Based on SNP-analysis of the Btr1 and BTr2 genes in 529 specimen of barley collected from all over the world, it came out that barley was first cultivated in Mesopotamia about 10.000 years ago and reached Japan via China about 3.000 years ago.
NIAS news release, July 31, 2015
Barley cultivation started 10.000 years ago in the Near East and reached Japan about 3000 years ago: NIAS