constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
quantum algorithms:
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)
Discussion with focus on optimization problems (quantum annealing):
Catherine C. McGeoch, Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice Synthesis Lectures on Quantum Computing doi:10.2200/S00585ED1V01Y201407QMC008))
Tameem Albash, Daniel A. Lidar, Adiabatic Quantum Computing, Rev. Mod. Phys. 90 (2018) 015002 arXiv:1611.04471, doi:10.1103/RevModPhys.90.015002
Erica K. Grant and Travis S. Humble, Adiabatic Quantum Computing and Quantum Annealing doi:10.1093/acrefore/9780190871994.013.32
Atanu Rajak, Sei Suzuki, Amit Dutta, Bikas K. Chakrabarti, Quantum Annealing: An Overview [arXiv:2207.01827]
See also:
References which make explicit that topological quantum computation with anyons is a form of adiabatic quantum computation:
Daniel P. Arovas, Robert Schrieffer, Frank Wilczek, Anthony Zee, Statistical mechanics of anyons, Nuclear Physics B 251 (1985) 117-126 (reprinted in Wilczek 1990, p. 173-182) doi:10.1016/0550-3213(85)90252-4
Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang, pp. 6 of Topological quantum computation, Bull. Amer. Math. Soc. 40 (2003), 31-38 (arXiv:quant-ph/0101025, doi:10.1090/S0273-0979-02-00964-3, pdf)
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, §II.A.2 (p. 6) of: Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys. 80 1083 (2008) arXiv:0707.1888, doi:10.1103/RevModPhys.80.1083
Meng Cheng, Victor Galitski, Sankar Das Sarma, Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors, Phys. Rev. B 84 (2011) 104529 arXiv:1106.2549, doi:10.1103/PhysRevB.84.104529
Chris Cesare, Andrew J. Landahl, Dave Bacon, Steven T. Flammia, Alice Neels, Adiabatic topological quantum computing, Phys. Rev. A 92 (2015) 012336 arXiv:1406.2690, doi:10.1103/PhysRevA.92.012336
Tudor D. Stanescu, p. 321 of: Introduction to Topological Quantum Matter & Quantum Computation, CRC Press 2020 (ISBN:9780367574116)
Yafis Barlas, Emil Prodan, Topological braiding of non-Abelian mid-gap defects in classical meta-materials, Phys. Rev. Lett. 124 (2020) 146801 arXiv:1903.00463, doi:10.1103/PhysRevLett.124.146801
Last revised on July 6, 2022 at 03:23:10. See the history of this page for a list of all contributions to it.