Quantum Fourier transform computational accuracy analysis

• DOI: 10.48550/arxiv.2502.10840
• Publication Date: 2025-02-15
• Authors: Marina O. Lisnich...; O. M. Kiselëv
• Keywords: Quantum Fourier transform

In this work, we present a rigorous accuracy analysis of the quantum Fourier transform (QFT), that identifies three natural sources degeneracy: (i) discretization inherited from classical sampling theory, (ii) degeneracy due to limited resolution in eigenvalue (phase) estimation, and (iii) resulting finite resources. We formalize these degradation by proving two theorems relate minimal amplitude number qubits. addition, describe gate-level implementation QFT simulation results on small-scale systems illustrate our theoretical findings. Our clarify interplay between signal limits hardware limitations, they provide guidelines for resource requirements needed achieve desired precision.