No-go theorem for one-way quantum computing on naturally occurring two-level systems

Abstract

The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin-5/2 and spin-3/2 systems. It is, of course, desirable to have a natural resource state in a spin-1/2, that is, qubit system. Here, we give a negative answer to this question for frustration-free systems with two-body interactions. In fact, it is shown to be impossible for any genuinely entangled qubit state to be a nondegenerate ground state of any two-body frustration-free Hamiltonian. What is more, we also prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states. In other words, there cannot be any interesting entanglement features in the ground state of such a qubit Hamiltonian.