  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.
