What do math optimization problems have to do with quantum gases?

A broad class of optimization problems used in engineering, machine learning, and quantum information turns out to be secretly equivalent to a thermodynamic system of independent quantum particles called bosons. At zero temperature, the gas settles into its ground state — and that state is exactly the solution to the optimization problem. This reframing yields better error bounds than standard solvers and suggests quantum algorithms that avoid a longstanding bottleneck: the need to bound the solution's size in advance.