Parameter Concentration in Quantum Approximate Optimization

Understand

The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development.

• In QAOA, a quantum circuit is trained -- by repeatedly adjusting circuit parameters -- to solve a problem.
• Several recent findings have reported parameter concentration effects in QAOA and their presence has become one of folklore: while empirically observed, the concentrations have not been defined and analytical approaches remain scarce, focusing on limiting system and not considering parameter scaling as system size increases.
• We found that optimal QAOA circuit parameters concentrate as an inverse polynomial in the problem size, providing an optimistic result for improving circuit training.