This is a particular instance of the functionality [link to secure delegated computation] running between two parties, a client and a server, where the server is quantum (so the computation is run quantumly), and the client is either classical or has very limited quantum resources [1]. 
Here, the important aspect is that a quantum server is, in general, capable of performing functionalities that are beyond the computational power of any efficient classical client, and the problem of verifiability, in the presence of an untrusted server, becomes crucial.

This is a specific instance of the secure delegated computation functionality, with the property of verifiability for quantum computation. As such, even though the broader classical functionality exists, this specific instance is inherently a “quantum” functionality.

The primary real-world motivation for Verifiable Delegated Quantum Computation (VDQC) is to enable a user to verify the correctness of a quantum computation performed by a remote quantum server. In practice, access to quantum hardware today is almost exclusively through cloud-based platforms, and users typically do not control the underlying physical device. This creates a fundamental trust gap: a user cannot easily tell whether the quantum server has performed the intended quantum computation correctly, or at all, especially when malicious or dishonest behaviour (e.g., simulating results classically) is possible.

VDQC provides the only known cryptographic solution to establish trust in such settings, allowing a user (who may be fully classical or have minimal quantum capabilities) to certify the correctness of the computation without needing to reproduce it themselves. In addition to detecting malicious behaviour, VDQC protocols can also identify non-malicious deviations, such as errors due to quantum noise or imperfect implementations, making it valuable for both security and fault diagnosis in near-term quantum systems.

The main properties of this functionality include:

Correctness: If Client and Server are honest and follow the protocol, the outcome will be correct.
Security against malicious server: It should either be robust against deviations of the malicious server or any malicious behaviours from the server should be detected.
Verifiability: The client should be able to check the correctness of the computation’s outcome, with their limited capability (related to the security)
Universality: The universality guarantees that the server is capable of running any general quantum computation in this setup without requiring prior knowledge of the specific subset.
Blindness: Any protocol having this property should not reveal any information about the outcome or the delegated computation to the server.
Client’s capability: The client can be classical or partially quantum (preferably only be able to prepare or measure single qubits)

1. Fitzsimons, Joseph F., and Elham Kashefi. “Unconditionally verifiable blind quantum computation.” Physical Review A 96, no. 1 (2017): 012303.