For his popular ballets and concertos, check commercial editions (Boosey & Hawkes, Sikorski, or Russian publishers) or library subscriptions.
Here is the text you can use for a search or reference regarding on IMSLP (International Music Score Library Project / Petrucci Music Library): Khachaturian on IMSLP khachaturian imslp
As of my last update, IMSLP contains several works by (1903–1978), though the collection is not complete due to copyright restrictions in some countries. For his popular ballets and concertos, check commercial