  We construct a classically verifiable succinct interactive argument for
quantum computation (BQP) with communication complexity and verifier runtime
that are poly-logarithmic in the runtime of the BQP computation (and polynomial
in the security parameter). Our protocol is secure assuming the post-quantum
security of indistinguishability obfuscation (iO) and Learning with Errors
(LWE). This is the first succinct argument for quantum computation in the plain
model; prior work (Chia-Chung-Yamakawa, TCC '20) requires both a long common
reference string and non-black-box use of a hash function modeled as a random
oracle.
  At a technical level, we revisit the framework for constructing classically
verifiable quantum computation (Mahadev, FOCS '18). We give a self-contained,
modular proof of security for Mahadev's protocol, which we believe is of
independent interest. Our proof readily generalizes to a setting in which the
verifier's first message (which consists of many public keys) is compressed.
Next, we formalize this notion of compressed public keys; we view the object as
a generalization of constrained/programmable PRFs and instantiate it based on
indistinguishability obfuscation.
  Finally, we compile the above protocol into a fully succinct argument using a
(sufficiently composable) succinct argument of knowledge for NP. Using our
framework, we achieve several additional results, including
  - Succinct arguments for QMA (given multiple copies of the witness),
  - Succinct non-interactive arguments for BQP (or QMA) in the quantum random
oracle model, and
  - Succinct batch arguments for BQP (or QMA) assuming post-quantum LWE
(without iO).
