  Ground states of spin lattices can serve as a resource for measurement-based
quantum computation. Ideally, the ability to perform quantum gates via
measurements on such states would be insensitive to small variations in the
Hamiltonian. Here, we describe a class of symmetry-protected topological orders
in one-dimensional systems, any one of which ensures the perfect operation of
the identity gate. As a result, measurement-based quantum gates can be a robust
property of an entire phase in a quantum spin lattice, when protected by an
appropriate symmetry.
