A superconducting Qbit as a universal approximant

Abstract: A single qubit can approximate any bounded complex function as stored in the degrees of freedom defining the quantum state. This result is analogue to two known theorems ensuring approximations for functions, namely Fourier series and the Universal Approximation Theorem (UAT), that holds for neural networks with a large enough single, intermediate hidden layer. The single qubit circuit becomes more accurate as the independent function variable is re-uploaded in an increasing number of gates, analogous to the classical methods that grow in accuracy with an increased number of intermediate steps. We further implement a one-qubit approximant in a real superconducting qubit device consisting of a transmon qubit in a three-dimensional cavity, explicitly showing how the ability to describe a set of functions improves with the depth of the quantum circuit.

Physics

Audience: researchers in the topic

XXVI IFT Christmas Workshop