Analyzing the barren plateau phenomenon in training quantum neural network with the ZX-calculus

02/03/2021
by   Chen Zhao, et al.
0

In this paper, we propose a general scheme to analyze the barren plateau phenomenon in training quantum neural networks with the ZX-calculus. More precisely, we extend the barren plateaus theorem from unitary 2-design circuits to any parameterized quantum circuits under certain reasonable assumptions. The main technical contribution of this paper is representing certain integrations as ZX-diagrams and computing them with the ZX-calculus. The method is used to analyze four concrete quantum neural networks with different structures. It is shown that, for the hardware efficient ansatz and the MPS-inspired ansatz, there exist barren plateaus, while for the QCNN and the tree tensor network ansatz, there exists no barren plateau.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/02/2021

Quantum Multiple-Valued Decision Diagrams in Graphical Calculi

Graphical calculi such as the ZH-calculus are powerful tools in the stud...
research
01/10/2023

The Basis of Design Tools for Quantum Computing: Arrays, Decision Diagrams, Tensor Networks, and ZX-Calculus

Quantum computers promise to efficiently solve important problems classi...
research
04/27/2022

Quantum Linear Optics via String Diagrams

We establish a formal bridge between qubit-based and photonic quantum co...
research
02/21/2020

PBS-calculus: A Graphical Language for Quantum-Controlled Computations

We introduce the PBS-calculus to represent and reason on quantum computa...
research
07/19/2023

The Qudit ZH-Calculus: Generalised Toffoli+Hadamard and Universality

We introduce the qudit ZH-calculus and show how to generalise all the ph...
research
05/11/2022

VyZX : A Vision for Verifying the ZX Calculus

Optimizing quantum circuits is a key challenge for quantum computing. Th...
research
12/18/2018

Quantum computing and the brain: quantum nets, dessins d'enfants and neural networks

In this paper, we will discuss a formal link between neural networks and...

Please sign up or login with your details

Forgot password? Click here to reset