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There are different theoretical models for quantum computing like the circuit model or the model of adiabatic quantum computers.

Between which of these models exist polynomial-time reductions?

Note that this question does not aim to cover physical implementations of quantum computers which are already discussed here.


marked as duplicate by Niel de Beaudrap, bytebuster, u32i64, Discrete lizard, ItamarG3 Apr 2 '18 at 8:55

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A non-exhaustive list of theoretical models of quantum computation are provided as answers to another question: "What are the methods of quantum computation?".

As to which models are polynomial-time equivalent — the following is an incomplete list of models which are provably universal for polynomial-time quantum computation, assuming perfect control:

  • The unitary circuit model is polynomial-time equivalent to adiabatic quantum computation [arXiv:quant-ph/0405098];
  • The unitary circuit model is polynomial-time equivalent to quantum circuits with intermediate measurements (by the principle of deferred measurement);
  • The one-way measurement-based model is polynomial-time equivalent to unitary circuits.

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