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Comment by thesz | Hacker News Reader

The difference is quantum oracles can be constructed [1] and Turing oracle can't be [2]: "An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939)."

  [1] https://arxiv.org/abs/2303.14959
  [2] https://en.wikipedia.org/wiki/Turing_machine

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This is meaningless. A Turing machine is defined in terms of state transitions. Between those state transitions, there is a pause in computation at any point where the operations takes time. Those pauses are just not part of the definition because they are irrelevant to the computational outcome.

And given we have no evidence that quantum oracles exceeds the Turing computable, all the evidence we have suggests that they are Turing machines.

  > This is meaningless.

Turing machines grew from the constructive mathematics [1], where proofs are constructions of the objects or, in other words, algorithms to compute them.

  [1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)#Constructive_mathematics

Saying that there is no difference between things that can be constructed (quantum oracles) and things that are given and cannot be constructed (Turing oracles - they are not even machines of any sort) is a direct refutation of the very base of the Turing machine theoretical base.

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