Experimental determination of Ramsey numbers

Area of Science:

• Mathematics
• Quantum Computing
• Computational Complexity

Background:

• Ramsey theory investigates order emergence in large, disordered systems.
• Ramsey numbers quantify the minimum size for guaranteed order, but are notoriously hard to compute.
• Adiabatic quantum evolution offers a potential method for calculating these numbers.

Purpose of the Study:

• To experimentally implement and validate an adiabatic quantum evolution algorithm for determining two-color Ramsey numbers R(m,n).
• To demonstrate the feasibility of using quantum computation for solving complex mathematical problems.

Main Methods:

• Implementation of a proposed algorithm utilizing adiabatic quantum evolution.
• Experimental execution on a quantum computing platform to compute specific Ramsey numbers.
• Utilized 84 qubits, with 28 designated as computational qubits for the R(8,2) calculation.

Main Results:

• The algorithm correctly determined the Ramsey numbers R(3,3) and R(m,2) for m ranging from 4 to 8.
• The R(8,2) computation represents the largest scientifically meaningful adiabatic evolution algorithm implemented to date.
• Validated the quantum algorithm's accuracy for calculating Ramsey numbers.

Conclusions:

• Experimental implementation of adiabatic quantum evolution is a viable method for calculating Ramsey numbers.
• This work establishes a new benchmark for large-scale, scientifically relevant adiabatic quantum computations.
• Advances in quantum computing can tackle previously intractable mathematical challenges.