For one quantum-simulation task, a less precise circuit produced better results than a Fourier transform on noisy hardware. In a preprint submitted on 1 October 2026, Etienne Granet and Henrik Dreyer report that adiabatic evolution prepared lower-energy ground states than a Fermionic Fourier Transform (FFT) above a system-size threshold on Quantinuum System Model H2—even though the approaches used the same gate count and circuit depth. They also report better spectral-function measurement with a less costly, less noisy momentum-measurement scheme. These findings concern specific tasks on one device, not a general win over FFTs.
What the researchers compared
Granet and Dreyer’s preprint, “Less precise but less noisy: local circuits for momentum-space state preparation and measurement”, studies momentum-space methods for a tight-binding chain. The authors compare approaches that trade resolution and circuit structure against sensitivity to noise.
For ground-state preparation, the comparison is between adiabatic evolution and the Fermionic Fourier Transform. The authors report that adiabatic evolution reached significantly lower energies once the system exceeded a size threshold. A 2 October 2026 report by Quantum Zeitgeist describes the crossover as approximately twenty qubits, but the paper’s abstract gives no numerical threshold. That estimate should not be treated as a universal cutoff.
The equal gate count and circuit depth are important: in this experiment, those resource counts alone did not predict which method performed better. The reported advantage was in the resulting energy, on the tested hardware and task.
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Why a coarser method may be more reliable
The authors’ explanation is a trade-off between momentum resolution and noise sensitivity. The FFT resolves momenta at spacing 1/N, where N is the system size. The paper says this resolution calls for long-range couplings in real space, which can propagate errors more quickly.
Adiabatic evolution instead uses local circuits and has coarser momentum resolution. According to the authors, errors propagate more slowly in this structure. If an application does not need the FFT’s finer momentum resolution, the local approach can yield a more useful result on noisy hardware despite being less precise in that respect.
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This is the authors’ explanation for the observed result, not evidence that locality always reduces errors or that lower resolution is always preferable. The useful choice depends on what the task needs to resolve and how noise affects the particular implementation.
The measurement result is a separate finding
The preprint also introduces a momentum-measurement scheme that is less precise than FFT but less costly and less noisy. On Quantinuum System Model H2, the authors report that it performed better for spectral-function measurement. This is distinct from the ground-state energy comparison: it concerns measuring a spectral function, not preparing a lower-energy ground state.
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What the results do—and do not—establish
- Established in the reported tests: on System Model H2, adiabatic evolution achieved lower energies than FFT beyond a system-size threshold for tight-binding-chain ground-state preparation, with equal gate count and circuit depth; a separate lower-cost, lower-noise measurement scheme performed better for spectral-function measurement.
- Not established: that the crossover always occurs at approximately twenty qubits, that either approach is superior on other quantum processors, or that the result generalizes to workloads beyond the stated tasks.
- Not specified in the paper’s abstract: the numerical ground-state crossover, detailed error bars, and sample counts. Those omissions limit how precisely the size and strength of the effect can be assessed from the abstract alone.
The preprint is arXiv:2610.01704, version 1, submitted on 1 October 2026. The reported findings are experimental results described by the authors; they should be read within that scope rather than as settled guidance for quantum algorithms generally.
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