Heart disease morbidity and mortality rates are increasing, which has a negative impact on public health and the global economy. Early detection of heart disease reduces the incidence of heart mortality and morbidity. Recent research has utilized quantum computing methods to predict heart disease with more than 5 qubits and are computationally intensive. Despite the higher number of qubits, earlier work reports a lower accuracy in predicting heart disease, have not considered the outlier effects, and requires more computation time and memory for heart disease prediction. To overcome these limitations, we propose hybrid random forest quantum neural network (HQRF) using a few qubits (two to four) and considered the effects of outlier in the dataset. Two open-source datasets, Cleveland and Statlog, are used in this study to apply quantum networks. The proposed algorithm has been applied on two open-source datasets and utilized two different types of testing strategies such as 10-fold cross validation and 70-30 train/test ratio. We compared the performance of our proposed methodology with our earlier algorithm called hybrid quantum neural network (HQNN) proposed in the literature for heart disease prediction. HQNN and HQRF outperform in 10-fold cross validation and 70/30 train/test split ratio, respectively. The results show that HQNN requires a large training dataset while HQRF is more appropriate for both large and small training dataset. According to the experimental results, the proposed HQRF is not sensitive to the outlier data compared to HQNN. Compared to earlier works, the proposed HQRF achieved a maximum area under the curve (AUC) of 96.43% and 97.78% in predicting heart diseases using Cleveland and Statlog datasets, respectively with HQNN. The proposed HQRF is highly efficient in detecting heart disease at an early stage and will speed up clinical diagnosis.