A computer with input and output, yes. Some representation of relevant neurotransmitters and sensory inputs and such seems necessary. Think whole brain emulation, rather than extracting the "mind information" while ignoring all the physical information.
And if I make 100 copies of this computer program and run them on 100 different computers, which one will I be aware is me? Or will I just be aware of being 100 different beings at once? I think it should be obvious that a simulation of reality is not the same thing as reality itself. For one thing, perhaps we need to know a lot more about how the universe works at the quantum level to even emulate reality faithfully.
They are all you, until they start reacting differently to their different inputs and anything stochastic within their simulation, and at which point they stop being "the same" you is basically up to you. The difference between them after a minute or two would probably be nothing compared to the difference between you and you a year ago; if you call the latter "you", the former should probably count too. You wouldn't be aware of being 100 beings, but 100 yous would be aware of existing.
Calculating down to the quantum level is hopefully not necessary (that seems impossible to get efficiently out of any computing substrate physics will let us have). The few people suggesting that physics at that scale impacts consciousness aren't taken very seriously by neuroscientists in general.
