  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 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.
