The traditional definition of quantum zero-knowledge stipulates that the knowledge gained by any quantum polynomial-time verifier in an interactive protocol can be simulated by a quantum polynomial-time algorithm. One drawback of this definition is that it allows the simulator to consume significantly more computational resources than the verifier. We argue that this drawback renders the existing notion of quantum zero-knowledge not viable for certain settings, especially when dealing with near-term quantum devices. In this work, we initiate a fine-grained notion of post-quantum zero-knowledge that is more compatible with near-term quantum devices. We introduce the notion of \((s,f)\) space-bounded quantum zero-knowledge. In this new notion, we require that an s-qubit malicious verifier can be simulated by a quantum polynomial-time algorithm that uses at most \(f(s)\) -qubits, for some function \(f(\cdot )\) , and no restriction on the amount of the classical memory consumed by either the verifier or the simulator. We explore this notion and establish both positive and negative results: