Life after death for quantum computers?

With an artificial intelligence program run on a quantum computer the processing (thinking) takes place either in computers in Everett's many worlds or else in the many dimensional Hilbert space. (see my blog of 13 Oct. 2015 and Bull. Am. Phys. Soc., March, 2016) If the computer in our world were destroyed while the program was running wouldn't the processing continue in other worlds? (But not forever.)