The Fundamental Limit of Quantum Computation (FLQC)

Abstract

This revision withdraws the claim, present in earlier circulated versions of this preprint, that FLQC renders Shor's algorithm physically unrealisable for RSA-2048 and sets an obstruction threshold at n* ≈ 100 bits (formerly §3.1). That argument rested on an invalid premise: that a single physical rotation gate must directly realise an exponentially small ideal phase angle. This is contradicted by established results in quantum-circuit compilation (Solovay–Kitaev/Ross–Selinger synthesis into a fixed discrete gate set; Coppersmith's approximate quantum Fourier transform) and by an explicit, quantitative treatment of exactly this question already in the peer-reviewed literature (Fowler & Hollenberg, Phys. Rev. A 70, 032329, 2004), which shows that factoring integers of thousands of bits requires no controlled rotation finer than - roughly 28 orders of magnitude coarser than the Δθmin estimate used throughout this work. The corrected argument is given in §3.1 and Part V.. Numerical simulation phase-resolution test protocol with qiskit: https://github.com/SergejMaterov/FLQC-Protocol