Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements

Yuki Takeuchi,Masahito Hayashi,Tomoyuki Morimae

doi:10.1038/s41598-019-49968-3

Abstract

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.

Highlights

Quantum computing is believed to solve several problems faster than classical computing[1,2,3]
In order to demonstrate an advantage of our hypergraph state, we propose a verifiable blind quantum computing (VBQC) protocol in which the client only needs X and Z-basis measurements
As the main result, we construct the universal hypergraph state that enables universal quantum computing with X and Z-basis measurements

Summary

Introduction

Quantum computing is believed to solve several problems faster than classical computing[1,2,3]. In MBQC, quantum computing proceeds via adaptive single-qubit measurements on a highly entangled state, a so-called universal resource state. This important advantage of MBQC, namely, the fact that all multi-qubit operations can be done offline, fits MBQC to several physical systems such as photons[9,10], cold atoms[11], ion traps[12], and superconducting circuits[13]. We can see that except for the Mølmer-Sørensen graph state[15], all previous universal resource states in Table 1 need at least three measurement bases. The Mølmer-Sørensen graph state is, on the other hand, not known to be efficiently verifiable using only Pauli-X and Z basis measurements.

Methods

Results

Conclusion