On the order problem in construction of unitary operators for the variational quantum eigensolver

Area of Science:

• Quantum computing
• Quantum algorithms

Background:

• The Variational Quantum Eigensolver (VQE) is a prominent hybrid quantum-classical algorithm for finding molecular and material ground-state energies.
• A key challenge in VQE is the construction of the problem-tailored unitary transformation, which involves selecting and ordering generators.

Purpose of the Study:

• To address the challenge of constructing unitary transformations in the VQE framework.
• To systematically eliminate the ordering problem associated with non-commuting generators.

Main Methods:

• Utilizing the connection between Lie algebra and Lie group theory.
• Applying closure relations derived from Lie algebra.

Main Results:

• A systematic approach to constructing unitary transformations in VQE.
• Elimination of the factorial complexity in ordering generators for unitary transformations.
• Improved efficiency and scalability of the VQE framework.

Conclusions:

• The proposed Lie algebra-based method offers a robust solution to the generator ordering problem in VQE.
• This approach enhances the practical applicability and efficiency of VQE for quantum chemistry and materials science simulations.