Entanglement as measure of electron–electron correlation in quantum chemistry calculations

Huang, Zhen; Kais, Sabre

doi:10.1016/j.cplett.2005.07.045

Cited by 117 publications

(147 citation statements)

References 27 publications

Supporting

Mentioning

132

Contrasting

Unclassified

Order By: Relevance

“…This has been possible because for these harmonic systems we have been able to calculate analytically not only the one-body reduced matrix for bosons and fermions, but also the von Neumann entropy in the bosonic case as well as the linear entropy in the fermionic case. In doing so, we complement and extend to harmonic systems with an arbitrary number of particles the study of entanglement recently done for various two-electron models [13,[21][22][23][24][25] as well as some helium-like systems [6,14,15,17] and certain quantum complex networks [49].…”

Section: Discussionmentioning

confidence: 99%

“…It is most interesting that recently the entanglement of some real helium-like atoms has been numerically shown to have an increasing dependence on the energy. This has been done both by the use of very accurate one-electron basis functions of Hylleraas-Kinoshita type [14,17] and some Gaussian or Slater type orbital basis sets [6,15]. As well it is observed from the models that the entanglement decrease of these systems in terms of the nuclear charge Z can also be understood as the result of the relative decrease of the electron-electron-interaction.…”

Section: Introductionmentioning

confidence: 99%

“…Either directly from the resulting one-particle reduced density matrix or, since the particles are assumed to interact pairwise, in terms of the twoparticle density matrix (6) which carries all the necessary information required for calculating the quantum-mechanical properties of the whole system. The symbol x stands for spatial and spin coordinates, x := (r, ς).…”

Section: The N-harmonium Problemmentioning

confidence: 99%

“…Therefore, entanglement plays an essential role not only in quantum communication between parties separated by macroscopic distances (see e.g., [3,4]), but also it is essential to characterize quantum correlations at short distances. The latter problem, where one should necessarily consider the indistinguishable character of the involved particles, has received relatively less attention until a short time ago [5][6][7][8][9][10]. This is a serious lack because of its relevance for quantum information processing in various physical systems (see e.g., [5,11]), to gain deeper insight into non-classical correlations of atomic and molecular systems as well as to fully understand the course of their dissociation processes and chemical reactions [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Entanglement in N-harmonium: bosons and fermions

Benavides-Riveros¹,

Toranzo²,

Dehesa³

2014

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of N particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically determined in terms of N and the relative interaction strength. For bosons, we compute the von Neumann entropy of the one-body reduced density matrix by using the corresponding natural occupation numbers. There exists a critical number N c of particles so that below it, for positive values of the coupling constant, the entanglement grows when the number of particles is increasing; the opposite occurs for N > N c . For fermions, we compute the one-body reduced density matrix for the closed-shell spinned case. In the strong coupling regime, the linear entropy of the system decreases when N is growing. For fixed N , the entanglement is found (a) to decrease (increase) for negatively (positively) increasing values of the coupling constant, and (b) to grow when the energy is increasing. Moreover, the spatial and spin contributions to the total entanglement are found to be of comparable size.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: The N-harmonium Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Entanglement in N-harmonium: bosons and fermions

Benavides-Riveros¹,

Toranzo²,

Dehesa³

2014

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

“…This simple model has been used to discuss the entanglement for H 2 molecule [26]. The general Hamiltonian for such a system is given by:…”

Section: Examplementioning

confidence: 99%

Electronic Structure Calculations and the Ising Hamiltonian

2017

Self Cite

View full text Add to dashboard Cite

The exact solution of the Schrödinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem for the field of atomic and molecular physics since inception. Recently, breakthroughs have been made in the development of hardwareefficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins through an Ising-type Hamiltonian. One of the most vital questions associated with these new devices is: "Can these machines be used to perform electronic structure calculations?" In this study, we discuss the general standard procedure used by these devices and show that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. The simulation results of the transformed Ising Hamiltonian for H2, He2, HeH + , and LiH molecules match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware.The determination of solutions to the Schrödinger equation is fundamentally difficult as the dimensionality of the corresponding Hilbert space increases exponentially with the number of particles in the system, requiring a commensurate increase in computational resources. Modern quantum chemistry -faced with difficulties associated with solving the Schrödinger equation to chemical accuracy (∼1 kcal/mole) -has largely become an endeavor to find approximate methods. A few products of this effort from the past few decades include methods such as: ab initio, Density Functional, Density Matrix, Algebraic, Quantum Monte Carlo and Dimensional Scaling [1,2,3,4]. However, all methods hitherto devised face the insurmountable challenge of escalating computational resource requirements as the calculation is extended either to higher accuracy or to larger systems. Computational complexity in electronic structure calculations [5,6,7] suggests that these restrictions are an inherent difficulty associated with simulating quantum systems.Electronic structure algorithms developed for quantum computers provide a new promising route to advance the field of electronic structure calculations for large systems [8,9]. Recently, there has been an attempt at using an adiabatic quantum computing model -as is implemented on the D-Wave machine -to perform electronic structure calculations [10]. The fundamental concept behind the adiabatic quantum computing (AQC) method is to define a problem Hamiltonian, H P , engineered to have its ground state encode the solution of a corresponding computational problem. The system is initialized in the ground state of a beginning Hamiltonian, H B , which is easily solved classically. The system is then allowed to evolve adiabatically as: The largest scale implementation of AQC to date is by D-Wave Systems [11,12]. In the case of the DWave device, the physical process undertaken which acts as an adiabatic evolution is more broadly called quantum annealing (QA). The quantum processor...

show abstract

Entanglement, Electron Correlation, and Density Matrices

Kais

2007

Advances in Chemical Physics

Self Cite

View full text Add to dashboard Cite

Entanglement as measure of electron–electron correlation in quantum chemistry calculations

Cited by 117 publications

References 27 publications

Entanglement in N-harmonium: bosons and fermions

Entanglement in N-harmonium: bosons and fermions

Electronic Structure Calculations and the Ising Hamiltonian

Entanglement, Electron Correlation, and Density Matrices

Contact Info

Product

Resources

About