Solving coupled non-linear schrödinger equations via quantum imaginary time evolution

Area of Science:

• Nuclear physics
• Quantum mechanics
• Computational physics

Background:

• Coupled non-linear Schrödinger equations are fundamental for modeling many-particle systems.
• The nuclear Hartree-Fock approach requires efficient methods to solve these complex equations.

Purpose of the Study:

• To introduce and evaluate a quantum imaginary time evolution (ITE) algorithm for solving coupled non-linear Schrödinger equations within the nuclear Hartree-Fock framework.
• To assess the algorithm's performance and identify areas for enhancement.

Main Methods:

• Implementation of a quantum imaginary time evolution (ITE) algorithm.
• Application to the nuclear Hartree-Fock approach using a simplified Skyrme interaction model.
• Calculation of the ground state energy for an oxygen-16 nucleus.

Main Results:

• The quantum ITE algorithm successfully calculated the ground state energy of the oxygen-16 nucleus.
• Results obtained from the quantum algorithm demonstrated agreement with the classical ITE algorithm.
• Identified bottlenecks and limitations within the developed quantum algorithm.

Conclusions:

• The quantum ITE algorithm is a viable method for solving nuclear Hartree-Fock equations.
• Further development is needed to address identified deficiencies and improve computational efficiency.
• The study provides a foundation for more advanced quantum simulations in nuclear physics.