# Does the D-Wave 2000Q satisfy DiVincenzo's criteria?

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:
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