Artificial bee colony (ABC) algorithm is a swarm intelligence optimization algorithm inspired by the intelligent behavior of honey bees when searching for food sources. The various versions of the ABC algorithm have been widely used to solve continuous and discrete optimization problems in different fields. In this paper a new binary version of the ABC algorithm inspired by quantum computing, called binary quantum-inspired artificial bee colony algorithm (BQIABC), is proposed. The BQIABC combines the main structure of ABC with the concepts and principles of quantum computing such as, quantum bit, quantum superposition state and rotation Q-gates strategy to make an algorithm with more exploration ability. The proposed algorithm due to its higher exploration ability can provide a robust tool to solve binary optimization problems. To evaluate the effectiveness of the proposed algorithm, several experiments are conducted on the 0/1 knapsack problem, Max-Ones and Royal-Road functions. The results produced by BQIABC are compared with those of ten state-of-the-art binary optimization algorithms. Comparisons show that BQIABC presents the better results than or similar to other algorithms. The proposed algorithm can be regarded as a promising algorithm to solve binary optimization problems.