Problems involving combinatorial and continuous optimization are ubiquitous in our modern life. Classic examples include lead compound optimization in the development of medicine, frequency band and/or transmission power optimization in wireless communications, sparse coding for compressed sensing, Boltzmann sampling in machine learning, portfolio optimization in Fin Tech, and many others. Most of those problems belong to the non-deterministic polynomial (NP), NP-complete, and NP-hard classes in complexity theory and require exponential resources as the problem size increases. The QNN exploits quantum parallel searching at below OPO threshold, collective symmetry breaking at OPO threshold, and exponential probability amplification of the solution state at above OPO threshold to address this limitation.