Ground State Energy Research Articles

Griffiths singularity in quasi-one-dimensional restricted ±J Ising spin glass.

We obtain the exact ground-state energy of the quasi-one-dimensional restricted ±J Ising spin glass in a uniform magnetic field using the transfer matrix method. Magnetic field dependence allows us to derive the magnetization as a function of concentration and magnetic field. It turns out that, in the limit of zero field, the magnetization tends to a nonzero value with a singular dependence on the magnetic field. We derive the explicit form of the singularity in thermodynamic quantities such as energy E≃E_{0}+m_{0}h+E_{1}e^{-h_{0}/h}, which is an essential singularity known as Griffiths singularity. We confirm our analytical results using the numerical approach based on iterative equations for energy.

Topological defects on relativistic quantum oscillator in wormhole space–time background

In this research work, the relativistic quantum dynamics of oscillator field in wormhole background with a topological defect produced by a cosmic string is investigated. We consider an example of Morris–Thorne-type wormhole including a osmic string and derived the wave equation of the relativistic quantum oscillator. Through the Heun equation, we solve analytically the radial equation and obtain the ground state energy level [Formula: see text] and the radial wave function [Formula: see text] as particular cases. In fact, it is shown that the eigenvalue solution of the oscillator field is influenced by the topological defect of cosmic string and shifted the result. Furthermore, the wormhole throat radius also modifies the energy levels and the wave function of the relativistic quantum oscillator.

Computational Study of Ground-State Destabilization Effects and Dipole-Dipole Interaction Energies in Amphidynamic Crystals.

Ground-state destabilization is a promising strategy to modulate rotational barriers in amphidynamic crystals. Density functional theory studies of polar phenylenes installed as rotators in pillared paddle-wheel metal organic frameworks were performed to investigate the effects of ground-state destabilization on their rotational dynamics. We found that as the steric size of phenylene substituents increases, the ground-state destabilization effect is also increased. Specifically, a significant destabilization of the ground-state energy occurred as the size of the substituents increased, with values ranging from 2 to 11.7 kcal/mol. An evaluation of the effects of substituents on dipole-dipole interaction energies and rotational barriers suggests that it should be possible to engineer amphidynamic crystals where the dipole-dipole interaction energy becomes comparable to the rotational barriers. Notably, while pure dipole-dipole interaction energies reached values ranging from 0.6 to 2.4 kcal/mol, the inclusion of electronic and steric effects can alter dipolar orientations to significantly greater values. We propose that careful selection of polar substituents with different sizes may help create temperature-responsive materials with switchable collective polarization.

Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers.

The variational quantum eigensolver (VQE) is a widely employed method to solve electronic structure problems in the current noisy intermediate-scale quantum (NISQ) devices. However, due to inherent noise in the NISQ devices, VQE results on NISQ devices often deviate significantly from the results obtained on noiseless statevector simulators or traditional classical computers. The iterative nature of VQE further amplifies the errors in each loop. Recent works have explored ways to integrate deep neural networks (DNN) with VQE to mitigate iterative errors, albeit primarily limited to the noiseless statevector simulators. In this work, we trained DNN models across various quantum circuits and examined the potential of two DNN-VQE approaches, DNN1 and DNNF, for predicting the ground state energies of small molecules in the presence of device noise. We carefully examined the accuracy of the DNN1, DNNF, and VQE methods on both noisy simulators and real quantum devices by considering different ansatzes of varying qubit counts and circuit depths. Our results illustrate the advantages and limitations of both VQE and DNN-VQE approaches. Notably, both DNN1 and DNNF methods consistently outperform the standard VQE method in providing more accurate ground state energies in noisy environments. However, despite being more accurate than VQE, the energies predicted using these methods on real quantum hardware remain meaningful only at reasonable circuit depths (depth = 15, gates = 21). At higher depths (depth = 83, gates = 112), they deviate significantly from the exact results. Additionally, we find that DNNF does not offer any notable advantage over VQE in terms of speed. Consequently, our study recommends DNN1 as the preferred method for obtaining quick and accurate ground state energies of molecules on current quantum hardware, particularly for quantum circuits with lower depth and fewer qubits.

Quantum computing for electronic structure analysis: Ground state energy and molecular properties calculations

The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue, we present a hybrid Classical-Quantum computational procedure that uses the Variational Quantum Eigensolver (VQE) algorithm. By mapping the quantum system to a set of qubits and utilising a quantum circuit to prepare the ground state wavefunction, our algorithm offers a streamlined process requiring fewer computational resources than classical methods. Our algorithm demonstrated similar accuracy in rigorous comparisons with conventional electronic structure methods, such as Density Functional Theory and Hartree–Fock Theory, on a range of molecules while utilising significantly fewer resources. These results indicate the potential of the algorithm to expedite the development of new materials and technologies. This work paves the way for overcoming the computational challenges of electronic structure calculations. It demonstrates the transformative impact of quantum computing on advancing our understanding of complex quantum systems.

Low-Energy Electron Scattering from Pyrrole and Its Isomers.

Low-energy electron scattering from pyrrole and its isomers, such as 2-H pyrrole, cyclopropanecarbonitrile, and Z-2 butenenitrile, is explored in detail in this article. The electron interaction with the target molecules was studied through R-matrix theory. We have used minimal STO-3G and advanced DZP basis sets on a fine energy grid from 0.1 to 12 eV electron energy in the calculation. The properties of the STO-3G and DZP-based targets, such as their ionization energy, polarizability, dipole moment, rotational constant, principal moment of inertia, ground-state energy, and orbital energies, were investigated and compared to previously reported data. The elastic and inelastic channels showed the appearance of shape and Feshbach resonances for pyrrole and its isomers. The ultralow-energy region resonance was observed for Z-2 butenenitrile at 0.47 eV. With STO-3G and DZP basis sets, we estimated elastic, excitation, and momentum-transfer cross sections. The differential cross section for the present polar molecules was studied at 5 eV. The dissociative electron attachment channel for pyrrole and its isomers was studied for the pyrrolide anion. The data presented here will be helpful in astrophysical, astrochemical, atmospheric, and low-energy plasma modeling due to the presence of pyrrole and its isomers and the pyrrolide anion in the celestial bodies. The estimated data are also helpful in the biomedical field, radiation therapy, and pharmaceuticals.

Enthalpy of the N+ + H2 → NH+ + H Reaction—Experimental Study of the Reverse Process

The formation of nitrogen hydrides in the interstellar medium is initiated by the nearly thermoneutral reaction of N+ + H2 → NH+ + H. Here, we experimentally determine the enthalpy of this reaction using the principle of detailed balance from a measurement of the rate coefficient of the reverse reaction NH+ + H → N+ + H2. The measurements were carried out in a linear radiofrequency 22-pole trap combined with an effusive beam source of atomic hydrogen at temperatures between 10 and 100 K. The resulting ground-state energy difference (or reaction enthalpy at 0 K) of ΔE 0 = (18 ± 4) meV confirms that there are no significant energy barriers on the reaction path.

Electronic and magnetic performance of MoS2 monolayer via Tc & Nb impurities defect and water adsorption

This study examined the effect of Tc & Nb impurity atoms on MoS2 (Tc-MoS2 & Nb-MoS2 ), and adsorption of water molecule on impurities defected MoS2 (Tc-W-MoS2 & Nb-W-MoS2) material from first-principles calculations. By the estimation of their ground state energy and binding energy, they are stable 2D materials. From band structure and density of states (DoS) calculations, Tc & Nbimpurities affect the nature of pristine MoS2. It is found that Tc-MoS2 has n-type & Nb-MoS2 has p-type semiconducting nature. Water interaction on Tc-MoS2 & Nb-MoS2 slightly changes the electronic properties and impacts the bandgap, which enhanced the electronic performance of material than that of pristine MoS2. The magnetic properties of Tc-MoS2, Nb-MoS2, Tc-W-MoS2, and Nb-W-MoS2 are analyzed and found to exhibit an uneven distribution of up-spin and down-spin states of electrons in the orbital of atoms near the Fermi level. It reflects that they have magnetic properties. The non-magnetic MoS2 material changes in to weak magnetic defected-MoS2 materials due to the presence of Tc, Nb and adsorbed water molecule. It means, impurity defects add to magnetic properties of pristine MoS2. Magnetic properties on defected MoS2 occurred due to the dominant contributions of spin states of 4d-orbital of Mo, Tc, Nb atoms, and 3p-orbital of S atoms in the structures. This study highlights the impact of Tc & Nb impurity atoms and adsorbed water molecule on impurities defected MoS2. The studied materials have potential applications in the fields of catalysis, nanoelectronics, biomedicine, and magnetic sensors on the basis of their electronic and magnetic properties.

Superdense Hexagonal BP and AlP with Quartz Topology: Crystal Chemistry and DFT Study

The superdense hexagonal phosphides BP and AlP, whose structures are formed by distorted tetrahedra and characterized by quartz-derived (qtz) topology, were predicted from crystal chemistry and first principles as potential high-pressure phases. From full geometry structure relaxations and ground state energy calculations based on quantum density functional theory (DFT), qtz BP and AlP were found to be less cohesive than the corresponding cubic zinc-blende (zb) phases with diamond-like (dia) topology, but were confirmed to be mechanically (elastic constants) and dynamically (phonons) stable. From the energy–volume equations of state, qtz phases were found to be energetically favorable at small volumes (high pressures), with zb-to-qtz transition pressures of 144 GPa for BP and 28 GPa for AlP. According to the electronic band structures and the site projected density of states, both phosphides exhibit larger band gaps of the zinc-blende phases compared to the qtz phases; the smaller values for the latter result from the smaller volumes per formula unit, leading to increased covalence.

Unitary coupled-cluster for quantum computation of molecular properties in a strong magnetic field.

In truncated coupled-cluster (CC) theories, non-variational and/or generally complex ground-state energies can occur. This is due to the non-Hermitian nature of the similarity transformed Hamiltonian matrix in combination with CC truncation. For chemical problems that deal with real-valued Hamiltonian matrices, complex CC energies rarely occur. However, for complex-valued Hamiltonian matrices, such as those that arise in the presence of strong magnetic fields, complex CC energies can be regularly observed unless certain symmetry conditions are fulfilled. Therefore, in the presence of magnetic fields, it is desirable to pursue CC methods that are guaranteed to give upper-bound, real-valued energies. In this work, we present the first application of unitary CC to chemical systems in a strong magnetic field. This is achieved utilizing the variational quantum eigensolver algorithm applied to the unitary coupled-cluster singles and doubles (UCCSD) method. We benchmark the method on the H2 molecule in a strong magnetic field and then calculate UCCSD energies for the H4 molecule as a function of both geometry and field angle. We show that while standard CCSD can yield generally complex energies that are not an upper-bound to the true energy, UCCSD always results in variational and real-valued energies. We also show that the imaginary components of the CCSD energy are largest in the strongly correlated region. Last, the UCCSD calculations capture a large percentage of the correlation energy.

Quantum entanglement in non-Hermitian Hubbard model

Quantum correlation, entanglement in the non-Hermitian Hubbard model where the non-Hermiticity led to a series of exotic phenomena when the system experiences dissipation to an environment on bipartite lattice is studied. Quantum entanglement measures given by the entanglement negativity and entropy of the density matrix have been analyzed. We investigate the effect of non-Hermitian imaginary hopping on entropy and negativity. Furthermore, in the large U limit, such non-Hermiticity contributes with a minus sign in the virtual exchange of quasiparticles and hence, the behavior of the ground state energy and low-lying excitations is reversed.

Eigensolutions, virial theorem and molecular study of nonrelativistic Krazer‐Fues potential

AbstractA Kratzer‐Fues potential is coupled with its self to form a double Kratzer‐Fues potential. The solutions of the radial Schrödinger equation with the combined potential are obtained via two different methodologies. Using the supersymmetric approach, the energy equation for a non‐approximated centrifugal term is obtained. The energy equation for the approximated centrifugal term is obtained using the parametric Nikiforov‐Uvarov method. Numerical results are computed for five molecules using MATLAB software program. The computed numerical values are compared with the experimental values and the ground state energy obtained from Herzberg's energy level equation. The study revealed that the results of the approximated centrifugal term are better than the results of the non‐approximated centrifugal term for four molecules.

Solving time-independent Schrödinger equation variationally using random numbers

Finding wavefunctions for even the simplest of interacting particle systems consisting of two particles is extremely difficult. It is therefore highly desirable that an accurate and easily implementable method be available to instructors and students of quantum-mechanics for obtaining wavefunctions for these particles. The usual approach taken to do this is to use parametrized functional form for the wavefunction in conjunction with the variational method to find approximate wavefunction and energy for the ground-state of such systems. In this paper, we employ random numbers to obtain ground-state wavefunctions and energies of two interacting particles in different one-dimensional potentials. The idea behind using random numbers is to search freely for functions that lead to lower and lower energy, converging eventually to its lowest value. The method presented is easily applicable numerically using a simple algorithm, and the wavefunctions obtained are highly accurate. Thus, the method presented makes study of two interacting particles accessible to instructors and students alike in a transparent manner.

First Principle Investigations on Structural, Mechanical, Electronic, And Thermoelectric Properties of XCoP (XTi, Zr, Hf) Half Heusler Alloys for Energy Recovery Application

AbstractXCoP (XTi, Zr, Hf) half Heusler alloys are investigated through density functional theory in stable non‐magnetic phase. The exchange‐correlation functional Generalized Gradient Approximation (GGA) is used to study these alloys. The equilibrium lattice constants and corresponding ground state energies of the studied alloys are calculated in stable γ‐phase. All these three reported alloys exhibit semiconducting behavior with corresponding bandgap values of 1.40, 1.29, and 1.38 eV for TiCoP, ZrCoP, and HfCoP, respectively. The studied alloys are mechanically stable and ductile in nature. The obtained thermoelectric figure of merit for p‐type TiCoP, ZrCoP and HfCoP are 0.5, 0.6, and 0.7 at 1200 K. Similarly, the figure of merit obtained for n‐type TiCoP, ZrCoP, HfCoP are 0.54, 0.37, and 0.31, respectively, at the same temperature. The investigated favorable transport properties of these alloys show that they are the potential candidates for waste heat energy harvesting application.

QREChem: quantum resource estimation software for chemistry applications

As quantum hardware continues to improve, more and more application scientists have entered the field of quantum computing. However, even with the rapid improvements in the last few years, quantum devices, especially for quantum chemistry applications, still struggle to perform calculations that classical computers could not calculate. In lieu of being able to perform specific calculations, it is important have a systematic way of estimating the resources necessary to tackle specific problems. Standard arguments about computational complexity provide hope that quantum computers will be useful for problems in quantum chemistry but obscure the true impact of many algorithmic overheads. These overheads will ultimately determine the precise point when quantum computers will perform better than classical computers. We have developed QREChem to provide logical resource estimates for ground state energy estimation in quantum chemistry through a Trotter-based quantum phase estimation approach. QREChem provides resource estimates which include the specific overheads inherent to problems in quantum chemistry by including heuristic estimates of the number of Trotter steps and number of necessary ancilla, allowing for more accurate estimates of the total number of gates. We utilize QREChem to provide logical resource estimates for a variety of small molecules in various basis sets, obtaining estimates in the range of 107–1015 for total number of T gates. We also determine estimates for the FeMoco molecule and compare all estimates to other resource estimation tools. Finally, we compare the total resources, including hardware and error correction overheads, demonstrating the need for fast error correction cycle times.

Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will require some degree of fault tolerance. While hardware is improving towards this milestone, optimizing quantum algorithms also brings it closer to the present. Existing methods for ground state energy estimation are costly in that they require a number of gates per circuit that grows exponentially with the desired number of bits in precision. We reduce this cost exponentially, by developing a ground state energy estimation algorithm for which this cost grows linearly in the number of bits of precision. Relative to recent resource estimates of ground state energy estimation for the industrially-relevant molecules of ethylene-carbonate and PF6−, the estimated gate count and circuit depth is reduced by a factor of 43 and 78, respectively. Furthermore, the algorithm can use additional circuit depth to reduce the total runtime. These features make our algorithm a promising candidate for realizing quantum advantage in the era of early fault-tolerant quantum computing.

Fault-tolerant quantum computation of molecular observables

Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the expectation values of other observables with respect to said ground states, which is important for many industrial applications. In this work we present a novel expectation value estimation (EVE) quantum algorithm which can be applied to estimate the expectation values of arbitrary observables with respect to any of the system's eigenstates. In particular, we consider two variants of EVE: std-EVE, based on standard quantum phase estimation, and QSP-EVE, which utilizes quantum signal processing (QSP) techniques. We provide rigorous error analysis for both both variants and minimize the number of individual phase factors for QSPEVE. These error analyses enable us to produce constant-factor quantum resource estimates for both std-EVE and QSP-EVE across a variety of molecular systems and observables. For the systems considered, we show that QSP-EVE reduces (Toffoli) gate counts by up to three orders of magnitude and reduces qubit width by up to 25% compared to std-EVE. While estimated resource counts remain far too high for the first generations of fault-tolerant quantum computers, our estimates mark a first of their kind for both the application of expectation value estimation and modern QSP-based techniques.

Exploring quantum critical phenomena in a nonlinear Dicke model through algebraic deformation

In this work, we use a deformed version of the Heisenberg–Weyl algebra in the Dicke Model to incorporate a Kerr medium and nonlinear interaction between matter and radiation fields. The deformed algebra allows us to define two distinct nonlinear coherent states for the radiation field. These coherent states, along with the conventional Heisenberg–Weyl coherent states and their symmetry-adapted versions, are employed as trial variational states in the energy-surface minimisation method. The obtained results reveal that the Kerr medium introduces a delay in reaching the super-radiant region, with the delay becoming more pronounced as the nonlinear parameter increases. To evaluate the different approaches, we analyse the behaviour of the critical coupling, ground-state energy, entropy of entanglement between matter and radiation, and fidelity between the numerical solution and the symmetry-adapted solution. We find that one particular deformed coherent state outperforms the other trial states in approximating the ground state of the system, providing an accurate description of the critical behaviour in the proposed nonlinear model.

Instantons, renormalons and the theta angle in integrable sigma models

Some sigma models which admit a theta angle are integrable at both \vartheta=0ϑ=0 and \vartheta=\piϑ=π. This includes the well-known O(3)O(3) sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, which can be computed with the Bethe Ansatz. We obtain explicit results for its non-perturbative corrections and we study the effect of the theta angle on them. We show that imaginary, exponentially small corrections due to renormalons remain unchanged, while instanton corrections change sign, as expected. We find in addition corrections due to renormalons which also change sign as we turn on the theta angle. Based on these results we present an explicit non-perturbative formula for the topological susceptibility of the O(3)O(3) sigma model in the presence of a magnetic field, in the weak coupling limit.

Ferrimagnetic half Heusler alloys for waste heat recovery application - First principle study using different exchange–correlation functionals

ZrMnSi and HfMnSi half Heusler alloys with magnetic ground state are investigated through density functional theory. The different exchange–correlation functionals (GGA, LDA, PBESol and WC) are used to study these alloys. The equilibrium lattice constants and corresponding ground state energies are calculated using these four approximation methods. From GGA functional, the obtained band gap for ZrMnSi is 1.268 eV and HfMnSi is 1.311 eV. The reported alloys are predicted to be half metals from different potentials, where those alloys show semiconductor character in minority spin channel and also exhibit metallic character in majority spin channel. The studied alloys are mechanically stable and ductile in nature. The total magnetic moment of −3μB is obtained in the reported ferrimagnetic alloys. The obtained thermoelectric figure of merit for ZrMnSi and HfMnSi is 0.46 at 1200 K and 0.31 at 1200 K respectively, it shows that these alloys are the potential candidates for waste heat recovery application, and they are also useful for spin flip device application.