Quantum annealing for systems of polynomial equations

Area of Science:

• Computational Mathematics
• Quantum Computing
• Numerical Analysis

Background:

• Solving systems of polynomial and linear equations is crucial for many scientific and engineering tasks.
• Classical methods like iterative solvers and matrix inversion have limitations, including variable convergence and sensitivity to condition numbers.

Purpose of the Study:

• To introduce and validate a direct quantum annealing method for solving general systems of polynomial equations.
• To explore the application of this quantum method in linear regression and analyze its scaling behavior for linear systems.

Main Methods:

• Developed a direct solution method for polynomial equations utilizing quantum annealing.
• Validated the method on a quantum annealer by solving second-order polynomial systems.
• Defined and tested an iterative annealing process for solving linear systems.

Main Results:

• Successfully solved systems of second-order polynomial equations using a commercial quantum annealer.
• Demonstrated the applicability of the quantum annealing approach to linear regression problems.
• Showcased the efficacy of the iterative annealing process in solving linear systems to a high tolerance (10^-8).

Conclusions:

• Quantum annealing provides a viable and direct alternative to classical iterative solvers for systems of polynomial equations.
• The quantum annealing method exhibits promising scaling behavior for linear systems, considering problem size, condition number, and precision.
• The developed iterative annealing process offers an efficient means to achieve high-precision solutions for linear systems.