Parameter Setting Heuristics Make the Quantum Approximate Optimization Algorithm Suitable for the Early Fault-Tolerant Era

Abstract: Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum heuristics for combinatorial optimization. While QAOA has been shown to perform well on small-scale instances and to provide an asymptotic speedup over state-of-the-art classical algorithms for some problems, fault-tolerance is understood to be required to realize this speedup in practice. The low resource requirements of QAOA make it particularly suitable to benchmark on early fault-tolerant quantum computing (EFTQC) hardware. However, the performance of QAOA depends crucially on the choice of the free parameters in the circuit. The task of setting these parameters is complicated in the EFTQC era by the large overheads, which preclude extensive classical optimization. In this paper, we summarize recent advances in parameter setting in QAOA and show that these advancements make EFTQC experiments with QAOA practically viable.