Phase-Fidelity-Aware Truncated Quantum Fourier Transform for Scalable Phase Estimation on NISQ Hardware

Quantum phase estimation (QPE) is central to numerous quantum algorithms, yet its standard implementation demands an calO\(m²\)-gate quantum Fourier transform (QFT) on m control qubits-a prohibitive overhead on near-term noisy intermediate-scale quantum (NISQ) devices. We introduce the 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 eps. Our central result establishes TV\(P_varphi,P_varphi^d\)leqπ(m{-}d)/2^d, showing that for d=calO\(log m\) circuit size collapses from calO\(m²\) to calO\(mlog m\) while estimation error grows by at most calO\(2^-d\). We characterise dstar=Floor{log₂\(2π/eps_2q\)} 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 noise-truncation synergy: PFA-TQFT outperforms full QFT under NISQ noise eps_2qgtrsim 2times10^-3.