Scalable Framework for Riemann Hypothesis Falsification: Quantum Algorithmic Complexity and Conformal Invariance Constraints

 This paper proposes a scalable quantum-classical hybrid computational frame
work for falsifying the Riemann hypothesis within finite ranges of nontrivial zeros.
 Core innovations include: (1) A hierarchical phase estimation algorithm achieving
 polynomial-time complexity verification for zeros at scales up to T = 1015; (2)
 A conformal field theory-based boundary operator ˆRN with conformally invari
ant norm ∥ · ∥CFT, eliminating arbitrary threshold selection; (3) A fault-tolerant
 implementation scheme using ion trap quantum processors. Theoretically, verifi
cation of zeros deviating from the critical line with |Im(s)| < 1015 is achievable
 using Nq = 103 qubits. Experimental validation demonstrates > 0.97 fidelity at
 T =1010 on an ion trap platform (d = 7 surface code) with 36-hour runtime