If we agree that consciousness is a physical process part of our universe, I think the better and simpler question is whether or not computers can simulate any physical process. Currently quantum processes might still be a frontier but quantum computers and their hardware should allow us to simulate them.

If we can simulate any physical process, it then becomes more philosophical in my opinion. Whether the simulation is the same as the real thing even though it is exactly the same. It becomes the same kind of question then for example whether or not your teleported self is still you after having been dematerialized and rematerialized from different atoms. The answer might be no, but you rematerialized self still definitely thinks it is yourself.