An efficient adaptive variational quantum solver of the Schrödinger equation based on reduced density matrices

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Adaptive variational quantum algorithms (e.g., ADAPT-VQE, IQEB-VQE) aim to reduce circuit depth.
• Current adaptive algorithms suffer from inefficiency due to a large number of required measurements.

Purpose of the Study:

• To reformulate ADAPT-VQE using reduced density matrices (RDMs) to eliminate measurement overhead.
• To develop more efficient quantum algorithms for calculating molecular energies.

Main Methods:

• Reformulation of ADAPT-VQE using Valdemoro's three-electron RDM reconstruction.
• Introduction of ADAPT-V and ADAPT-Vx algorithms based on RDM-driven operator pool screening.
• Generalization of the RDM-based scheme to the IQEB-VQE algorithm.

Main Results:

• ADAPT-V and ADAPT-Vx algorithms avoid additional measurements, with ADAPT-Vx reducing gradient evaluations.
• Numerical benchmarks show accurate ground- and excited-state potential energy curves for small molecules.
• The RDM-based scheme significantly reduces measurements for the IQEB-VQE algorithm.

Conclusions:

• The RDM-based approach offers a more efficient alternative to existing adaptive variational quantum algorithms.
• These new algorithms (ADAPT-V, ADAPT-Vx, and RDM-generalized IQEB-VQE) enhance accuracy and reduce quantum resource demands.
• The developed methods provide a pathway for more practical quantum simulations in chemistry.