Machine Learning the period finding algorithm

TL;DR

This paper explores using differentiable programming and neural networks to discover and analyze alternative unitary matrices for quantum period finding, beyond the standard inverse Fourier transform, revealing multiple effective transformations.

Contribution

It introduces a method to learn and identify various unitary matrices suitable for quantum period finding, expanding the understanding of possible transformations.

Findings

Multiple distinct unitary matrices can perform the same period finding task.

Neural networks can distinguish learned unitaries from random matrices.

Learned unitaries have characteristic features detectable by neural networks.

Abstract

We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that that this is not the only unitary matrix appropriate for the period finding algorithm, There exist several unitary matrices that can affect out the same transformation and they are significantly different from each other as well. These unitary matrices can be learned by an algorithm. Neural networks can be applied to differentiate such unitary matrices from randomly generated ones indicating that these unitaries do have characteristic features that cannot otherwise be discerned easily.