This paper proposed a quantum bald eagle brainstorm (QBBSO) based on quantum initialization and combined with the bald eagle optimization algorithm in light of the original Brain Storm Optimization (BSO) algorithmβs strong local search ability, which would result in local optimization, a poor optimization effect, and difficult development. To accomplish the randomness of the number and increase the randomness of the population, we first modified the initialization method of the original brainstorming population, introduced the idea of quantum code, and then translated the binary numbers 0 and 1 to the decimal number. To achieve the best outcome, the original step size formula was employed for global selection, local search, and final selection using the vulture search method. The original BSO was then optimized to attract more global individuals. The algorithm versions were compared using the common benchmark function test. The findings demonstrated that QBBSO had a greater capacity for global search and a faster convergence speed. This research also applied the QBBSO algorithm to the long-term and short-term memory network (LSTM) to forecast the NOx concentration in the boiler, further demonstrating the algorithmβs superiority in real-world settings.