1. Combine first 4 ingredients. Rub rosemary mixture over duck. Cover and chill 1 hours. Rinse duck with cold water, pat dry.
2. Heat oil in a large nonstick skillet over medium-high heat. Add duck, cook for 5 minutes on each side or until done. Remove from pan, and let stand for 10 minutes.
3. Combine granulated sugar and vinegar in a small saucepan, and bring to a boil. Cook until thick and amber-colored (about 5 minutes). Add apricots. Reduce heat, and cook 1 minute or until apricots begin to soften. Cut duck diagonally across the grain into slices, arrange on serving plates.