Quantum Interactive Oracle Proofs

2026-01-19

AI Summary

This work investigates whether QMA admits quantum interactive oracle proof systems (qIOPs) as a relaxed formulation of the quantum PCP conjecture. By restricting the verifier’s quantum resources—specifically, the number of queries and circuit complexity—the paper presents two unconditional qIOP constructions: one requiring only a constant number of queried qubits, and another using only a constant number of qubits throughout the entire verification process. Key technical ingredients include shared EPR pairs, multi-round quantum interactive protocols, constant-query mechanisms, and a novel single-prover multi-qubit test. The results establish various trade-offs between communication complexity and verifier resource requirements, offering new tools for quantum complexity theory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• quantum Interactive Oracle Proofs
• QMA
• quantum PCP Conjecture
• limited quantum resources
• communication complexity

Innovation

• quantum Interactive Oracle Proofs
• QMA
• constant-query verification
• EPR pairs
• single-prover many-qubits test