Symmetry-protected phases for measurement-based quantum computation

Dominic V. Else, Ilai Schwarz, Stephen D. Bartlett, Andrew C. Doherty

Published 2012-01-23, updated 2012-06-18Version 3

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.