Phase-fidelity-aware Truncated Quantum Fourier Transform For Scalable Phase Estimation On NISQ Hardware

Abstract

Quantum phase estimation~(QPE) is central to numerous quantum algorithms, yet its standard implementation demands an $\text{calO}(m^{\{}2\})$-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~$\text{eps}$. Our central result establishes $\text{TV}(P_{\{}\phi \},P_{\{}\phi {\}}^{\{}d\})\le \pi (m\{-\}d)/2^{\{}d\}$, showing that for $d=\text{calO}(logm)$ circuit size collapses from $\text{calO}(m^{\{}2\})$ to $\text{calO}(mlogm)$ while estimation error grows by at most $\text{calO}(2^{\{}-d\})$. We characterise $\text{dstar}=\text{Floor}\{lo{g}_{\{}2\}(2\pi /{\text{eps}}_{\{}2q\})\}$ 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 accu