We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming:

* The quantum hardness of learning with errors (LWE).
* Post-quantum indistinguishability obfuscation for emph{classical} circuits.
* A notion of “dual-mode” classical verification of quantum computation (CVQC).

We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM).

Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.

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