Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Simulation

Background:

• Noisy-intermediate-scale quantum (NISQ) devices present challenges for quantum advantage realization.
• Maintaining qubit coherence and reducing algorithm complexity are critical for quantum simulations.
• Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum chemistry on NISQ hardware.

Purpose of the Study:

• To investigate a reduced qubit mapping strategy for VQE to analyze ground state energy.
• To develop a correction scheme for non-bosonic excitations in electron correlation models.
• To assess the accuracy of the proposed method for molecular ground state energies.

Main Methods:

• Reduced mapping of one spatial orbital to a single qubit.
• Mapping Pauli operators to creation/annihilation of singlet electron pairs.
• Introducing a correction scheme for non-bosonic excitations using geometrical mean of bosonic terms.
• Employing the corrected model within a VQE algorithm.

Main Results:

• Accurate ground state energies for H₂O, N₂, and Li₂O were obtained using significantly fewer qubits (6, 8, and 12, respectively).
• Quantum gate depths scaled quadratically with qubit counts.
• The seniority-zero approximation reduced qubit requirements by half compared to conventional VQE.
• The non-bosonic correction method achieved reliable quantum chemistry simulations for tested systems.

Conclusions:

• The proposed VQE approach with reduced mapping and non-bosonic correction enables efficient and accurate quantum simulations on NISQ computers.
• This method significantly lowers qubit requirements and computational complexity for quantum chemistry.
• The findings pave the way for practical quantum advantage in computational chemistry.