Optimization, simulation and sampling

Almost every compute bottleneck people post is one of three shapes. Recognizing yours is the fastest way to know which methods are worth trying.

You choose the best combination from a huge discrete set: which assets, which routes, which candidates, which schedule. These problems often become mixed-integer programs (MILP) or quadratic unconstrained binary optimization (QUBO) problems.

• Classical tools: MILP solvers such as Gurobi or CPLEX, heuristics, metaheuristics.
• Hybrid and quantum tools: quantum annealers and hybrid solvers that natively work on QUBO and Ising models, and gate-based algorithms such as QAOA.

You evolve a physical system: molecular dynamics, electronic structure, fluid flow, climate. Electronic-structure problems in chemistry and materials are among the most-studied long-term targets for quantum computers, but large, fault-tolerant machines are needed for most production-scale cases.

You need many draws from a distribution: risk estimates, Bayesian posteriors, rare events. Quantum amplitude estimation promises a quadratic reduction in samples in theory; practical gains depend on hardware that is still maturing.

Today, the most practical wins on current hardware tend to come from optimization problems run on hybrid solvers, where a classical computer handles decomposition and a quantum processor works on the hardest sub-problems.