We study the problem of minimizing round complexity in the context of succinct classical argument systems for quantum computation. All prior works either require at least 8 rounds of interaction between the quantum prover and classical verifier, or rely on the idealized quantum random oracle model (QROM). We design: Unlike all prior works, we do not rely on “state-preserving” succinct arguments of knowledge (AoKs) for \(\boldsymbol{\textrm{NP}}\) for proving soundness. Our main technical contribution is a new approach to prove soundness without rewinding cheating provers. We bring the notion of straight-line partial extractability to argument systems for quantum computation.