Solving the Schrödinger equation using program synthesis

Area of Science:

• Computational Physics
• Quantum Chemistry
• Algorithm Development

Background:

• Solving the time-independent Schrödinger equation is crucial for understanding quantum systems.
• Traditional methods often rely on approximations or complex mathematical functions.
• Developing efficient and accurate algorithms is an ongoing challenge in computational quantum chemistry.

Purpose of the Study:

• To demonstrate a novel program synthesis approach for generating algorithms.
• To approximate ground-state solutions for one-dimensional time-independent Schrödinger equations.
• To explore an alternative route for developing quantum chemistry algorithms.

Main Methods:

• Utilizing a linear code representation for algorithm construction.
• Employing discrete optimization with simulated annealing.
• Generating algorithms that operate on input vectors, matrices, and constants defining the potential energy surface (PES).

Main Results:

• Successfully generated algorithms that approximate ground-state wavefunctions (ψ(x)).
• The synthesized algorithms directly compute solutions from system inputs, not just approximate functions.
• Demonstrated the approach for bound polynomial potential energy surfaces.

Conclusions:

• Program synthesis offers a viable method for creating quantum chemistry algorithms.
• This approach yields complete algorithms capable of solving the Schrödinger equation.
• The findings pave the way for novel computational methods in quantum chemistry.