Scalable Framework for Riemann Hypothesis Falsification: Quantum Algorithmic Complexity and Conformal Invariance Constraints
Scalable Framework for Riemann Hypothesis Falsification: Quantum Algorithmic Complexity and Conformal Invariance Constraints
This paper proposes a scalable quantum-classical hybrid computational framework 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 invariant norm ∥ · ∥CFT, eliminating arbitrary threshold selection; (3) A fault-tolerant implementation scheme using ion trap quantum processors. Theoretically, verification of zeros deviating from the critical line with |Im(s)| 0.97 fidelity at T =1010 on an ion trap platform (d = 7 surface code) with 36-hour runtime
Riemann hypothesis; Quantum algorithms; Conformal invariance; Ion trap quantum computing; Surface code error correction; Complexity analysis; Zero veri f icatio, Riemann hypothesis; Quantum algorithms; Conformal invariance; Ion trap quantum computing; Surface code error correction; Complexity analysis; Zero veri f icatio
Riemann hypothesis; Quantum algorithms; Conformal invariance; Ion trap quantum computing; Surface code error correction; Complexity analysis; Zero veri f icatio, Riemann hypothesis; Quantum algorithms; Conformal invariance; Ion trap quantum computing; Surface code error correction; Complexity analysis; Zero veri f icatio
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