Zero-knowledge proofs for QMA have first been studied in a work of Broadbent et al (FOCS'16). There, the authors show that any language in QMA has an (interactive) zero-knowledge proof. In this talk, I will describe a way to remove interaction, at the cost of adding an instance-independent preprocessing step. Assuming LWE is hard for quantum computers, the resulting protocol is a non-interactive zero-knowledge argument for QMA, with a preprocessing step that consists of (i) the generation of a CRS and (ii) a single (instance-independent) quantum message from the verifier to the prover.

This is based on joint work with Thomas Vidick and Tina Zhang