Less precise but less noisy: local circuits for momentum-space state preparation and measurement
Abstract
Quantum algorithms are usually optimized for gate count or circuit depth. We find on Quantinuum System Model H2 quantum computer that for a tight-binding chain ground state preparation, there is a system size N beyond which the adiabatic evolution reaches significantly lower energies than the Fermionic Fourier Transform (FFT), with the same number of gates, and with the same circuit depth. We attribute this high noise sensitivity of the FFT to its high precision, being able to distinguish momenta by 1/N. This high resolution in momentum space requires long-range couplings in real space, which propagates errors faster. In contrast, although local and physical circuits such as the adiabatic evolution have a coarser momentum resolution, they also propagate errors more slowly. For physical applications, high momentum resolution is rarely required and is often worth trading for low noise sensitivity. We also introduce a momentum measurement scheme that although less precise than FFT, is less costly and less noisy. We show that it achieves better performance than FFT for spectral function measurement on Quantinuum System Model H2 quantum computer. Our work emphasizes the importance of reducing the noise sensitivity of quantum algorithms, beyond the number of gates or circuit depth.
Related
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BibTeX
@misc{granet2026less,
title = {{Less precise but less noisy: local circuits for momentum-space state preparation and measurement}},
author = {Etienne Granet and Henrik Dreyer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01704},
eprint = {2610.01704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01704},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Less precise but less noisy: local circuits for momentum-space state preparation and measurement
AU - Etienne Granet
AU - Henrik Dreyer
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01704
UR - https://arxiv.org/abs/2610.01704
AB - Quantum algorithms are usually optimized for gate count or circuit depth. We find on Quantinuum System Model H2 quantum computer that for a tight-binding chain ground state preparation, there is a system size N beyond which the adiabatic evolution reaches significantly lower energies than the Fermionic Fourier Transform (FFT), with the same number of gates, and with the same circuit depth. We attribute this high noise sensitivity of the FFT to its high precision, being able to distinguish momenta by 1/N. This high resolution in momentum space requires long-range couplings in real space, which propagates errors faster. In contrast, although local and physical circuits such as the adiabatic evolution have a coarser momentum resolution, they also propagate errors more slowly. For physical applications, high momentum resolution is rarely required and is often worth trading for low noise sensitivity. We also introduce a momentum measurement scheme that although less precise than FFT, is less costly and less noisy. We show that it achieves better performance than FFT for spectral function measurement on Quantinuum System Model H2 quantum computer. Our work emphasizes the importance of reducing the noise sensitivity of quantum algorithms, beyond the number of gates or circuit depth.
ER -