Are there any algorithms or logical operations which are only unique to topological quantum computing architecture ?
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"Are there any algorithms or logical operations which are only unique to topological quantum computing architecture?"
No.
Any "universal" quantum computer that is capable of executing a universal set of quantum gates has essentially the capabilities of a "quantum Turing machine" if given enough qubits and time. This is true whether the qubits are spins in nitrogen atoms, or atoms in an ion trap, or topological qubits, or any other "implementation" of quantum computing.
One might ask, where could you have found this answer yourself?
In the Topological quantum computer Wikipedia page, the section titled "Topological vs. standard quantum computer" opens with the following sentences:
"Topological quantum computers are equivalent in computational power to other standard models of quantum computation, in particular to the quantum circuit model and to the quantum Turing machine model.[10] That is, any of these models can efficiently simulate any of the others."
answered Mar 20 at 10:27
user1271772 No more free timeuser1271772 No more free time
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2$\begingroup$ Thanks @MarkSpinelli. If the question didn't get a negative score, it would have become a "hot network question" because my answer came within 8 hours and got a couple upvotes so quickly. I think it was a reasonable question for a beginner that doesn't know about the quantum equivalent of a Turing machine, because some algorithms such as for evaluating a Jones polynomial, are more "natural" to perform on topological quantum computers than other types of quantum computers (but any universal quantum computer can still execute the algorithm). $\endgroup$ Commented Mar 20 at 18:24
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1$\begingroup$ Well one of the reason I asked the question, because I read somewhere about fusion and Braiding gates. I thought they are not implementable on conventional qc and moreover would provide some advantage somewhere. Anyway I don't care about negative score. $\endgroup$ Commented Mar 20 at 18:59
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2$\begingroup$ The question is not unreasonable and I can't figure out the +2/-3 votes. Then again, we are often rightly counseled not to respond to earnestly asked questions with something as simple as "have you bothered to look at Wikipedia?" I thought the framing of your answer, especially w.r.t. Wikipedia, did a great job of being helpful and of not being snarky or belittling. $\endgroup$ Commented Mar 20 at 19:01
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$\begingroup$ @ChetanWaghela I think the question might have profited from adding a tiny bit more details/context, even if just another two sentences. $\endgroup$ Commented Mar 21 at 6:41