As I posted before in: How long after Europeans discovered America did stuff like potatoes, yams and tomatoes start showing up in "The Far East"?, the cultivation of Potatoes had already been introduced in Japan during Edo Period (1603-1868).
While the old Japanese name of potato (Jagatara Imo) is said to derive from the name of Jakarta, Indonesia (thus a Dutch colony), however, we are not sure where the Dutch merchants really brought these plant to these plants at first around 1600, a customarily date of the first arrival of potato in Japan.
The cultivation of potato was gradually spread mainly in the eastern and northern part of Japan by the end of the 18th century, mainly thanks for repeated famines in the middle to late Edo period (18th and 19th centuries), though sweet potatoes, probably also introduced to southern Japan by way of China and Ryukyu Islands, got popular earlier in the 18th century.