Variational decision diagrams for quantum-inspired machine learning applications

TL;DR

This paper introduces variational decision diagrams (VDDs), a new graph-based approach combining decision diagrams with variational methods, to efficiently represent and train quantum states for quantum machine learning applications.

Contribution

It presents VDDs as a novel structure for quantum states, demonstrating their trainability and potential as an alternative to traditional variational ansätze in QML.

Findings

VDDs can be trained without signs of barren plateaus.

Gradient variance analysis indicates trainability of VDDs.

VDDs offer an efficient way to simulate quantum states in QML.

Abstract

Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability amplitudes. However, their application in quantum machine learning (QML) has remained unexplored. This paper introduces variational decision diagrams (VDDs), a novel graph structure that combines the structural benefits of DDs with the adaptability of variational methods for efficiently representing quantum states. We investigate the trainability of VDDs by applying them to the ground state estimation problem for transverse-field Ising and Heisenberg Hamiltonians. Analysis of gradient variance suggests that training VDDs is possible, as no signs of vanishing gradients--also known as barren plateaus--are observed. This work provides new insights into the use of decision diagrams in QML as an alternative to design and train variational ans\"atze.