Probabilistically Checking Quantum Proofs, with Interaction

• URL: http://arxiv.org/abs/2606.09588v1
• Date: Mon, 08 Jun 2026 14:59:51 GMT
• Title: Probabilistically Checking Quantum Proofs, with Interaction
• Abstract summary: We study a quantum analogue of interactive proofs (qIOP) in which the verifier and communication are both allowed to be quantum oracles.<n>Our main result is a qIOP for any language in which the total communication is but the verifier only reads a polylogarithmic number of qubits in total.
• Score: 2.0482700732041397
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The model of interactive oracle proofs (IOP) generalizes the notion of probabilistically checkable proof (PCP), in which a static proof is verified probabilistically by querying a small number of bits, to the interactive setting: a polynomial-time verifier interacts with an unbounded prover, but is restricted to only reading a small number of bits, in total, from the messages sent by the prover. IOPs provide a relaxed setting in which to study local probabilistic verification. They have proved instrumental in devising efficient methods for verification through subsequent compilation into non-interactive or succinct protocols. We study a quantum analogue of interactive oracle proofs (qIOP) in which the verifier and communication are both allowed to be quantum; yet the verifier is restricted to perform measurements only on a small number of qubits received from the prover. Our main result is a qIOP for any language in QMA, in which the total communication is polynomial but the verifier only reads a polylogarithmic number of qubits in total. The protocol has completeness parameter exponentially close to $1$ and soundness bounded away from $1$ by a constant. In the absence of a quantum PCP theorem, this provides the first information-theoretically sound local and robust characterization of QMA, albeit interactive. Our protocol combines the use of a quantum locally testable code (LTC) with classical techniques, notably probabilistically checkable proofs of proximity (PCPP). We avoid the necessity for complex multi-qubit tests employed in other settings by leveraging the local indistinguishability property of the quantum LTC.

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