Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms

We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\in[-1,1]$, and hence non-uniform in the angle $θ=\arccos x$, a setting that QFT-based quantum Cheb