Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions

Understand

The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms.

• We introduce the Fourier Series Loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits.
• The FSL method prepares a ($Dn$)-qubit state encoding the $2^{Dn}$-point uniform discretization of a $D$-dimensional function specified by a $D$-dimensional Fourier series.
• A free parameter $m < n$ determines the number of Fourier coefficients, $2^{D(m+1)}$, used to represent the function.