Quantum Measurements and Universal Computation

Yuki Takeuchi, Tomoyuki Morimae, Masahito Hayashi

Measurement-based quantum computing is one of the most promising quantum computing models. Although various universal resource states have been proposed so far, it was open whether only two Pauli bases are enough for both of universal measurement-based quantum computing and its verification. In this paper, we construct a universal hypergraph state that only requires X and Z-basis measurements for universal measurement-based quantum computing. We also show that universal measurement-based quantum computing on our hypergraph state can be verified in polynomial time using only X and Z-basis measurements. Furthermore, in order to demonstrate an advantage of our hypergraph state, we construct a verifiable blind quantum computing protocol that requires only X and Z-basis measurements for the client.

Gerard J Milburn, Cassius D'Helon

Yuki Takeuchi

There are two types of universality in measurement-based quantum computation (MBQC): strict and 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.

Hans J. Briegel, Dan E. Browne, Wolfgang Dür +2 more

Craig S. Lent

Simon Perdrix, Philippe Jorrand

Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In order to formalize these other forms of computation, while pointing out the role and the necessity of classical control in measurement-based computation, and for establishing a new upper bound of the minimal resources needed to quantum universality, a formal model is introduced by means of Measurement-based Quantum Turing Machines.