A Geometric Criterion for Noise-Free Quantum Evolution: Corrected Null-Decoherence Condition and a Practical Roadmap Toward Intrinsically Noise-Free Quantum Computing

AI Trinity Labo

Published Dec 11, 2025• 0 citations

Abstract

This work presents the complete corrected formulation of the null-decoherence condition derived from Fubini–Study distance invariance in projective Hilbert space. The corrected geometric criterion shows that probability amplitudes remain invariant if and only if the Hamiltonian satisfies a real-valued projection condition aligned with the computational basis. We derive the condition rigorously, classify physical Hamiltonians that naturally satisfy it, identify compatible hardware platforms (including superconducting qubits, spin systems, topological qubits, and integrable models), and provide a practical engineering roadmap toward intrinsically noise-free quantum computing. This framework establishes the first fully geometric blueprint for hardware-level decoherence elimination, with direct implications for scalable quantum architectures beyond error-corrected models.

DOI: 10.5281/zenodo.17902942

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