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

Da Bean Han1, Kang-Min Hu2,3, Hyang-Tag Lim2,3

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Two quantum algorithms, subspace search variational quantum eigensolver (SSVQE) and iterative quantum phase estimation (IQPE), successfully computed multilevel molecular orbital energies. Quantum circuit design critically impacts accuracy on near-term quantum hardware.

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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.