Variational quantum computing, which merges ideas from condensed matter physics, quantum computation and machine learning and has emerged as the preeminent model for quantum computing for noisy quantum hardware. Quantum approximate optimization algorithm (QAOA) is an important class of variational algorithms which are known to provide solutions for combinatorial problems. A thorough theoretical analysis of the algorithm is however still largely lacking. We take a step towards this direction in our current study, where we simulate QAOA using matrix product states (MPS). In the process we learn about the role of entanglement in QAOA.