Abstract
Quantum phase estimation~(QPE) is central to numerous quantum algorithms, yet its standard implementation demands an (m²)-gate quantum Fourier transform~(QFT) on m control qubits-a prohibitive overhead on near-term noisy intermediate-scale quantum (NISQ) devices. We introduce the \emph{Phase-Fidelity-Aware Truncated QFT} (PFA-TQFT), a family of approximate QFT circuits parameterised by a truncation depth~d that omits controlled-phase rotations below a hardware-calibrated fidelity threshold~. Our central result establishes (P_ϕ,P_ϕ^d)≤π(m-d)/2^d, showing that for d=(log m) circuit size collapses from (m²) to (mlog m) while estimation error grows by at most (2^-d). We characterise =log₂(2π/_2q) directly from native gate fidelities, demonstrating 31.3 -43.7\% at m = 30, gate-count reduction on IBM Eagle/Heron and IonQ~Aria with negligible accuracy loss. Numerical experiments on the transverse-field Ising model confirm all theoretical predictions and reveal a \emph{noise-truncation synergy}: PFA-TQFT outperforms full QFT under NISQ noise _2q 2×10⁻³.