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This paper proposes a reduced-complexity partial transmit sequences (PTS) approach based on the quantum-inspired evolutionary algorithm (QEA) for the reduction of peak-to-average power ratio (PAPR) in an orthogonal frequency division multiplexing (OFDM) system. The conventional PTS technique improves the PAPR statistics for OFDM signals, but the considerable computational complexity for an exhaustive search over all combinations of allowed phase factors is a potential problem for practical implementation. To reduce the computational complexity while still obtaining the desirable PAPR reduction, we introduce the QEA, an effective algorithm that solves various combinatorial optimization problems, to search the optimal phase factors. The simulation results show that the proposed QEA achieves significant PAPR reduction with low computational complexity.