Ground State Energy Research Articles

Range-separated density functional theory using multiresolution analysis and quantum computing.

Quantum computers are expected to outperform classical computers for specific problems in quantum chemistry. Such calculations remain expensive, but costs can be lowered through the partition of the molecular system. In the present study, partition was achieved with range-separated density functional theory (RS-DFT). The use of RS-DFT reduces both the basis set size and the active space size dependence of the ground state energy in comparison with the use of wave function theory (WFT) alone. The utilization of pair natural orbitals (PNOs) in place of canonical molecular orbitals (MOs) results in more compact qubit Hamiltonians. To test this strategy, a basis-set independent framework, known as multiresolution analysis (MRA), was employed to generate PNOs. Tests were conducted with the variational quantum eigensolver for a number of molecules. The results show that the proposed approach reduces the number of qubits needed to reach a target energy accuracy.

Meta-optimization of resources on quantum computers

The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all information encoded in the calculation. Even if the technology advances fast within the next years, any use of quantum computers will be limited to short and simple tasks, serving as subroutines of more complex classical procedures. Even for these applications the resource efficiency, measured in the number of quantum computer runs, will be a key parameter. Here we suggest a general meta-optimization procedure for hybrid quantum-classical algorithms that allows finding the optimal approach with limited quantum resources. This method optimizes the usage of resources of an existing method by testing its capabilities and setting the optimal resource utilization. We demonstrate this procedure on a specific example of variational quantum algorithm used to find the ground state energy of a hydrogen molecule.

Nuclear Physics in the Era of Quantum Computing and Quantum Machine Learning

AbstractIn this paper, the application of quantum simulations and quantum machine learning is explored to solve problems in low‐energy nuclear physics. The use of quantum computing to address nuclear physics problems is still in its infancy, and particularly, the application of quantum machine learning (QML) in the realm of low‐energy nuclear physics is almost nonexistent. Three specific examples are presented where the utilization of quantum computing and QML provides, or can potentially provide in the future, a computational advantage: i) determining the phase/shape in schematic nuclear models, ii) calculating the ground state energy of a nuclear shell model‐type Hamiltonian, and iii) identifying particles or determining trajectories in nuclear physics experiments.

Scalable semidefinite programming approach to variational embedding for quantum many-body problems

In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. We exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.

Complexity of Supersymmetric Systems and the Cohomology Problem

We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with N=2 supersymmetry and show that the problem remains QMA-complete. Our main motivation for studying this is the well-known fact that the ground state energy of a supersymmetric system is exactly zero if and only if a certain cohomology group is nontrivial. This opens the door to bringing the tools of Hamiltonian complexity to study the computational complexity of a large number of algorithmic problems that arise in homological algebra, including problems in algebraic topology, algebraic geometry, and group theory. We take the first steps in this direction by introducing the k-local Cohomology problem and showing that it is QMA1-hard and, for a large class of instances, is contained in QMA. We then consider the complexity of estimating normalized Betti numbers and show that this problem is hard for the quantum complexity class DQC1, and for a large class of instances is contained in BQP. In light of these results, we argue that it is natural to frame many of these homological problems in terms of finding ground states of supersymmetric fermionic systems. As an illustration of this perspective we discuss in some detail the model of Fendley, Schoutens, and de Boer consisting of hard-core fermions on a graph, whose ground state structure encodes l-dimensional holes in the independence complex of the graph. This offers a new perspective on existing quantum algorithms for topological data analysis and suggests new ones.

Quantum mechanical analysis of yttrium-stabilized zirconia and alumina: implications for mechanical performance of esthetic crowns

BackgroundYttrium-stabilized zirconia (YSZ) and alumina are the most commonly used dental esthetic crown materials. This study aimed to provide detailed information on the comparison between yttrium-stabilized zirconia (YSZ) and alumina, the two materials most often used for esthetic crowns in dentistry.MethodologyThe ground-state energy of the materials was calculated using the Cambridge Serial Total Energy Package (CASTEP) code, which employs a first-principles method based on density functional theory (DFT). The electronic exchange–correlation energy was evaluated using the generalized gradient approximation (GGA) within the Perdew (Burke) Ernzerhof scheme.ResultsOptimization of the geometries and investigation of the optical properties, dynamic stability, band structures, refractive indices, and mechanical properties of these materials contribute to a holistic understanding of these materials. Geometric optimization of YSZ provides important insights into its dynamic stability based on observations of its crystal structure and polyhedral geometry, which show stable configurations. Alumina exhibits a distinctive charge, kinetic, and potential (CKP) geometry, which contributes to its interesting structural framework and molecular-level stability. The optical properties of alumina were evaluated using pseudo-atomic computations, demonstrating its responsiveness to external stimuli. The refractive indices, reflectance, and dielectric functions indicate that the transmission of light by alumina depends on numerous factors that are essential for the optical performance of alumina as a material for esthetic crowns. The band structures of both the materials were explored, and the band gap of alumina was determined to be 5.853 eV. In addition, the band structure describes electronic transitions that influence the conductivity and optical properties of a material. The stability of alumina can be deduced from its bandgap, an essential property that determines its use as a dental material. Refractive indices are vital optical properties of esthetic crown materials. Therefore, the ability to understand their refractive-index graphs explains their transparency and color distortion through how the material responds to light..The regulated absorption characteristics exhibited by YSZ render it a highly attractive option for the development of esthetic crowns, as it guarantees minimal color distortion.ConclusionThe acceptability of materials for esthetic crowns is strongly determined by mechanical properties such as elastic stiffness constants, Young's modulus, and shear modulus. YSZ is a highly durable material for dental applications, owing to its superior mechanical strength.

Information flow in parameterized quantum circuits

Abstract In this work, we introduce a new way to quantify information flow in quantum systems, especially for parameterized quantum circuits. We use a graph representation of the circuits and propose a new distance metric using the mutual information between gate nodes. We then present an optimization procedure for variational algorithms using paths based on the distance measure. We explore the
features of the algorithm by means of the variational quantum eigensolver, in which we compute the ground state energies of the Heisenberg model. In addition, we employ the method to solve a binary classification problem using variational quantum classification. From numerical simulations, we show that our method can be successfully used for optimizing the parameterized quantum circuits primarily used in near-term algorithms. We further note that information-flow based paths can be used to improve convergence of existing stochastic gradient based methods.

Analyzing the Time Evolution of a Particle by Decomposes the Initial State Confinement in 1D Well into the Lowest Eigenstates Energy

In this work, we obtained the time evolution of the wave function of a limited quantum system (1D Box), hence getting a mathematical model to describe the system. By using programming computes, it performs a time evolution that decomposes the initial state into the 2,10, and 20 lowest energy eigenstates. Finally, by comparing numerical de-composition coefficients for the wave function to the analytical values, it found the number of knots increases directly versus the energy of the particle's quantum state. As a result, the mean bending given by the second derivative which is proportional to the kinetic energy operator should increase. We found there is a negligible mean and standard deviation of the energy in units of the ground state energy.

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

Confinement of N-Body Systems and Non-integer Dimensions

The squeezing process of a three-dimensional quantum system by use of an external deformed one-body oscillator potential can also be described by the d-method, without external field and where the dimension can take non-integer values. In this work we first generalize both methods to N particles and any transition between dimensions below 3. Once this is done, the use of harmonic oscillator interactions between the particles allows complete analytic solutions of both methods, and a direct comparison between them is possible. Assuming that both methods describe the same process, leading to the same ground state energy and wave function, an analytic equivalence between the methods arises. The equivalence between both methods and the validity of the derived analytic relation between them is first tested for two identical bosons and for squeezing transitions from 3 to 2 and 1 dimensions, as well as from 2 to 1 dimension. We also investigate the symmetric squeezing from 3 to 1 dimensions of a system made of three identical bosons. We have in all the cases found that the derived analytic relations between the two methods work very well. This fact permits to relate both methods also for large squeezing scenarios, where the brute force numerical calculation with the external field is too much demanding from the numerical point of view, especially for systems with more than two particles.

Magnetic properties of the spin-1 J 1 − J 3 Heisenberg model on a triangular lattice

We study the spin-1 J 1 − J 3 Heisenberg model with antiferromagnetic nearest neighbors J 1 > 0 and the ferromagnetic third nearest neighbor J 3 < 0 for a triangular lattice. The ground-state and thermodynamic properties are evaluated under the Popov-Fedotov functional integral method and the Luttinger-Tisza procedure. Perturbation expansion of the auxiliary field around mean-field theory was carried out to investigate the effect of thermal fluctuations on ground state energy and sublattice magnetization. The results are compared with those of the spin wave approximation and other methods.

Normalized ground state of a mixed dispersion nonlinear Schrodinger equation with combined power-type nonlinearities

We study the existence of normalized ground state solutions to a mixed dispersion fourth-order nonlinear Schrodinger equation with combined power-type nonlinearities. By analyzing the subadditivity of the ground state energy with respect to the prescribed mass, we employ a constrained minimization method to establish the existence of ground state that corresponds to a local minimum of the associated functional. Under certain conditions, by studying the monotonicity of ground state energy as the mass varies, we apply the constrained minimization arguments on the Nehari-Pohozaev manifold to prove the existence of normalized ground state solutions.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2024/29/abstr.html

Bound state energies and critical bound region in the semiclassical dense hydrogen plasmas

We calculate the bound state energies of the hydrogen atom in semiclassical dense hydrogen plasmas modeled by the effective screened interaction potential developed by Ramazanov et al. [Phys. Rev. E 92, 023104 (2015)]. It is shown that the quantum degenerate and exchange-correlation effects of plasma electrons do not play significant roles in the region where the system exhibits bound states. The bound-continuum critical transition lines and the distribution of the ground state energies in the plasma density-temperature phase diagrams are obtained, both with and without taking into account the screening effect of the plasma ions. The dipole transition oscillator strengths and static dipole polarizabilities of the electron-ion subsystems in semiclassical dense hydrogen plasmas are calculated in a wide range of plasma parameters.

Structural mode coupling in perovskite oxides using hypothesis-driven active learning

Finding the ground-state structure with minimum energy is paramount to designing any material. In ABO3-type perovskite oxides with Pnma symmetry, the lowest energy phase is driven by an inherent trilinear coupling between the two primary order parameters such as rotation and tilt with antiferroelectric displacement of the A-site cations as established via hybrid improper ferroelectric mechanism. Conventionally, finding the relevant mode coupling driving phase transition requires performing first-principles calculations which is computationally time-consuming as well as expensive. It involves following an intuitive iterative hit and trial method of (a) adding two or multiple mode vectors, followed by (b) evaluating which combination would lead to the ground-state energy. In this study, we show how a hypothesis-driven active learning framework can identify suitable mode couplings within the Landau free energy expansion with minimal information on amplitudes of modes for a series of double perovskite oxides with A-site layered, columnar and rocksalt ordering. This scheme is expected to be applicable universally for understanding atomistic mechanisms derived from various structural mode couplings behind functionalities, for e.g. polarization, magnetization and metal–insulator transitions.

How do spin-scaled double hybrids designed for excitation energies perform for noncovalent excited-state interactions? An investigation on aromatic excimer models.

Time-dependent double hybrids with spin-component or spin-opposite scaling to their second-order perturbative correlation correction have demonstrated competitive robustness in the computation of electronic excitation energies. Some of the most robust are those recently published by our group (M. Casanova-Páez, L. Goerigk, J. Chem. Theory Comput. 2021, 20, 5165). So far, the implementation of these functionals has not allowed correctly calculating their ground-state total energies. Herein, we define their correct spin-scaled ground-state energy expressions which enables us to test our methods on the noncovalent excited-state interaction energies of four aromatic excimers. A range of 22 double hybrids with and without spin scaling are compared to the reasonably accurate wavefunction reference from our previous work (A. C. Hancock, L. Goerigk, RSC Adv. 2023, 13, 35964). The impact of spin scaling is highly dependent on the underlying functional expression, however, the smallest overall errors belong to spin-scaled functionals with range separation: SCS- and SOS- PBEPP86, and SCS-RSX-QIDH. We additionally determine parameters for DFT-D3(BJ)/D4 ground-state dispersion corrections of these functionals, which reduce errors in most cases. We highlight the necessity of dispersion corrections for even the most robust TD-DFT methods but also point out that ground-state based corrections are insufficient to completely capture dispersion effects for excited-state interaction energies.

Density Functional Theory Analysis that Explains the Volume Expansion in Prelithiated Silicon Nanowires

This research is a theoretical study that simulates the volume expansion of a prelithiated silicon nanowire during lithium-ion insertion and the application of an electric current. Utilizing density functional theory (DFT) the ground state energy Eg (x) of prelithiated silicon (LixSi) is defined as a function of the lithium-ion (Li+) concentration (x). As the Li+ are increased, Eg (x) become increasingly stable from x = 1.00 through x = 2.415 and decrease in stability as the lithium-ion concentration becomes x &gt; 2.415 until full lithiation of the silicon nanowire is reached at x = 3.75. After the determination of the lithiated silicon ground state energies, an electric current is applied to the lithiated silicon nanowire at various Li+ concentrations x. It was discovered that the volume expansion began at approximately x = 3.25 and increased to over 300% of the original volume of a pristine silicon nanowire at x = 3.75 which at this point was full lithiation. This is in sharp contrast to prior research studies where the ground state energy was not considered. In previous studies, the computation of the volume expansion starts approximately at x = 0.75 and produces a continuous nonlinear volume expansion until the process is terminated at full lithiation.

Estimation of Electrostatic Interaction Energies on a Trapped-Ion Quantum Computer.

We present the first hardware implementation of electrostatic interaction energies by using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of NO to N2O catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would require in the straightforward supermolecular approach.

On discrete ground states of rotating Bose–Einstein condensates

The ground states of Bose–Einstein condensates in a rotating frame can be described as constrained minimizers of the Gross–Pitaevskii energy functional with an angular momentum term. In this paper we consider the corresponding discrete minimization problem in Lagrange finite element spaces of arbitrary polynomial order and we investigate the approximation properties of discrete ground states. In particular, we prove a priori error estimates of optimal order in the L 2 L^2 - and H 1 H^1 -norm, as well as for the ground state energy and the corresponding chemical potential. A central issue in the analysis of the problem is the missing uniqueness of ground states, which is mainly caused by the invariance of the energy functional under complex phase shifts. Our error analysis is therefore based on an Euler–Lagrange functional that we restrict to certain tangent spaces in which we have local uniqueness of ground states. This gives rise to an error decomposition that is ultimately used to derive the desired a priori error estimates. We also present numerical experiments to illustrate various aspects of the problem structure.

Exploring how molluscan purple has survived throughout the Ages: The excited state dynamics of 6,6′-dibromoindigotin

The color purple has long been used as a symbol of royalty and power in art, fashion, and architecture. This correlation with aristocracy can be traced back to the use of molluscan purple, a rich purple dye that is still presently more expensive than gold, by royalty as early as the 18th century BCE. While the molluscan purple dye is composed of a mixture of various proteins, its color is derived from indigotin, indirubin and their brominated derivatives, including the molecule, 6,6′-dibromoindigotin, an analogue of the indigotin dye which is also widely used in various modern industries. Both dyes can exhibit high stability, in particular against photodamage from UV and Visible radiation. In this study, we present the gas phase absorption spectrum and excited-state lifetimes of 6,6′-dibromoindigotin combined with static calculations of the excited and ground-state potential energy surfaces. The lifetime measurements reveal that molluscan purple has nearly the same relaxation rate as indigotin providing new insights in the possible relaxation mechanisms of the indigotin family of dye molecules.

Folded Spectrum VQE: A Quantum Computing Method for the Calculation of Molecular Excited States.

The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.