Quantum Optics Seminar: Adiabatic preparation of symmetry-protected topological phases

Zhi-Yuan Wei (MPQ):
We study the adiabatic preparation of various paradigm states in SPT phases using the algorithm in Ref. [1].

October 22, 2021

Zhi-Yuan Wei (MPQ)
Group seminar (hybrid format: Zoom/seminar room B2.46)
Fri, 22. October, 14:30 pm (MEZ)

Abstract:

We study the adiabatic preparation of various paradigm states in SPT phases using the algorithm in Ref. [1]. First, we show the 1D AKLT state of N particles can be prepared under an adiabatic dynamics of time T=O[polylog(N)], and the Hamiltonian for this dynamics can further be replaced by its local and commuting version [1]. This allows us to further construct a low-depth local circuit to prepare it with high precision.
Then, by studying the preparation of various MPS in the interpolation path between the cluster state and the GHZ state [2], we show the state preparation time T is strongly influenced by the correlation length, i.e. it takes longer to prepare states with longer correlation lengths.
In the end, we show some ongoing effort toward the efficient preparation of the 2D AKLT state in the honeycomb lattice [3], which is a universal resource for measurement-based quantum computation.
[1] Y. Ge et al., PRL 116, 080503 (2016)
[2] M. M. Wolf et al., PRL 97, 110403 (2006)
[3] I. Affleck et al., Phys. Rev. Lett. 59, 799 (1987) , Tzu-Chieh Wei et al., PRL 106, 070501 (2011)

Anyone interested in discussing or chatting, can join the meeting half an hour earlier, at 14:00.