Ab initio extended Hubbard model of short polyenes for efficient quantum computing.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Materials Science

Background:

• Accurate molecular electronic structure calculations are crucial for understanding chemical systems.
• Current quantum computing methods face challenges with scalability due to complex Hamiltonians.
• Ab initio downfolding is a method typically used for periodic materials.

Purpose of the Study:

• To adapt the ab initio downfolding method for efficient quantum computing of molecular electronic structure.
• To reduce the computational complexity of first-principles Hamiltonians for quantum simulations.
• To enable more scalable quantum chemical calculations.

Main Methods:

• Introduced an extended Hubbard Hamiltonian derived via ab initio downfolding.
• Coarse-grained the first-principles Hamiltonian by eliminating high-energy electronic degrees of freedom.
• Incorporated dynamical electron correlation using constrained random phase approximation.
• Mapped the model Hamiltonian to a fermion-to-qubit representation.

Main Results:

• Reduced the number of electron repulsion integral terms from O(N4) to O(N2).
• Validated the method on vertical excitation energies and characters of ethylene, butadiene, and hexatriene.
• Captured trends consistent with experimental and high-level quantum chemical calculations.
• Demonstrated a significantly lower L1-norm for mapped Hamiltonians, indicating improved scalability.

Conclusions:

• The ab initio extended Hubbard Hamiltonian shows significant potential for quantum chemical calculations on quantum computers.
• The method offers improved scalability for molecular electronic structure simulations.
• This approach facilitates efficient quantum computation of complex chemical systems.