Orthogonal State Reduction Variational Eigensolver for the Excited-State Calculations on Quantum Computers.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Variational quantum eigensolver (VQE) is a leading quantum algorithm for ground-state energy calculations.
• Excited-state calculations on quantum computers lag behind ground-state methods.
• Developing efficient quantum algorithms for excited states is crucial for advancing quantum chemistry.

Purpose of the Study:

• To propose a novel quantum algorithm for calculating excited-state energies.
• To extend the capabilities of the variational quantum eigensolver (VQE) framework.
• To address the limitations in current quantum excited-state computation methods.

Main Methods:

• Introduction of the orthogonal state reduction variational eigensolver (OSRVE) algorithm.
• Theoretical derivation to ensure energy minimization and orthogonality.
• Application of OSRVE to H4 and H2O molecular systems.

Main Results:

• OSRVE successfully determines excited-state energies, including degenerate states.
• Numerical simulations confirm OSRVE's efficacy for H4 and H2O molecules.
• OSRVE demonstrates advantages in calculating lower-order excited states compared to existing algorithms.

Conclusions:

• OSRVE is a viable extension of VQE for excited-state energy calculations.
• The algorithm can be implemented on near-term noisy intermediate-scale quantum computers.
• OSRVE offers a promising approach for advancing quantum computational chemistry.