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In quantum computing, the variational quantum algorithms (VQAs) are wellsuited for finding optimal combinations of things in specific applicationsranging from chemistry all the way to finance. The training of VQAs withgradient descent optimization algorithm has shown a good convergence. At anearly stage, the simulation of variational quantum circuits on noisyintermediate-scale quantum (NISQ) devices suffers from noisy outputs. Just likeclassical deep learning, it also suffers from vanishing gradient problems. Itis a realistic goal to study the topology of loss landscape, to visualize thecurvature information and trainability of these circuits in the existence ofvanishing gradients. In this paper, we calculate the Hessian and visualize theloss landscape of variational quantum classifiers at different points inparameter space. The curvature information of variational quantum classifiers(VQC) is interpreted and the loss function's convergence is shown. It helps usbetter understand the behavior of variational quantum circuits to tackleoptimization problems efficiently. We investigated the variational quantumclassifiers via Hessian on quantum computers, starting with a simple 4-bitparity problem to gain insight into the practical behavior of Hessian, thenthoroughly analyzed the behavior of Hessian's eigenvalues on training thevariational quantum classifier for the Diabetes dataset. Finally, we show howthe adaptive Hessian learning rate can influence the convergence while trainingthe variational circuits.

Variational Quantum Classifiers Through the Lens of the Hessian