Kernel-subtraction post-processing for DOS-QPE

Derive and validate a kernel-subtraction procedure that removes the contribution of the DOS-QPE sampling kernel from estimated spectral moments, thereby relaxing the register-size requirement for higher-order moment features.

Background

DOS-QPE samples a density convolved with a finite-register phase-estimation kernel. The paper shows that this convolution introduces a register-dependent bias, especially for high-order standardized moments, and that increasing the number of shots cannot remove this bias.

Because the kernel is known in closed form and cumulants add under convolution, the authors note that its contribution may be subtractable in post-processing. They do not develop or test such a correction, leaving open whether it can reliably reduce the register requirements without introducing prohibitive statistical or numerical errors.