Symmetry protected measurement-based quantum computation in finite spin chains

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order and their usefulness as resources for measurement-based quantum computation (MBQC). It is known that SPT phases (applicable to infinite spin chains) protected by a finite abelian symmetry group exhibit uniform computational power. In this work, we extend these ideas to finite spin chains which are more realistic resources for physical computation. Herein, we relate the usefulness of MBQC resource states to a non-vanishing string-order parameter. Furthermore, using the techniques developed, we show that hard-to-think-about regimes of computation are actually more efficient than the textbook prescription. Our results strengthen the connection between condensed matter and quantum computation and also provide the necessary tools to explore such connections in the state-of-the-art noisy small quantum devices. As an outlook, we discuss how this newly developed formalism can potentially be used to identify non-traditional resource states for MBQC and be extended to higher dimensions, leading to universal quantum computation.Science, Faculty ofPhysics and Astronomy, Department ofGraduat