nLab adiabatic quantum computation




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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)




  • Andrew Childs, Overview of adiabatic quantum computation, talk at CIFAR Workshop on Quantum Information Processing (2013) [pdf, pdf]

On robustness of adiabatic quantum computation (such as against decoherence):

In optimization – quantum annealing

Review with focus on optimization problems (quantum annealing):

See also:

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

On adiabatic quantum computation combined with parameterized quantum circuits:

  • Ioannis Kolotouros, Ioannis Petrongonas, Miloš Prokop, Petros Wallden, Adiabatic quantum computing with parameterized quantum circuits [arXiv:2206.04373]

Geometric phase gates, holonomic quantum computation

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

In topological quantum computation

References which make explicit that topological quantum computation by braiding of anyon worldlines is a form of adiabatic quantum computation:

Last revised on July 25, 2023 at 07:28:31. See the history of this page for a list of all contributions to it.