  Recently, there are more and more organizations offering quantum-cloud
services, where any client can access a quantum computer remotely through the
internet. In the near future, these cloud servers may claim to offer quantum
computing power out of reach of classical devices. An important task is to make
sure that there is a real quantum computer running, instead of a simulation by
a classical device. Here we explore the applicability of a cryptographic
verification scheme that avoids the need of implementing a full quantum
algorithm or requiring the clients to communicate with quantum resources. In
this scheme, the client encodes a secret string in a scrambled IQP
(instantaneous quantum polynomial) circuit sent to the quantum cloud in the
form of classical message, and verify the computation by checking the
probability bias of a class of output strings generated by the server. 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 $2.5\%$ 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.
