One qubit as a universal approximant

A single-qubit circuit can approximate any bounded complex function stored in the degrees of freedom defining its quantum gates. The approximant presented this work is operated through a series gates that take as their parameterization independent variable target and an additional set adjustable parameters. re-uploaded every gate while parameters are optimized for each function. output state becomes more accurate number re-uploadings increases, i. e., layers parameterized with applied. In work, we provide two different proofs claim related to both Fourier Universal Approximation Theorem Neural Networks, benchmark methods against classical counterparts. We further implement real superconducting qubit device, demonstrating how ability describe functions improves depth circuit. This shows robustness re-uploading technique on Quantum Machine Learning.