1From Physics to Logic
QAOA uses the laws of physics to solve logical problems. By mapping a cost function to the energy of a quantum system, we can use the 'natural' tendency of the system to find the lowest energy state.
2The p-level Advantage
As we increase the number of layers in QAOA, the algorithm theoretically converges to the exact solution. However, deeper circuits are more susceptible to noise on current hardware.
3Step-by-Step Breakdown
Combinatorial Opt. Finding the best solution from a finite set of possibilities.
Cost Hamiltonian. We encode the problem we want to solve into a Hamiltonian matrix.
Mixer Hamiltonian. The mixer allows the system to explore different states.
QAOA Circuit. Applying cost and mixer layers alternately.
Repetitions. The depth 'p' determines the quality of the approximation.
Optimization. Training beta and gamma parameters to find the minimum energy.
Check. What happens as the depth 'p' of QAOA increases?
- →Result gets worse
- →Result approaches optimum
Max-Cut Problem. Partitioning nodes of a graph to maximize the number of edges between them.
Adiabatic Link. QAOA is a trotterized version of adiabatic quantum computing.
End. QAOA mastered.
Compute a Real MaxCut Cost. Finish counting how many graph edges get cut by a given partition — the objective QAOA optimizes.
