Electronic Structure Calculations and the Ising Hamiltonian.

Area of Science:

• Quantum computing
• Theoretical chemistry
• Computational physics

Background:

• Solving the Schrödinger equation for accurate electronic structure calculations remains a significant challenge.
• Recent advancements in quantum hardware, such as quantum optimizers and coherent Ising machines, offer new possibilities for complex simulations.

Purpose of the Study:

• To investigate the feasibility of using current quantum hardware for electronic structure calculations.
• To establish a direct mapping between the electronic structure Hamiltonian and the Ising Hamiltonian.

Main Methods:

• Reviewing the operational procedures of quantum optimizers and coherent Ising machines.
• Developing and proving an exact mathematical mapping between electronic and Ising Hamiltonians.
• Performing simulations using the transformed Ising Hamiltonian for small molecules.

Main Results:

• An exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian was demonstrated.
• Simulations of H2, He2, HeH+, and LiH molecules using the mapped Ising Hamiltonian yielded results consistent with exact numerical calculations.
• The feasibility of implementing molecular Hamiltonian mappings on existing quantum hardware was shown.

Conclusions:

• The study confirms that quantum hardware can be utilized for electronic structure calculations via an Ising Hamiltonian mapping.
• This work represents a foundational step towards generalized quantum computational methods in chemical physics.
• The findings pave the way for leveraging quantum devices to tackle complex problems in molecular simulation.