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

• URL: http://arxiv.org/abs/2604.05456v1
• Date: Tue, 07 Apr 2026 05:39:21 GMT
• Title: Phase-Fidelity-Aware Truncated Quantum Fourier Transform for Scalable Phase Estimation on NISQ Hardware
• Abstract summary: We introduce the emphPhase-Fidelity-Aware Truncated QFT (PFA-TQFT)<n>PFA-TQFT omits controlled-phase rotations below a hardware-calibrated fidelity threshold$eps$.<n>We demonstrate 31.3 -43.7% at m = 30, gate-count reduction on IBM Eagle/Heron and IonQAria with negligible accuracy loss.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Quantum phase estimation~(QPE) is central to numerous quantum algorithms, yet its standard implementation demands an $\calO(m^{2})$-gate quantum Fourier transform~(QFT) on $m$ control qubits-a prohibitive overhead on near-term noisy intermediate-scale quantum (NISQ) devices. We introduce the \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~$\eps$. 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 $\calO(m^{2})$ to $\calO(m\log m)$ while estimation error grows by at most $\calO(2^{-d})$. We characterise $\dstar=\Floor{\log_{2}(2π/\eps_{2q})}$ 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 \emph{noise-truncation synergy}: PFA-TQFT outperforms full QFT under NISQ noise $\eps_{2q}\gtrsim 2\times10^{-3}$.

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