# Machine Learning the period finding algorithm

**Authors:** John George Francis, Anil Shaji  
**arXiv:** [2103.05708](https://arxiv.org/abs/2103.05708)  
**Date:** 2021-03-09  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2103.05708v1/

## Key points

- Researchers use differentiable programming and gradient descent to find unitary matrices for the period finding algorithm
- Goal is to extract period information from a quantum computer after applying an oracle
- Traditionally, inverse quantum Fourier transform has been used, but this research suggests multiple unitary matrices can achieve the same transformation and differ significantly
- Researchers propose using an algorithm to learn these alternative unitary matrices
- Neural networks can differentiate these unitary matrices from randomly generated ones, indicating unique characteristic features
- Related works cited include studies on differentiable programming, genetic programming, machine learning algorithms, Simon's algorithm, and period finding techniques
- Research highlights potential of neural networks in learning and identifying alternative unitary matrices for period finding algorithm in quantum computing

## Summary

In this study, the researchers utilize differentiable programming and gradient descent to find unitary matrices that can be applied in the period finding algorithm. The goal is to extract period information from the state of a quantum computer after the application of an oracle. Traditionally, the inverse quantum Fourier transform has been used as the standard procedure for this purpose. However, the findings of this research suggest that there are multiple unitary matrices that can achieve the same transformation and they significantly differ from each other. To explore these alternative unitary matrices, the researchers propose using an algorithm to learn them. They demonstrate that neural networks can be employed to differentiate these unitary matrices from randomly generated ones. This indicates that these specific unitaries possess characteristic features that are not easily discernible through other means. The authors provide additional context by referencing related works in machine learning and quantum computing. They cite studies on differentiable programming [4], genetic programming [6], and machine learning algorithms [7]. Additionally, they mention relevant papers on quantum algorithms such as Simon's algorithm [9] and period finding techniques [17]. Overall, this research highlights the potential for using neural networks to learn and identify alternative unitary matrices for the period finding algorithm in quantum computing. By expanding our understanding of these unitaries, we can enhance our ability to extract valuable information from quantum systems post-oracle application.