Succinct Arguments for QMA in the Quantum Random Oracle Model
Abstract
Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.
Related
- Succinct Arguments for QMA from Collapsing Hash Functions
- Quantum Time-Lock Puzzles in the Quantum Random Oracle Model
- Black Hole Radiation Decoding in the Haar Random Oracle Model
- Random-Oracle Unitary Synthesis is Impossible
- Beyond NISQ Assumptions: One-time Memory in the Classically Accessible Random-Oracle Model
BibTeX
@misc{chiesa2026succinct,
title = {{Succinct Arguments for QMA in the Quantum Random Oracle Model}},
author = {Alessandro Chiesa and Zihan Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37429},
eprint = {2609.37429},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37429},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Succinct Arguments for QMA in the Quantum Random Oracle Model
AU - Alessandro Chiesa
AU - Zihan Hu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.37429
UR - https://arxiv.org/abs/2609.37429
AB - Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.
ER -