Bridging Classical and Quantum with SDP initialized warm-starts for QAOA

We study the Quantum Approximate Optimization Algorithm (QAOA) in the context of the Max-Cut problem. Noisy quantum devices are only able to accurately execute QAOA at low circuit depths, while classically-challenging problem instances may call for a relatively high circuit-depth. This is due to the need to build correlations between reachable pairs of vertices in potentially large graphs [16]. To enhance the solving power of low-depth QAOA, we introduce a classical pre-processing step that initializes QAOA with a biased superposition of possible cuts in the graph, referred to as a warm-start. In particular, we initialize QAOA with a solution to a low-rank semidefinite programming relaxation of the Max-Cut problem. Our experimental results show that this variant of QAOA, called QAOA-warm, is able to outperform standard QAOA on lower circuit depths in solution quality and training time. While this improvement is partly due to the classical warm-start, we find strong evidence of further improvement using QAOA circuit at small depth. We provide experimental evidence of improved performance as well as theoretical properties of the proposed framework.