The 2D AKLT state is a universal quantum computational resource

Quantum computation promises exponential speedup over classical computation by exploiting the quantum mechanical nature of physical processes [1]. In addition to the standard circuit models, surprisingly, local measurement alone provides the same power of computation, given only a prior sufficiently entangled state [2]. Cluster states are the first known resource states for such measurement-based quantum computation (MBQC) [2, 3]. They can arise as the unique ground state of fivebody interacting Hamiltonian on a square lattice; however, they cannot be the exact unique ground state of any two-body Hamiltonian [4, 5]. Fundamentally, could there be unique ground states of any two-body interacting Hamiltonian that are universal resources? In searching for such resourceful ground states of physically reasonable Hamiltonians, Chen et al. made some important progress by constructing a spin-5/2 resourceful state on a honeycomb lattice, which is an unique ground state of a two-body interacting Hamiltonian [6]. Later Cai et al. approached this issue by patching ground states of Affleck-Kennedy-Lieb-Tasaki (AKLT) chains [7] into an effective 2D spin-3/2 state [8]. This construction reduced the local Hilbert-space dimension from 6 of Chen et al. to 4. However, both engineered Hamiltonians, even though consisting of only two-body interaction, turn out be complicated and possess less symmetry than the original AKLT Hamiltonians. After many works on utilizing AKLT chains for quantum computation [9–11], it remains open whether any of the original 2D AKLT states can be universal resources for MBQC.