QAOA
A hybrid algorithm for combinatorial optimisation — the quantum computer proposes, a classical optimiser adjusts, and round it goes.
The Quantum Approximate Optimization Algorithm was presented by Farhi, Goldstone and Gutmann in 2014. The problem is encoded so that the lowest energy corresponds to the best solution. A short circuit with a number of tunable angles is run, the result measured, and a classical optimiser proposes new angles. Circuit depth is deliberately kept low because the hardware tolerates no more.
The algorithm drew considerable attention as one of few candidates for practical value on NISQ hardware. That picture has dimmed: for most problems studied, classical heuristics have continued to perform at least as well, and whether QAOA delivers a genuine advantage remains open.