I will first review the measurement-based quantum computation with a two-dimensional cluster model and demonstrate its ability to do universal quantum computation. Then I will review the ground state of the AKLT model as a resource of computation. Finally, I will show that for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase, affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Ref

[1] Computational Power of Symmetry-Protected Topological Phases. (PRL 119, 010504 (2017))

[2] Quantum Computation by Local Measurement. (Annu. Rev. Condens. Matter Phys. 2012. 3:239–61)

[3] Measurement-Based Quantum Computation. (arXiv:2109.10111)