Decohering tensor network quantum machine learning models

Tensor network quantum machine learning (QML) models are promising applications on near-term quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished performance can be compensated for by adding ancillas to the models and accordingly increasing the virtual bond dimension of the models. Can an increased bond dimension fully compensates for the decoherence of the network, and shed light on the role of quantum coherence in QML? We investigate here the competition between decoherence and adding ancillas on the classification performance of two models, with an analysis of the decoherence effect from the perspective of regression. We present numerical evidence that the fully-decohered unitary tree tensor network (TTN) with two ancillas performs at least as well as the non-decohered unitary TTN, suggesting that it is beneficial to add at least two ancillas to the unitary TTN regardless of the amount of decoherence may be consequently introduced.