The answer is “lots”! This vegetable is eaten quite commonly in Asia – in some countries it is almost like the Iceberg lettuce or romaine lettuce of the West, but cooked. It has also been studied some in research circles, but mostly in Asia.
Since sweet potato leaves are considered a type of dark green leafy vegetable, they are a great vegetable choice. The consumption of dark green leafy vegetables (like kale, collard greens, spinach etc.) has been associated with heart health and reduced cancer risk in epidemiological studies.
The sweet potato leaf contains quite an array of nutrients, although most in very very small amounts. These macronutrients and micronutrients are: carbohydrate, protein, fiber, calcium, iron, magnesium, phosphorus, potassium, sodium, zinc, vitamin C, B vitamins (thiamin, riboflavin, niacin, vitamin B6, folate), vitamin A, vitamin E, vitamin K, and a good range of fatty acids (saturated fatty acids, mono unsaturated fatty acids, polyunsaturated fatty acids). Vitamins A, E, C are considered antioxidants which are good for health.
If you were to eat 1 cup cooked (steamed, without salt) of sweet potato leaves (64 grams in weight), it would provide you roughly 1.2 g of fiber, 200 mg of potassium, 1881 international units of vitamin A, 69.5 µg of vitamin K, and very very tiny amounts of the other nutrients. Note that quite a few different kinds and varieties of sweet potato and sweet potato leaves exist, so there can be some slight differences in nutritional content and results from research depending on the specific kind of sweet potato leaf studied. However, there isn’t much difference in the nutrient value between cooked and raw versions of sweet potato leaves, so feel free to consume these as part of salads, stirfried with garlic, sautéed, steamed or even cooked then pureed for your little one!
(Source: USDA National Nutrient Database for Standard Reference. http://ndb.nal.usda.gov/)