# Quantum annealing vs adiabatic quantum computation

I had this impression that quantum annealing is an optimization technique which may or may not produce exact solutions. On the other hand adiabatic quantum computation always gives exact solutions when it gives a solution. But this D-Wave report says as follows:

D-Wave processors compute by piggybacking on quantum annealing. A quantum annealing processor can be operated as a universal quantum computer. In this regime of operation, the computational model is referred to as adiabatic quantum computation (AQC), which can be thought of as the long-time limit of quantum annealing.

Should I think that adiabatic quantum computation is an application of quantum annealing?

• Doesn't Scott's recent blog post D-Wave: Truth finally starts to emerge answer your question? – Kaveh May 20 '13 at 14:47
• Also have you checked en.wikipedia.org/wiki/Quantum_annealing and en.wikipedia.org/wiki/Adiabatic_quantum_computation? – Kaveh May 20 '13 at 15:09
• Adiabatic quantum computation doesn't necessarily always give an exact solution. Nor, let me note, does conventional digital computation; it depends on the algorithm you're running. The situation in adiabatic quantum computation is similar; it's not an algorithm, it's a computational model. – Peter Shor May 20 '13 at 18:35
• The paper proposed the computational model and the algorithm. Scott clearly means the algorithm by "quantum adiabatic optimization", while your quote from the D-Wave report (whch my comment was responding to) specifically says that "adiabatic quantum computation" is a model. Ideally, one should distinguish the two, but unfortunately "adiabatic quantum computation" is used to refer to both the algorithm and the model. – Peter Shor May 22 '13 at 14:08
• @Omar: I don't believe there are such papers yet. – Peter Shor May 31 '13 at 18:57

Adiabatic quantum computing (AQC) is a computational model (as Peter said in the comments). Compare AQC with other models of computation such as:

1. circuit-based quantum computing (CBQC)
2. Adleman-Lipton model (a model for computing using DNA)
3. Turing machine model (a model where computations are done with symbols on a tape)

One can devise algorithms using the AQC model, such as this algorithm for factoring integers: http://arxiv.org/abs/1411.6758.

Quantum annealing is a physical process which attempts to implement such algorithms. Start with a set of quantum states, and a time-dependent Hamiltonian $H(t)$ such that the ground state of $H(t_F)$ at a final time $t_F$, encodes the solution to your problem. Let the states evolve according to $H(t)$, and hope that in the end one of the candidate states ends up in the ground state of $H(t_F)$.

If you're lucky enough to have a qubit that starts in the ground state of $H(0)$, and $H(0)$ evolves into $H(t_F)$ slowly enough, then according to the "adiabatic theorem", the qubit always remains in the ground state of $H(t)$ for all $t$, and you are guaranteed to get the right answer which is encoded in the ground state of $H(t_F)$. This is what the AQC model has in mind, but since it is experimentally difficult to start in the ground state, we sometimes try to implement AQC algorithms using quantum annealing, which unfortunately might not end up in the ground state.

• New here. I wanted to contribute by editing some questions and leaving some comments, but needed reputation for it, so gave a shot at this answer. – user1271772 Aug 14 '15 at 10:41