  The emergence of Quantum Machine Learning (QML) to enhance traditional
classical learning methods has seen various limitations to its realisation.
There is therefore an imperative to develop quantum models with unique model
hypotheses to attain expressional and computational advantage. In this work we
extend the linear quantum support vector machine (QSVM) with kernel function
computed through quantum kernel estimation (QKE), to form a decision tree
classifier constructed from a decision directed acyclic graph of QSVM nodes -
the ensemble of which we term the quantum random forest (QRF). To limit
overfitting, we further extend the model to employ a low-rank Nystr\"{o}m
approximation to the kernel matrix. We provide generalisation error bounds on
the model and theoretical guarantees to limit errors due to finite sampling on
the Nystr\"{o}m-QKE strategy. In doing so, we show that we can achieve lower
sampling complexity when compared to QKE. We numerically illustrate the effect
of varying model hyperparameters and finally demonstrate that the QRF is able
obtain superior performance over QSVMs, while also requiring fewer kernel
estimations.
