Summary of Fourier Analysis Of Variational Quantum Circuits For Supervised Learning, by Marco Wiedmann and Maniraman Periyasamy and Daniel D. Scherer
Fourier Analysis of Variational Quantum Circuits for Supervised Learning
by Marco Wiedmann, Maniraman Periyasamy, Daniel D. Scherer
First submitted to arxiv on: 5 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Quantum Physics (quant-ph)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary VQC (Variational Quantum Circuit) analysis reveals that its function space can be represented as a truncated Fourier sum. Our findings show that the variational part of the circuit constrains certain Fourier coefficients to zero, effectively removing frequencies from the spectrum. We provide an algorithm to compute the exact spectrum and Fourier coefficients for any given VQC. Moreover, we demonstrate how comparing the Fourier transform of a dataset with available spectra can predict which VQC will best fit the data. Our contributions include describing the functional dependence of Fourier coefficients on variational parameters as trigonometric polynomials and providing a method to determine the optimal VQC for a given task. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine trying to understand a special kind of computer program called a Variational Quantum Circuit (VQC). We found that by looking at the math behind how these programs work, we can use something called Fourier analysis to understand them better. This allows us to figure out which parts of the program are important and which aren’t. We also developed a way to test which VQC will be best for a specific task, just like how you might choose a tool for a job. Overall, our discoveries help us better understand these powerful computer programs and how they can be used. |
