Sprecher
Beschreibung
Projected entangled pair states (PEPs) describe area law states that are believed to be ground states of gapped Hamiltonians in 2 and higher dimension. I will present a few results concerning a class of PEPs which additionally satisfy an injectivity condition - these PEPs can describe states that are not topologically ordered but are still ground states of gapped local Hamiltonians. First, I will show that all such PEPs can be prepared with polylog(N) depth geometrically local circuits from a trivial product state: In addition to providing a state-preparation algorithm, this provides the first formal proof that injective PEPs with gapped parent Hamiltonian are in the same phase as a product state. Next, I will consider certain simple dissipative strategies to prepare these PEPs and provide results on how a rapid-mixing dissipative algorithm with several rigorous guarantees can be devised to prepare these PEPs.