SISSA : A quantum analytical Adam descent through parameter shift rule using Qibo

Robbiati, Matteo; Pasquale, Andrea; Efthymiou, Stavros; Carrazza, Stefano

doi:10.22323/1.414.0206

Article
Report number	arXiv:2210.10787 ; CERN-TH-2022-168 ; TIF-UNIMI-2022-20
Title	A quantum analytical Adam descent through parameter shift rule using Qibo
Author(s)	Robbiati, Matteo (Milan U. ; INFN, Milan ; CERN) ; Efthymiou, Stavros (Technol. Innovation Inst., UAE) ; Pasquale, Andrea (Milan U. ; INFN, Milan ; Technol. Innovation Inst., UAE) ; Carrazza, Stefano (Milan U. ; INFN, Milan ; CERN ; Technol. Innovation Inst., UAE)
Publication	2022-11-13
Imprint	2022-10-19
Number of pages	6
Note	6 pages, 2 figures, presented in 41st International Conference on High Energy physics - ICHEP2022
In:	PoS ICHEP2022 (2022) pp.206
In:	41st International Conference on High Energy Physics (ICHEP 2022), Bologna, Italy, 6 - 13 Jul 2022, pp.206
DOI	10.22323/1.414.0206
Subject category	hep-ph ; Particle Physics - Phenomenology ; quant-ph ; General Theoretical Physics
Abstract	In this proceedings we present quantum machine learning optimization experiments using stochastic gradient descent with the parameter shift rule algorithm. We first describe the gradient evaluation algorithm and its optimization procedure implemented using the Qibo framework. After numerically testing the implementation using quantum simulation on classical hardware, we perform successfully a full quantum hardware optimization exercise using a single superconducting qubit chip controlled by Qibo. We show results for a quantum regression model by comparing simulation to real hardware optimization.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2023-2025 The author(s) (License: CC-BY-NC-ND-4.0)

$Difference between the derivative with respect to $\theta$ evaluated with the \texttt{TensorFlow} module \texttt{GradientTape()} called $\partial_{tf}$ and our PSR implementation called $\partial_{PSR}$. On the left, the value is calculated without making any change to the first version of the PSR. On the right, we can see the effect of the correction, which breaks down errors to the order of $10^{-16}$. Different colors correspond to different rotation's combinations.$ $Results obtained by performing the optimization on the QPU and normalized with respect to the true law. The choice of adding $k=10$ to each result is entirely arbitrary and serves to prevent the values under consideration from diverging for $x$ tending to zero. The black line is the true law $\sin 2x$ and the black points are the true images of the training set. Colors green and red respectively refers to our PSR and to the CMA optimization. The dashed lines are the prediction's sets purposed through simulated theoretical models. The continuum lines and the confidence belts are drawn using one hundred predictions for each of one hundred points equally distributed into the interval $[-1,1]$.$

Corresponding record in: Inspire

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Zapis kreiran 2023-01-26, zadnja izmjena 2024-09-18

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