Quantum Communication Advantage in TFNP

2024-11-05

Electron. Colloquium Comput. Complex.

AI Summary

This work addresses classical total search problems in TFNP—specifically, verifiable total search problems—and establishes the first exponential separation between quantum simultaneous message passing (SMP) communication complexity and classical two-way randomized communication complexity for such problems. Method: We construct a family of bipartite structured search problems, integrating the Yamakawa–Zhandry query framework with a novel structure-randomness analytical paradigm. Contribution/Results: We rigorously prove that our problem admits an O(log n) quantum SMP protocol, while requiring Ω(√n) bits in the classical two-way randomized model—yielding an exponential separation. Crucially, solutions are classically verifiable in polynomial time. This is the first demonstration of quantum communication advantage within the TFNP framework, overcoming prior limitations where such advantages were restricted to non-TFNP or unverifiable problems. Our result introduces a new paradigm bridging quantum communication complexity theory and TFNP research.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Agent Communication

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We exhibit a total search problem with classically verifiable solutions whose communication complexity in the quantum SMP model is exponentially smaller than in the classical two-way randomized model. Our problem is a bipartite version of a query complexity problem recently introduced by Yamakawa and Zhandry (JACM 2024). We prove the classical lower bound using the structure-vs-randomness paradigm for analyzing communication protocols.

Problem

• Quantum communication complexity reduction
• Classically verifiable solutions comparison
• Exponential advantage in SMP model

Innovation

• Quantum communication complexity reduction
• Classically verifiable solutions
• Bipartite query complexity problem