Avoiding barren plateaus via Gaussian Mixture Model

TL;DR

This paper introduces a Gaussian Mixture Model-based initialization strategy for variational quantum algorithms, effectively avoiding barren plateaus and improving trainability regardless of qubit number or circuit depth.

Contribution

The paper presents a novel initialization method using Gaussian Mixture Models that guarantees avoidance of barren plateaus in quantum circuit training.

Findings

Gradient norm lower bound is independent of qubit number

Lower bound increases with circuit depth

Method enhances trainability of quantum circuits

Abstract

Variational quantum algorithms is one of the most representative algorithms in quantum computing, which has a wide range of applications in quantum machine learning, quantum simulation and other related fields. However, they face challenges associated with the barren plateau phenomenon, especially when dealing with large numbers of qubits, deep circuit layers, or global cost functions, making them often untrainable. In this paper, we propose a novel parameter initialization strategy based on Gaussian Mixture Models. We rigorously prove that, the proposed initialization method consistently avoids the barren plateaus problem for hardware-efficient ansatz with arbitrary length and qubits and any given cost function. Specifically, we find that the gradient norm lower bound provided by the proposed method is independent of the number of qubits $N$ and increases with the circuit depth $L$. Our results strictly highlight the significance of Gaussian Mixture model initialization strategies in determining the trainability of quantum circuits, which provides valuable guidance for future theoretical investigations and practical applications.