Variational decision diagrams for quantum-inspired machine learning applications
This work addresses the problem of efficiently representing and training quantum states in quantum machine learning, offering an alternative variational ansatz, though it appears incremental as it builds on existing decision diagram and variational method concepts.
The paper tackled the unexplored application of decision diagrams in quantum machine learning by introducing variational decision diagrams, a novel graph structure that combines decision diagrams with variational methods, and demonstrated their trainability on ground state estimation problems for quantum Hamiltonians without observing vanishing gradients.
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 ansätze.