# Assessing the Trainability of the Variational Quantum State Diagonalization Algorithm at Scale

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## Date

2022-04-28

## Authors

Arrow, Joan

## Advisor

Yard, Jon

## Journal Title

## Journal ISSN

## Volume Title

## Publisher

University of Waterloo

## Abstract

Quantum algorithm development is a famously difficult problem. The lack of intuition
concerning the quantum realm makes constructing quantum algorithms which solve partic-
ular problems of interest difficult. In addition, modern hardware limitations place strong
restrictions on the types of algorithms which can be implemented in noisy circuits.
These challenges have produced several solutions to the problem of quantum algorithm
development in the modern Near-term Intermediate Scale Quantum (NISQ) Era. One of
the most prominent of these is the use of classical machine learning to discover novel quan-
tum algorithms by minimizing a cost function associated with the particular application
of interest.
This quantum-classical hybrid approach, also called Variational Quantum Algorithms
(VQAs) has emerged as a major interest for both academic and industrial research due to its
flexible framework and existing applications in both optimization and quantum chemistry.
What is still unclear, is whether these algorithms will work at scale in the noisy training
environment of the NISQ era. This is mainly due to the phenomenon of exponentially
vanishing training gradients, commonly referred to as the Barren Plateaus problem, which
prevents training of the classical machine learning model.
Recent results have shown that some types of cost functions used in training result in
Barren Plateaus, while others do not. This cost function dependence of barren plateaus
has implications for the entire field of VQAs which appear to be relatively unexplored thus
far.
In this thesis I revisit a 2018 paper my collaborators and I published, which established a
new Variational Quantum State Diagonalization (VQSD) algorithm, and demonstrate that
this algorithm’s cost function will encounter a Barren Plateau at scale. I then introduce a
simple modification to this cost function which preserves the function of VQSD while also
ensuring trainability at scale.

## Description

## Keywords

quantum algorithms, machine learning, barren plateaus, VQE, VQSD, VQA