The analogy Statistical Mechanics: The behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature Combinatorial Optimization: Finding the minimum of a given function depending on many variables Analogy: If a liquid material cools and anneals too quickly, then the material will solidify into a sub-optimal configuration. If the liquid material cools slowly, the crystals within the material will solidify optimally into a state of minimum energy (i.e. ground state This ground state corresponds to the minimum of the cost function in an optimization problemThe Analogy • Statistical Mechanics: The behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature. • Combinatorial Optimization: Finding the minimum of a given function depending on many variables. • Analogy: If a liquid material cools and anneals too quickly, then the material will solidify into a sub-optimal configuration. If the liquid material cools slowly, the crystals within the material will solidify optimally into a state of minimum energy (i.e. ground state). – This ground state corresponds to the minimum of the cost function in an optimization problem