Parity Quantum Computing as yz-Plane Measurement-Based Quantum Computing.

We show that universal parity quantum computing employing a recently introduced constant depth decoding procedure is equivalent to measurement-based quantum computation (MBQC) on a bipartite graph using only yz-plane measurements. We further show that any unitary MBQC using only yz-plane measurements must occur on a bipartite graph. These results have a number of consequences and open new research avenues for both frameworks.

Computationally Universal Phase of Quantum Matter.

We provide the first example of a symmetry protected quantum phase that has universal computational power. This two-dimensional phase is protected by one-dimensional linelike symmetries that can be understood in terms of the local symmetries of a tensor network. These local symmetries imply that every ground state in the phase is a universal resource for measurement-based quantum computation.