Experimental demonstration of the Quantum Fourier Transform on up to 100 qubits using a convolutional compilation strategy

We present and experimentally validate the `Convolutional QFT': a constructive compilation strategy for the Quantum Fourier Transform (QFT) subroutine on a linear nearest neighbor (LNN) qubit topology. We first introduce a novel strategy that compiles the $n$-qubit QFT onto an LNN topology using only $n^2 - n$ $CX$ gates, matching requirements of a direct compilation on an all-to-all architecture. We then derive the convolutional variant used in our experiments, which requires an additional two $CX$ gates in total, and is realized via a compact, translation-invariant kernel circuit gadget that traverses a quantum register. We demonstrate the power of the convolutional compilation strategy on the IBM Quantum Platform by executing QFT benchmarking circuits. We measure a process fidelity of 11.4% at 50 qubits, and 1.8% at 80 qubits. The correct output state remains clearly distinguishable above background noise up to 100 qubits. These results constitute the largest experimental QFT demonstrated on any quantum computing hardware to date.