Breaking the 100-qubit barrier: Executing the Quantum Fourier Transform at scale on IBM hardware Quantum algorithms rely heavily on key subroutines such as the Quantum Fourier Transform (QFT), which underpin applications ranging from phase estimation to quantum factoring (Shor’s algorithm). However, error accumulation and routing overhead are bottlenecks to executing large-scale quantum subroutines on real quantum hardware. In our latest technical manuscript, Q-CTRL researchers overcame these hardware limits to demonstrate a 100-qubit QFT on IBM Quantum computers. These results represent the largest experimental QFT on any quantum hardware to date by a factor of two. At Q-CTRL, our mission is to make quantum technology useful. This work highlights our focus on optimizing hardware performance and extracting the most useful results. Finding the signal from 2¹⁰⁰ possibilities The ultimate test of this algorithmic subroutine is whether hardware can extract the correct high-dimensional quantum state period. In our benchmarking trials, we encoded periodic signals into quantum registers of 50, 80, and 100 qubits that represent a Hilbert space signal dimension of 2¹⁰⁰. At this scale, there are more than 10^30 (quadrillion times quadrillion) wrong answers, but only one correct frequency that the QFT must find. Successfully isolating the exact target frequency on a noisy device demonstrates that quantum processors can extract meaningful global information from high-dimensional quantum states. When executed on a 156-qubit IBM Heron r3 processor, our compilation strategy delivered remarkable fidelity and selectivity at every tier: - 100-qubit resolution: Across every test circuit up to 100 qubits, the correct target integer frequency emerged as the unique mode result (the single most frequently measured bitstring), standing out clearly above the background noise. - 50-qubit selectivity: At 50 qubits, the target bitstring was 8.4 times more frequent than any single incorrect output in the raw measurement data. The unitary process fidelity reached