Sony has said today that PS Classics support will be added to Vita via the systems version 1.8 firmware update. Although this was previously announced, this is the first time that Sony has mentioned the firmware by number.
Firmware version 1.8 firmware update was mentioned during Sonys announcement of the PlayStation 2 Game Archives service for PlayStation 3 which hits Japan soon the latter is already available in the US and Europe.
There is currently no date for PS Vita Firmware V1.8 other than Summer.
(Sorry if old)