Abstract This paper proposes an evolutionary computing method called quantum buzzard optimization algorithm (QBUZO). The QBUZO algorithm is a modification of the BUZO algorithm based on quantum system. In quantum, the particle can be represented by its instantaneous motion and the energy of its wave function. In QBUZO, each particle is defined with quantum state in this system and is established with a wave function instead of the position and capability vector in BUZO algorithm. The idea is to allow all particles to have quantum behavior instead of the classical Newtonian random motion. We present the individual particle of a BUZO system moving in quantum multidimensional space, and create a quantum delta potential well model for BUZO. The effectiveness of QBUZO is demonstrated by experimental results on some benchmark mathematical functions in optimization. The comparison of performances with six other optimization algorithms represents that QBUZO is superior to other algorithms.