# Succinct Classical Verification of Quantum Computation

arXiv: https://arxiv.org/abs/2206.14929 · HTML: https://mlsanity.com/paper/2206.14929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [Position: Quantum Program Generation Must Prioritize Validity Over Probabilistic Scaling](https://mlsanity.com/paper/2607.15313/) (2026)

## Abstract (arXiv)

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).