Ramsey numbers and adiabatic quantum computing

Area of Science:

• Quantum Computing
• Graph Theory
• Combinatorial Optimization

Background:

• Ramsey numbers are fundamental in graph theory but computationally challenging.
• Only a few two-color Ramsey numbers R(m,n) for m, n≥3 are known due to calculation difficulty.

Purpose of the Study:

• To present a novel quantum algorithm for computing Ramsey numbers R(m,n).
• To demonstrate the feasibility of using adiabatic quantum evolution for solving Ramsey number problems.

Main Methods:

• Mapping Ramsey number computation to a combinatorial optimization problem.
• Employing adiabatic quantum evolution to find solutions.
• Numerical simulation of the adiabatic quantum algorithm.

Main Results:

• The quantum algorithm correctly determined R(3,3) and R(2,s) for 5≤s≤7.
• The study explored the experimental implementation of the proposed algorithm.
• Ramsey number computation was shown to belong to the quantum Merlin Arthur complexity class.

Conclusions:

• Adiabatic quantum evolution offers a viable approach for computing Ramsey numbers.
• Quantum computation holds promise for tackling complex problems in graph theory.
• The research advances the understanding of quantum complexity for combinatorial problems.