Characterizing measurement-based quantum gates in quantum many-body systems using correlation functions

In measurement-based quantum computation (MBQC), local adaptive measurements are performed on the quantum state of a lattice of qubits. Quantum gates are associated with a particular measurement sequence, and one way of viewing MBQC is that such a measurement sequence prepares a resource state suitable for `gate teleportation'. We demonstrate how to quantify the performance of quantum gates in MBQC by using correlation functions on the pre-measurement resource state.