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arXiv · 1710.09078

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

Dorit Aharonov·Ayal Green
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Abstract

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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Dorit Aharonov, Ayal Green. 2018-03-13. A Quantum inspired proof of $P^{\#P} \subseteq IP$. https://arxiv.org/abs/1710.09078

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