Interactive Oracle Arguments in the QROM and Applications to Succinct Verification of Quantum Computation

This work is motivated by the following question: can an untrusted quantum server convince a classical verifier of the answer to an efficient quantum computation using only polylogarithmic communication? We show how to achieve this in the quantum random oracle model (QROM), after a non-succinct instance-independent setup phase. We introduce and formalize the notion of post-quantum interactive oracle arguments for languages in QMA, a generalization of interactive oracle proofs (Ben-Sasson–Chiesa–Spooner). We then show how to compile any non-adaptive public-coin interactive oracle argument (with private setup) into a succinct argument (with setup) in the QROM. To conditionally answer our motivating question via this framework under the post-quantum hardness assumption of LWE, we show that the ZX local Hamiltonian problem with at least inverse-polylogarithmic relative promise gap has an interactive oracle argument with instance-independent setup, which we can then compile. Assuming a variant of the quantum PCP conjecture that we introduce called the weak ZX quantum PCP conjecture, we obtain a succinct argument for QMA (and consequently the verification of quantum computation) in the QROM (with non-succinct instance-independent setup) which makes only black-box use of the underlying cryptographic primitives.