Quantum infrastructure software provider Q-CTRL has demonstrated an experimental execution of the Quantum Fourier Transform (QFT) subroutine on up to 100 physical qubits. Published on arXiv (arXiv:2608.05435), the research presents a constructive compilation architecture termed the Convolutional QFT. Executed on the IBM Heron R3 superconducting processor ibm_boston, the demonstration resolves periodic signal frequencies across a 2100-dimensional Hilbert space, marking the largest experimental execution of a functional QFT algorithm on quantum hardware to date.
A primary bottleneck in scaling subroutines like the QFT on near-term and fault-tolerant architectures is the two-qubit gate overhead required to route interactions across restricted connectivity layouts. Standard direct implementations on linear nearest-neighbor (LNN) topologies incur substantial routing penalties compared to all-to-all connected architectures. Q-CTRL’s compilation strategy eliminates this routing overhead entirely on LNN layouts by leveraging identity cancellations, matching the theoretical baseline of an all-to-all architecture using n2 – n two-qubit CX gates for a full n-qubit QFT, and d(2n – d – 1) CX gates for an Approximate QFT (AQFT) retaining the d largest phase rotation angles.
To optimize execution on physical hardware, the authors refined the LNN layout into the Convolutional AQFT by incorporating a single ancilla qubit and two additional CX gates. The addition of the ancilla reverses the directional dependency chain of initial entangling operations, allowing the algorithm to synthesize as a compact, translation-invariant kernel circuit gadget spanning d + 2 qubits. As the kernel steps along the quantum register with a stride length of 1, it minimizes the average number of two-qubit gates in the causal light-cone history of each physical qubit, suppressing noise propagation into downstream logic.
| [ QFT Compilation Strategies & Performance Benchmarks (ibm_boston) ] | ||
|---|---|---|
| Compilation Strategy & Metrics | CX Gate Complexity & Depth | Experimental Fidelity & Signal Fidelity |
| All-to-All Baseline | • CX Count: n2 – n • AQFT CX: d(2n – d – 1) | • Theoretical baseline (requires all-to-all physical connectivity) |
| Low-CX LNN Compilation | • CX Count: n2 – n • AQFT CX: d(2n – d – 1) | • Zero routing overhead on linear nearest-neighbor topologies • CX Depth: (2d – 1)n – d(d + 1) + 3 |
| Convolutional AQFT (Q-CTRL Hardware Implementation) | • CX Count: n2 – n + 2 • AQFT CX: d(2n – d – 1) + 2 | • 50 Qubits: 11.4% Process Fidelity (10.8× signal peak) • 80 Qubits: 1.8% Process Fidelity (7.5× signal peak) • 100 Qubits: Target state remains mode output (Signal-to-Noise > 1) |
During execution, qubits participate briefly in the dense convolutional kernel before entering long idle windows. These idle periods were protected against decoherence and crosstalk using Q-CTRL’s robust, crosstalk-suppressing dynamical decoupling sequences integrated with ‘as late as possible’ (ALAP) gate scheduling. In experimental benchmarks across 20 randomly sampled target frequencies, the Convolutional QFT achieved a readout-mitigated process fidelity of 11.4% at 50 qubits and 1.8% at 80 qubits. Up to 100 qubits, the correct integer frequency bitstring consistently emerged as the highest-probability measurement outcome above background noise.
Review the research preprint on arXiv (Convolutional QFT) here.
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