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This paper proposes a new binary particle swarm optimization (BPSO) approach inspired by quantum computing, namely quantum-inspired BPSO (QBPSO). Although BPSO-based approaches have been successfully applied to the combinatorial optimization problems in various fields, the BPSO algorithm has some drawbacks such as premature convergence when handling heavily constrained problems. The proposed QBPSO combines the conventional BPSO with the concept and principles of quantum computing such as a quantum bit and superposition of states. The QBPSO adopts a Q-bit individual for the probabilistic representation, which replaces the velocity update procedure in the particle swarm optimization. To improve the search capability of the quantum computing, this paper also proposes a new rotation gate, that is, a coordinate rotation gate for updating Q-bit individuals combined with a dynamic rotation angle for determining the magnitude of rotation angle. The proposed QBPSO is applied to unit commitment (UC) problems for power systems which are composed of up to 100-units with 24-h demand horizon.