Quantum Communication Advantage in TFNP
Mika Göös, Tom Gur, Siddhartha Jain, Jiawei Li
TL;DR
This work proves an exponential quantum advantage in a total two-party NP search problem (TFNP) by introducing a bipartite variant of the Yamakawa--Zhandry problem, BiNC, and converting an average-case quantum SMP separation into a worst-case total-relations result (T-BiNC). The core strategy combines a carefully chosen folded Reed--Solomon code with a structure-vs-randomness framework to establish a lower bound against classical two-way protocols, while a poly$(n)$-qubit quantum SMP protocol accomplishes BiNC efficiently without entanglement or shared randomness. By XORing inputs with a common hash and using multiple instances, the authors obtain totality and demonstrate exponential quantum advantages under reasonable input models. The findings significantly advance the understanding of exponential quantum speedups in TFNP-like settings and chart avenues for future explorations in total-function separations, multiparty models, and NISQ-era demonstrations.
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.