Experimental cryptographic verification for near-term quantum cloud computing

An important task for quantum cloud computing is to make sure that there is a real quantum computer running, instead of classical simulation. Here we explore the applicability of a cryptographic verification scheme for verifying quantum cloud computing. We provided a theoretical extension and implemented the scheme on a 5-qubit NMR quantum processor in the laboratory and a 5-qubit and 16-qubit processors of the IBM quantum cloud. We found that the experimental results of the NMR processor can be verified by the scheme with about 1.4% error, after noise compensation by standard techniques. However, the fidelity of the IBM quantum cloud is currently too low to pass the test (about 42% error). This verification scheme shall become practical when servers claim to offer quantum-computing resources that can achieve quantum supremacy.