Catalytic Transformation from Computationally Universal to Strictly Universal Measurement-Based Quantum Computation

Abstract: There are two types of universality in measurement-based quantum computation (MBQC): ${\it strict}$ and ${\it computational}$. It is well known that the former is stronger than the latter. We present a method of transforming from a certain type of computationally universal MBQC to a strictly universal one. Our method simply replaces a single qubit in a resource state with a Pauli-$Y$ eigenstate. We applied our method to show that hypergraph states can be made strictly universal with only Pauli measurements, while only computationally universal hypergraph states were known.