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

TL;DR

The paper introduces PFA-TQFT, an approximate quantum Fourier transform that reduces circuit complexity on NISQ devices by truncating low-fidelity rotations, maintaining accuracy with fewer gates.

Contribution

It proposes a fidelity-aware truncation method for QFT circuits, significantly reducing gate count while preserving phase estimation accuracy on NISQ hardware.

Findings

Circuit size reduces from O(m^2) to O(m log m) with truncation.

Estimation error increases at most by O(2^{-d}) due to truncation.

Numerical experiments confirm theoretical predictions and show improved performance under noise.

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 $\TV(P_{\varphi},P_{\varphi}^{d})\leq\pi(m{-}d)/2^{d}$, 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 $\dstar=\Floor{\log_{2}(2\pi/\eps_{2q})}$ 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 $\eps_{2q}\gtrsim 2\times10^{-3}$.