Verification of colorable hypergraph states with stabilizer test

Abstract

Many-body quantum states, as a matter of fact, are extremely essential to solve certain mathematical problems or simulate quantum systems in measurement-based quantum computation. However, how to verify large-scale quantum states, such as hypergraph states, is an exceedingly hard task for many-body quantum systems. Here, we propose a novel fault-tolerant solution for the verification of colorable hypergraph states by using the stabilizer test. Furthermore, our protocol is dramatically facilitated by making only Pauli-X and Pauli-Z measurements. For geometric structure hypergraph states, the computational complexity of our protocol is polynomial. As to appliance, it will be also applied to blind quantum computing based on the no-signaling principle.