Sequential generation of tensor network states

The sequential generation of tensor network states provides a way to deterministically prepare entangled states on both matter-based and photon-based quantum devices. In this talk, first, we discuss two implementations to sequentially generate photonic matrix product states, one based on a Rydberg atomic array [1], and another based on a microwave cavity dispersively coupled to a transmon [2]. We show both implementations can generate a large number of entangled photons. Then, we introduce plaquette projected entangled-pair states (p-PEPS)[3], a class of states in a lattice that can be generated by applying sequential unitaries acting on plaquettes of overlapping regions. They satisfy area-law entanglement, possess long-range correlations, and naturally generalize other relevant classes of tensor network states. We identify a subclass that can be more efficiently prepared in a radial fashion and that contains the family of isometric tensor network states. We also show how such subclass can be efficiently prepared using an array of photon sources, and devise a physical realization by extending the above cavity-transmon setup [2].

[1] Zhi-Yuan Wei et al., Physical Review Research, 3(2), 023021. 

[2] Zhi-Yuan Wei et al., arXiv:2109.06781

[3] Zhi-Yuan Wei et al., arXiv:2107.05873