Gradient Analysis of Barren Plateau in Parameterized Quantum Circuits with multi-qubit gates

TL;DR

This paper develops a theoretical framework to analyze the gradient behavior of parameterized quantum circuits with multi-qubit gates, addressing the Barren Plateau problem in quantum machine learning.

Contribution

It introduces a general method for calculating gradient expectation and variance without Haar assumptions, extending analysis to multi-qubit gate circuits.

Findings

Gradient variance depends on multi-qubit gate size and circuit depth.

Analytical results for single-layer and deep-layer circuits.

Numerical simulations confirm theoretical predictions.

Abstract

The emergence of the Barren Plateau phenomenon poses a significant challenge to quantum machine learning. While most Barren Plateau analyses focus on single-qubit rotation gates, the gradient behavior of Parameterized Quantum Circuits built from multi-qubit gates remains largely unexplored. In this work, we present a general theoretical framework for analyzing the gradient properties of Parameterized Quantum Circuits with multi-qubit gates. Our method generalizes the direct computation framework, bypassing the Haar random assumption on parameters and enabling the calculation of the gradient expectation and variance. We apply this framework to single-layer and deep-layer circuits, deriving analytical results that quantify how gradient variance is co-determined by the size of the multi-qubit gate and the number of qubits, layers, and effective parameters. Numerical simulations validate our findings. Our study provides a refined framework for analyzing and optimizing Parameterized Quantum Circuits with complex multi-qubit gates.