DiVincenzo's criteria for quantum computation are the following:

  1. A scalable physical system with well characterized qubits.
  2. The ability to initialize the state of the qubits to a simple fiducial state.
  3. Long relevant decoherence times.
  4. A “universal” set of quantum gates.
  5. A qubit-specific measurement capability.

Are they satisfied by the D-Wave 2000Q?


This was originally part of this question but is better suited to be a separate question.

First, it is important to note that DiVincenzo's criteria were first published in a February 2000 paper which was a time when circuit-based quantum computing was the only type of quantum computing known to David DiVincenzo. The D-Wave 2000Q does not do circuit-based quantum computing. It solves problems based on the adiabatic quantum computation (AQC) model of quantum computing, which was first introduced in a January 2000 paper. The ~30 days between these two papers, was not enough time for David DiVincenzo to even consider AQC when formulating his criteria. Nevertheless it is still an interesting question to see how the D-Wave 2000Q performs on DiVincenzo's criteria!

  1. A scalable physical system with well characterized qubits.

Yes. This is D-Wave's strongest aspect from a hardware perspective. Their qubits are well characterized and the 2048 qubits in the 2000Q machine is the largest number of qubits out of any programmable device ever to exist. The challenge is more in compiling problems1 into a form that D-Wave can work on efficiently, which is difficult because the gap between the ground state and the first excited state needs to be kept sufficiently large, but this is a software issue and DiVincenzo's criteria are only about hardware.

  1. The ability to initialize the state of the qubits to a simple fiducial state.

Yes. This is easy for D-Wave machines. They initialize the state of the qubits in an equal superposition of all possible states. They do this by applying at time $T=0$ a field in the $x$-direction. The ground state of $X_1 + X_2 + \cdots X_n$ is precisely the equal superposition of all possible states: $\frac{1}{2^n}\left(|00\ldots 00\rangle + |00\ldots 01\rangle +\cdots + |11\ldots 11\rangle\right)$.

  1. Long relevant decoherence times.

Yes. This is where David DiVincenzo would probably have changed his criteria if he knew about AQC. In AQC, coherence times are not as important as in circuit-based quantum computing, see for example this sentence: enter image description here
from Towards a feasible implementation of quantum neural networks using quantum dots1 (please feel free to edit my answer if you know a better reference). Long quantum coherence times are still relevant to AQC, but not as much as in circuit-based quantum computation, and they are not considered to be the limiting factor in the D-Wave 2000Q.

  1. A “universal” set of quantum gates.

NO. First of all, the 2000Q is not a gate-based quantum machine, so this question is another criterion that would have been phrased differently if DiVincenzo wrote his paper a few years later after learning about AQC. However the word "gate" can be replaced by "Hamiltonian" and this question would still make perfect sense.

The answer to the modified criterion would still be no, because the 2000Q can only implement Hamiltonians for the form $Z_i$ and $Z_iZ_j$. D-Wave does have a universal quantum computer but it is not the D-Wave 2000Q.

  1. A qubit-specific measurement capability.

Yes. Measurements have never been a significant issue for D-Wave machines.


In conclusion, the 2000Q does a good job of satisfying all of DiVincenzo's criteria except for being universal (criterion number 4). The satisfaction of criteria 1 and 3 would ideally be much better (i.e. ideally we would have an even more scalable architecture and even longer coherence times) but the 2000Q satisfies these criteria better than any other hardware currently in existence.

1 Note: I'm an author

  • 1
    (1) When you describe D-WAVE's qubits as well-characterised, why do you link to another question here about D-WAVE, instead of something in the literature, or even something on D-WAVE's website? (2) In your answer about long coherence times, why is the linked-to article about Quantum Neural Networks (and not AQC)? (3) Is there a theoretical reason why AQC would be less susceptible to decoherence than circuits? Isn't this why 'quantum annealing' is a thing (where they still worry about decoherence)? (4) Why is the link to D-WAVE's universal QC another link to a question here? – Niel de Beaudrap Oct 8 at 11:30
  • (1) I actually wrote an answer about the qubits being well characterised, to that question, but it got deleted. (2) the linked paper about QNN's has the sentence "where the coherence requirements are not as strict as in circuit-based QC" ... I agree that a better reference would be nice, and would welcome edits with better references. (3) the theoretical reason is complicated, and perhaps should be asked as a separate question, though answering it might warrant an entire paper. Yes we still need long coherence because otherwise we have to run the annealing schedule faster, and perhaps – user1271772 Oct 8 at 11:36
  • faster than the adiabatic theorem allows, but in general, to satisfy the adiabatic theorem to within the precision required, we can tolerate faster decoherence than in circuit-based quantum computing. (4) The link to D-Wave's universal QC is a link to a question here, because that is maybe the only place where there is evidence of D-Wave having YY coupling? It was a picture from a conference. The material in the talk might not have been published in a paper yet, but hundreds of people were there. – user1271772 Oct 8 at 11:38
  • 1
    I suppose there isn't an enormous amount of discussion about what 'characterised' is intended to mean in this context, but in the context of scalability, what I'd be interested in is not only how qubits are encoded but to what extent the noise processes are understood and how they might be mitigated in principle, because that surely is a prerequisite to be scalable. I could understand a narrower historical meaning of 'characterised' in light of the problems with liquid NMR, but at the moment your answer (the one you point to) is about how they may be used rather than how they're characterised. – Niel de Beaudrap Oct 8 at 12:41
  • 1
    I'm not concerned about the fact that your quote (in support of your coherent times statement) could be confusing. I'm concerned with the fact that it's not a very good statement in support: I wouldn't feel comfortable using ellipses [...] to gloss over the picky parts, and that's basically what you're doing. While I can sympathise with the difficulty of supporting ideas in the folklore (and to be fair you do invite better sources), this citation is not a very good substitute. I think you'd be better off writing a footnote to your answer containing something along the lines of your comment. – Niel de Beaudrap Oct 8 at 12:44

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