Conservative Motion Theory – PNP V The Fredholm–Quantum Barrier: Why BQP Cannot Simulate NP Search

Kawasaki, Hideyo

Published Nov 20, 2025• 0 citations

Abstract

Within Conservative Motion Theory (CMT), quantum computation corresponds tounitary conservative motion with strictly preserved Fredholm mass and entropy.We prove that NP search operators possess an intrinsic Fredholm–entropy and non–conservativemass that cannot be reproduced, compressed, or interferometrically encoded by any polynomialsizeunitary quantum circuit.Thus BQP, the class of polynomial-time quantum computations, is strictly containedin the conservative sector and cannot simulate the exponential non-conservative branchingrequired for NP search.BQP does not contain NP.This establishes the Fredholm–Quantum Barrier: quantum interference preserves conservativerank and entropy and therefore cannot emulate NP search dynamics.

DOI: 10.5281/zenodo.17658994

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