A Quantum inspired proof of $P^{\#P} \subseteq IP$.
arXiv: Quantum Physics(2017)
摘要
We provide a new, quantum inspired, proof for the celebrated claim of [LFKN92] that $P^{#P} subseteq IP$. 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.
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