Smoothly noise-robust modification of the FFT

Construct a smooth modification of the Fermionic Fourier Transform that continuously reduces noise sensitivity while continuously sacrificing momentum-space precision.

Background

The paper attributes the high noise sensitivity of the FFT to its global, long-range structure and its ability to resolve momentum differences of order 1/N. Local circuits reduce this sensitivity but also provide coarser momentum resolution. The authors leave open whether this tradeoff can be achieved through a continuous deformation of the FFT rather than by replacing it with an adiabatic-evolution circuit.

References

Another open direction is whether the FFT could be modified in a smooth way (instead of completely changing the circuit into an adiabatic evolution circuit) so as to smoothly decrease noise sensitivity, at the cost of smoothly decreasing momentum precision.

— Less precise but less noisy: local circuits for momentum-space state preparation and measurement  (2610.01704 - Granet et al., 1 Oct 2026) in Section Discussion and outlook