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Logic synthesis of reversible circuits has received considerable attention in the light of advances recently made in quantum computation. Implementation of a reversible circuit is envisaged by deploying several special types of quantum gates, such as k-CNOT. Although the classical stuck-at fault model is widely used for testing conventional CMOS circuits, new fault models, namely single missing-gate fault (SMGF), repeated-gate fault (RGF), partial missing-gate fault (PMGF), and multiple missing-gate fault (MMGF), have been found to be more suitable for modeling defects in quantum k-CNOT gates. This article presents an efficient algorithm to derive an optimal test set (OTS) for detection of multiple missing-gate faults in a reversible circuit implemented with k-CNOT gates. It is shown that the OTS is sufficient to detect all single missing-gate faults (SMGFs) and all detectable repeated gate faults (RGFs). Experimental results on some benchmark circuits are also reported.