  We present the first non-interactive zero-knowledge argument system for QMA
with multi-theorem security. Our protocol setup constitutes an additional
improvement and is constructed in the malicious designated-verifier (MDV-NIZK)
model (Quach, Rothblum, and Wichs, EUROCRYPT 2019), where the setup consists of
a trusted part that includes only a common uniformly random string and an
untrusted part of classical public and secret verification keys, which even if
sampled maliciously by the verifier, the zero knowledge property still holds.
The security of our protocol is established under the Learning with Errors
Assumption. Our main technical contribution is showing a general transformation
that compiles any sigma protocol into a reusable MDV-NIZK protocol, using NIZK
for NP. Our technique is classical but works for quantum protocols and allows
the construction of a reusable MDV-NIZK for QMA.
