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As I understand it, quantum circuits as a model are equivalent to quantum Turing machines, or at least they can be simulated on each other.

So my question is, why have quantum circuits become the chosen implementation rather than quantum Turing machines, such as in the IBM Q?

Is it related to entanglement and reversible gates? I wondered if quantum Turing machines could not take full advantage of entanglement.

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    $\begingroup$ In short: quantum circuits are easier to comprehend than Turing machines. Similar to why programmers don't code in machine language. Re: "I wondered if quantum Turing machines could not take full advantage of entanglement."...that doesn't make much sense as the two models are equivalent. $\endgroup$ – S.D. May 9 '19 at 11:00
  • $\begingroup$ [cont.] You might be interested in John Watrous' answer to In a Quantum Turing Machine, how is the decision to move along the memory tape made?. $\endgroup$ – S.D. May 9 '19 at 14:42
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I've popped up here 7 months too late but in response to the question here's my short-ish answer: Quantum Turing machines are physically unreasonable. Prof. Peter Shor originally wrote his factoring algorithm using a Turing machine and so from a theoretical perspective they work just fine. However, it requires the tape heads to be entangled, which is why you couldn't realistically make it work. The Circuit model (which has been around longer than Turing machines) also has it's own problems which is why Turing needed his machine. One main reason (there are others) is that circuits are designed for a given input size whereas Turing machines are independent of input size. Therefore the circuit model is better suited to quantum computation as it is a more realistic reflection of the devices we could build.

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