Quantum Interactive Oracle Proofs
Baocheng Sun, Thomas Vidick
TL;DR
This work develops quantum Interactive Oracle Proofs (qIOPs), a quantum analogue of classical IOPs that enables multi-round interaction while constraining the verifier’s quantum resources. It proves two unconditional constructions for QMA: (i) a qIOP with constant query complexity and polynomially many shared EPR pairs and (ii) a stronger variant with constant queries but exponential communication, using a novel single-prover many-qubits test. The constructions leverage teleportation, PCP proximity proofs, Hadamard codes, and energy tests on Clifford-Hamiltonians to certify quantum witnesses with limited read access. The results illuminate the landscape between qPCP and qIOP, open questions about polynomial-communication strong qIOPs, and hint at cryptographic applications, while introducing robust tools for testing multi-qubit observables in a single prover setting. Overall, the paper advances quantumproof systems by connecting quantum PCPs, interactive proofs, and nonlocal-game techniques through information-theoretic, unconditional constructions for QMA.
Abstract
We initiate the study of quantum Interactive Oracle Proofs (qIOPs), a generalization of both quantum Probabilistically Checkable Proofs and quantum Interactive Proofs, as well as a quantum analogue of classical Interactive Oracle Proofs. In the model of quantum Interactive Oracle Proofs, we allow multiple rounds of quantum interaction between the quantum prover and the quantum verifier, but the verifier has limited access to quantum resources. This includes both queries to the prover's messages and the complexity of the quantum circuits applied by the verifier. The question of whether QMA admits a quantum interactive oracle proof system is a relaxation of the quantum PCP Conjecture. We show the following two main constructions of qIOPs, both of which are unconditional: - We construct a qIOP for QMA in which the verifier shares polynomially many EPR pairs with the prover at the start of the protocol and reads only a constant number of qubits from the prover's messages. - We provide a stronger construction of qIOP for QMA in which the verifier not only reads a constant number of qubits but also operates on a constant number of qubits overall, including those in their private registers. However, in this stronger setting, the communication complexity becomes exponential. This leaves open the question of whether strong qIOPs for QMA, with polynomial communication complexity, exist. As a key component of our construction, we introduce a novel single prover many-qubits test, which may be of independent interest.