly dependent on the winding number transition path. This dependence is explained using energy band diagrams corresponding to the paths. Following this, the effect of the winding number transition path on transport is investigated. We find that the velocities of maximum transport channels varied along the winding number transition path. This variation depends on the path we choose, i.e., it increases or decreases depending upon the path. An analysis of the coefficient maps, energy spectrum, and spatial structure of the edge states of the final quench Hamiltonian provides an understanding of the path-dependent velocity variation phenomenon., Comment: 9 pages with 9 figures

We investigate the Rayleigh-Taylor instability at the two interfaces in a phase-separated three-component Bose-Einstein condensate in the mean-field framework. The subsequent dynamics in the immiscible three-component condensate has been studied in detail for different cases of instigating the instability in the system. The rotational symmetry of the system breaks when the atom-atom interaction is tuned in such a way that the interface between the components becomes unstable giving rise to non-linear patterns of mushroom shapes which grow exponentially with time. We also identify these non-linear patterns as the solutions of the angular Mathieu equation, representing the normal modes., Comment: 12 pages, 11 figures

The recent realization of binary dipolar BEC [Phys. Rev. Lett. 121, 213601 (2018)] opens new exciting aspects for studying quantum droplets and supersolids in a binary mixture. Motivated by this experiment, we study groundstate phases and dynamics of a Dy-Dy mixture. Dipolar bosonic mixture exhibits qualitatively novel and rich physics. Relying on the three-dimensional numerical simulations in the extended Gross-Pitaevskii framework, we unravel the groundstate phase diagrams and characterize different groundstate phases. The emergent phases include both miscible and immiscible single droplet (SD), multiple droplets (MD), supersolid (SS), and superfluid (SF) states. More intriguing mixed groundstates may occur for an imbalanced binary mixture, including a combination of SS-SF, SS-MD, and SS-SS phases. We observed the dynamical transition from a miscible MD state to an immiscible MD state with multiple domains formed along the axial direction by tuning the inter-species scattering length. Also by linear quenches of intra-species scattering lengths across the aforementioned phases, we monitor the dynamical formation of supersolid clusters and droplet lattices. Although we have demonstrated the results for a Dy-Dy mixture and for a specific parameter range of intra-species and inter-species scattering lengths, our results are generally valid for other dipolar mixtures and may become an important benchmark for future experimental scenarios., Comment: 15 pages, 14 figures

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms. In literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular 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 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 (UCC) 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 (CG), limited-memory Broyden-Fletcher-Goldfarb-Shanno bound (L_BFGS)B), and sequential least squares programming (SLSQP) optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and POWELL perform most efficiently among the gradient-free methods. However, in noisy quantum circuit conditions, Simultaneous Perturbation Stochastic Approximation (SPSA), POWELL, and COBYLA are among the best-performing optimizers.

We conduct a theoretical study of the creation and dynamics of vortices in a two-dimensional binary Bose-Einstein condensate with a mass imbalance between the species. To initiate the dynamics, we use one or two rotating paddle potentials in one species, while the other species is influenced only via the interspecies interaction. In both species, the number and the dominant sign of the vortices are determined by the rotation frequency of the paddle potential. Clusters of positive and negative vortices form at a low rotation frequency comparable to that of the trap when using the single paddle potential. In contrast, vortices of the same sign tend to dominate as the rotation frequency of the paddle increases, and the angular momentum reaches a maximum value at a paddle frequency, where the paddle velocity becomes equal to the sound velocity of the condensate. When the rotation frequency is sufficiently high, the rapid annihilation of vortex-antivortex pairs significantly reduces the number of vortices and antivortices in the system. For two paddle potentials rotating in the same direction, the vortex dynamics phenomenon is similar to that of a single paddle. However, when the paddle potentials are rotated in the opposite direction, both positive and negative signed vortices occur at all rotational frequencies. At the low rotation frequencies, the cluster of like-signed vortices produces the $k^{-5/3}$ and $k^{-3}$ power laws in the incompressible kinetic energy spectrum at low and high wavenumbers, respectively, a hallmark of the quantum turbulent flows., Comment: 14 pages, 13 figures