Contents

### Context

#### Computation

intuitionistic mathematics

# Contents

## Idea

By adiabatic quantum computation one means models of quantum computation on parameterized quantum systems where the quantum gates are unitary transformations on a gapped (and possibly topologically ordered) ground state which are induced, via the quantum adiabatic theorem, by sufficiently slow movement of external parameters.

Often the term adiabatic quantum computation is used by default for optimization problems (“quantum annealing”, see the references below).

On the other hand, the possibly most prominent example of adiabatic quantum computation is often not advertized as such (but see CLBFN 2015), namely topological quantum computation by adiabatic braiding of defect anyons (whose positions is the external parameter, varying in a configuration space of points). This is made explicit in Freedman, Kitaev, Larsen & Wang 2003, pp. 6; Nayak, Simon, Stern & Freedman 2008, §II.A.2 (p. 6); and Cheng, Galitski & Das Sarma 2011, p. 1; see also Arovas, Schrieffer, Wilczek & Zee 1985, p. 1 and Stanescu 2020, p. 321; Barlas & Prodan 2020.

The following graphics shows this with labelling indicative of momentum-space anyons:

(graphics from SS22)

## References

### In optimization – quantum annealing

Review with focus on optimization problems (quantum annealing):

Proof that quantum annealing is universal for quantum computation:

A more high-brow mathematical desription via “tangle machines”:

### Geometric phase gates

References which consider quantum gates operating by (nonabelian) geometric Berry phases due to adiabatic parameter movement:

### In topological quantum computation

Specifically, references which make explicit that topological quantum computation with anyons is a form of adiabatic quantum computation:

Last revised on November 19, 2022 at 12:33:31. See the history of this page for a list of all contributions to it.