English

A Quantum inspired proof of $P^{\#P} \subseteq IP$

Quantum Physics 2018-03-14 v2

Abstract

We provide a new, quantum inspired, proof for the celebrated claim of [LFKN92] that P#PIPP^{\#P} \subseteq IP. The protocol is fundamentally different from the original sum-check protocol of [LFKN92, Sha92], as well as from variants of this proof [GKR08, Mei09], though it still possesses the overall structure of inductively checking consistency between subsequent step. The protocol is inspired by [AAV13]. Hopefully, this protocol will be helpful in making progress towards two major open problems: resolving the quantum PCP question, and verification of quantum computations using a classical BPP verifier. Given the historical importance of the sum-check protocol in classical computational complexity, we hope that the new protocol will also find applications in classical complexity theory.

Cite

@article{arxiv.1710.09078,
  title  = {A Quantum inspired proof of $P^{\#P} \subseteq IP$},
  author = {Dorit Aharonov and Ayal Green},
  journal= {arXiv preprint arXiv:1710.09078},
  year   = {2018}
}
R2 v1 2026-06-22T22:24:56.110Z