Exploring Hückel Molecular Orbital Energies through Variational and Phase Estimation Quantum Algorithms

Area of Science:

• Quantum computing
• Computational chemistry
• Molecular modeling

Background:

• Quantum technologies enable new molecular energetics computations.
• Existing methods primarily focus on ground-state energies, neglecting multilevel systems.
• There's a need for quantum algorithms addressing complex molecular orbital energetics.

Purpose of the Study:

• To explore and benchmark two quantum algorithms for multilevel molecular orbital (MO) energetics: SSVQE and IQPE.
• To assess the impact of quantum circuit design and noise on SSVQE performance.
• To evaluate the feasibility of these algorithms on near-term quantum hardware.

Main Methods:

• Utilized subspace search variational quantum eigensolver (SSVQE) and iterative quantum phase estimation (IQPE).
• Employed an exactly solvable Hamiltonian from the Hückel method for benchmarking.
• Investigated quantum circuit design and measurement noise effects on SSVQE.

Main Results:

• Both SSVQE and IQPE accurately reproduced molecular orbital energies.
• Quantum circuit design was found to critically influence computational accuracy.
• SSVQE demonstrated potential feasibility for implementation on noisy, near-term quantum devices.

Conclusions:

• SSVQE and IQPE are viable quantum algorithms for calculating multilevel molecular orbital energetics.
• Optimizing quantum circuit design is crucial for achieving accurate results.
• Further research can advance the application of these algorithms on current quantum hardware.