Sequential Hamiltonian Assembly: Enhancing the training of combinatorial optimization problems on quantum computers

TL;DR

This paper introduces Sequential Hamiltonian Assembly (SHA), a novel method for improving the training of parameterized quantum circuits in quantum machine learning by approximating global loss functions with local components, reducing vanishing gradients.

Contribution

SHA is a new iterative approach that assembles global loss functions from local parts, enhancing trainability of PQCs and demonstrated on Max-Cut problems with significant performance gains.

Findings

SHA outperforms conventional training by 43.89% in accuracy.

SHA surpasses Layer-VQE by 29.08% in mean accuracy.

The method mitigates vanishing gradients in quantum circuit training.

Abstract

A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs). Much like in deep learning, vanishing gradients pose significant obstacles to the trainability of PQCs, arising from various sources. One such source is the presence of non-local loss functions, which require the measurement of a large subset of qubits involved. To address this issue and facilitate parameter training for quantum applications using global loss functions, we propose Sequential Hamiltonian Assembly (SHA). SHA iteratively approximates the loss by assembling it from local components. To further demonstrate the feasibility of our approach, we extend our previous case study by introducing a new partitioning strategy, a new merger between QAOA and SHA, and an evaluation of SHA onto the Max-Cut optimization problem. Simulation results show that SHA outperforms conventional parameter training by 43.89% and the empirical state-of-the-art, Layer-VQE by 29.08% in the mean accuracy for Max-Cut. This paves the way for locality-aware learning techniques, mitigating vanishing gradients for a large class of practically relevant problems.