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QI: Fachverband Quanteninformation
QI 15: Quantum Computing Theory
QI 15.1: Invited Talk
Wednesday, March 20, 2024, 09:30–10:00, HFT-FT 101
Computationally Universal Phases of Quantum Matter — •Robert Raussendorf1, Cihan Okay2, Dongsheng Wang3, David Stephen4, and Hendrik P Nautrup5 — 1Leibniz Universtät Hannover — 2Bilkent University Ankara, Turkey — 3Chinese Academy of Sciences, China — 4University of Colorado, Boulder, USA — 5University of Innsbruck
In measurement based quantum computation, the computational power hinges on the resource quantum state. Some states give universal computational power, but most states provide no computational power at all [1]. This picture changes in the presence of symmetry. Namely, for phases of ground states of symmetric Hamiltonians, i.e., symmetry-protected topological (SPT) phases, it has been found that computational power is uniform across those phases. This observation gave rise to the term `computational phases of quantum matter* [2,3]. In my talk, I give a short history of this line of research, and then present examples of symmetry protected quantum phases that have universal computational power [4 - 6].
[1] D. Gross, S. T. Flammia, and J. Eisert, PRL 102, 190501 (2009).
[2] A. C. Doherty and S. D. Bartlett, PRL 103, 020506 (2009).
[3] A. Miyake, Phys. Rev. Lett. 105, 040501 (2010).
[4] R. Raussendorf et al., Phys. Rev. Lett. 122, 090501 (2019).
[5] D.T. Stephen et al., Quantum 3, 142 (2019).
[6] A.K. Daniel, R.N. Alexander, A. Miyake, Quantum 4, 228 (2020).
Keywords: symmetry protected topological order; measurement based quantum computation; computational phases of quantum matter