Prof. Dr. Robert Raussendorf 
Uni Hannover

Computationally Universal Phases of Quantum Matter

Abstract: Measurement based quantum computation is a scheme of universal quantum computation in which the computational process is driven by measurements alone [1]. No unitary evolution takes place. In fact, the measurements employed are all local, and thus the computational power hinges on the initial quantum state—hence called the resource state.
Some resource states give universal computational power, but most quantum states in Hilbert space provide no computational power at all [2]. 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’ [3,4]. 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 [5 - 7].

Joint work with: Cihan Okay, Dong-Sheng Wang, David T. Stephen, and Hendrik Poulsen Nautrup

[1] R. Raussendorf and H.J.Briegel, Phys. Rev. Lett. 86, 5188 (2001).
[2] D. Gross, S. T. Flammia, and J. Eisert, Phys. Rev. Lett. 102, 190501 (2009).
[3] A. C. Doherty and S. D. Bartlett, Phys. Rev. Lett. 103, 020506 (2009).
[4] A. Miyake, Phys. Rev. Lett. 105, 040501 (2010).
[5] R. Raussendorf et al., Phys. Rev. Lett. 122, 090501 (2019).
[6] D.T. Stephen et al., Quantum 3, 142 (2019).
[7] A.K. Daniel, R.N. Alexander, A. Miyake, Quantum 4, 228 (2020).