Reduction of the molecular hamiltonian matrix using quantum community detection

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Quantum Computing

Background:

• Calculating molecular ground and excited states requires solving the electronic Schrödinger equation.
• Exact solutions are computationally infeasible for most molecules, necessitating approximate methods.
• Current approximate methods, like post-Hartree-Fock, face significant computational complexity.

Purpose of the Study:

• To introduce a novel quantum computing approach for reducing molecular Hamiltonian matrices.
• To approximate ground and excited state energies of molecular systems using quantum computation.
• To demonstrate the potential of quantum community detection for solving electronic structure problems.

Main Methods:

• Utilized Quantum Community Detection on a D-Wave quantum annealer.
• Represented molecular Hamiltonians as matrices of Slater determinants.
• Treated Slater determinant connectivity as a graph adjacency matrix for community detection via modularity maximization.
• Employed a perturbation theory-based gauge metric to identify the lowest energy cluster.

Main Results:

• Successfully reduced the molecular Hamiltonian matrix without prior chemical knowledge.
• Calculated approximate ground and excited state energies within chemical accuracy for various molecules.
• Demonstrated proof-of-principle results for bond dissociation cases.
• Showcased the general applicability of the quantum approach.

Conclusions:

• Quantum Community Detection offers a viable method for approximating molecular electronic structure.
• This quantum computing approach has the potential to reduce the computational cost of advanced quantum chemistry methods.
• Future advancements in quantum hardware could further enhance the efficiency and applicability of this technique.