Variational Quantum Classifiers Through the Lens of the Hessian

05/21/2021
by   Pinaki Sen, et al.
10

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.

READ FULL TEXT

page 1

page 2

page 5

page 6

page 7

page 8

page 9

research
11/09/2021

Mode connectivity in the loss landscape of parameterized quantum circuits

Variational training of parameterized quantum circuits (PQCs) underpins ...
research
11/26/2021

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Variational quantum algorithms are expected to demonstrate the advantage...
research
10/13/2022

Noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient de...
research
11/25/2021

Mitigating Noise-Induced Gradient Vanishing in Variational Quantum Algorithm Training

Variational quantum algorithms are expected to demonstrate the advantage...
research
06/19/2022

Laziness, Barren Plateau, and Noise in Machine Learning

We define laziness to describe a large suppression of variational parame...
research
07/28/2020

Noise-Induced Barren Plateaus in Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage...
research
12/16/2019

PyHessian: Neural Networks Through the Lens of the Hessian

We present PyHessian, a new scalable framework that enables fast computa...

Please sign up or login with your details

Forgot password? Click here to reset