I'll remind you of the quote that started this thread:

"Do quantum computing folks really think that we are borrowing capacity from other universes for these calculations?"

In this context, your opinion and Deutsch's opinion don't matter. The question is about whether the idea is common in the field or not.

Okay. I just don't understand. Are you saying Quantum Computers are also implemented without assuming the computations run in parallel universe?

Correct. The laws of quantum mechanics (used for building quantum computers among other things) make very little assumptions on the nature of the universe, and support multiple interpretations, many-worlds being only one of them.

Quantum mechanics is a tool to calculate observable values, and this tool works very successfully without needing to make strong assumptions about the nature of the universe.

I don't know what he's saying, but I'm saying that the answer to your question is "Yes," unless quantum computers behave differently than expected.