Because privacy problems with big data impede progress at all phases of the pipeline that can create value from data, Alice and Bob have to perform private queries in order to obtain the private comparison results of big data. Suppose that the cloud devices are with the capacity of conventional and quantum computation, an efficient quantum private comparison protocol with ring-trip transmission by safe cloud quantum computing in the quantum Internet is proposed. Two participant parties Alice and Bob, with the help of a semi-trusted third party and cloud device by simple quantum measurements and mathematical operation, can compare the equality of their secret information without revealing the content of secret information. We show that our protocol can resist the eavesdropper Eve's intercept-resend attack, entangle-measure attack, and Trojan horse attack to cloud device, participant's intercept-measure-resend attack, and third party's attack. The qubit efficiency of our protocol approaches to 100%. We also analyze the connection between Eve's obtained information and the fidelity of secret information in detail.