Variational Quantum Classifiers Through the Lens of the Hessian
- URL: http://arxiv.org/abs/2105.10162v1
- Date: Fri, 21 May 2021 06:57:34 GMT
- Title: Variational Quantum Classifiers Through the Lens of the Hessian
- Authors: Pinaki Sen and Amandeep Singh Bhatia
- Abstract summary: In quantum computing, variational quantum algorithms (VQAs) are well suited for finding optimal combinations of things.
The training of VQAs with gradient descent optimization algorithm has shown a good convergence.
Just like classical deep learning, variational quantum circuits suffer from vanishing gradient problems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In quantum computing, the variational quantum algorithms (VQAs) are well
suited for finding optimal combinations of things in specific applications
ranging from chemistry all the way to finance. The training of VQAs with
gradient descent optimization algorithm has shown a good convergence. At an
early stage, the simulation of variational quantum circuits on noisy
intermediate-scale quantum (NISQ) devices suffers from noisy outputs. Just like
classical deep learning, it also suffers from vanishing gradient problems. It
is a realistic goal to study the topology of loss landscape, to visualize the
curvature information and trainability of these circuits in the existence of
vanishing gradients. In this paper, we calculated the Hessian and visualized
the loss landscape of variational quantum classifiers at different points in
parameter space. The curvature information of variational quantum classifiers
(VQC) is interpreted and the loss function's convergence is shown. It helps us
better understand the behavior of variational quantum circuits to tackle
optimization problems efficiently. We investigated the variational quantum
classifiers via Hessian on quantum computers, started with a simple 4-bit
parity problem to gain insight into the practical behavior of Hessian, then
thoroughly analyzed the behavior of Hessian's eigenvalues on training the
variational quantum classifier for the Diabetes dataset.
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