Research on near-term quantum machine learning has explored how classical machine learning algorithms endowed with access to quantum kernels (similarity measures) can outperform their purely classical counterparts. Although theoretical work has shown provable advantage on synthetic data sets, no work done to date has studied empirically whether quantum advantage is attainable and with what data. In this paper, we report the first systematic investigation of empirical quantum advantage (EQA) in healthcare and life sciences and propose an end-to-end framework to study EQA. We selected electronic health records (EHRs) data subsets and created a configuration space of 5-20 features and 200-300 training samples. For each configuration coordinate, we trained classical support vector machine (SVM) models based on radial basis function (RBF) kernels and quantum models with custom kernels using an IBM quantum computer, making this one of the largest quantum machine learning experiments to date. We empirically identified regimes where quantum kernels could provide advantage and introduced a terrain ruggedness index, a metric to help quantitatively estimate how the accuracy of a given model will perform. The generalizable framework introduced here represents a key step towards a priori identification of data sets where quantum advantage could exist.INDEX TERMS artificial intelligence, digital health, electronic health records, empirical quantum advantage, machine learning, quantum kernels, real-world data, small data sets, support vector machines

Introduction: Prospectively identifying patient characteristics associated with myocardial infarction (MI) readmission would help target patients at high risk of recurrent events for improved clinical management. This study aimed to build and evaluate machine learning models based solely on real world data to identify predictors of rehospitalization or death within one year following acute MI. Methods: The study population consisted of adult patients who experienced a first hospitalization for MI between January 1, 2013 and December 31, 2017 in the Optum® Clinformatics® Data Mart, an administrative health claims database from a large US national managed care company. Logistic Regression (LR), Extreme Gradient Boosting (XGBoost), and Deep Neural Network (DNN) models were developed and tested. Model variables included patient demographics, clinical characteristics, and specific treatments. Variable importance for model prediction was ranked. Results: Among 96,244 patients who had an initial MI, 15,925 (16.5%) had rehospitalization/death within a year. The LR, XGBoost, and DNN models performed similarly (area under the curve 0.762, 0.774, and 0.785 respectively). The XGBoost was selected as the primary model to assess the relative importance of the variables in predicting MI rehospitalization/death. Of the most impactful variables, older age, higher Charlson Comorbidity Index, presence of chronic kidney disease (all stages), previous heart failure, and no previous coronary arterial bypass graft were highly predictive of MI rehospitalization/death (Figure). Conclusions: The machine learning models developed in this study can be implemented within clinical systems to identify patients at high risk for MI readmission to improve care and decision-making. However, these models require external validation in other datasets. Furthermore, performance of the models might be improved by including information such as LDL-C levels and PCSK9 inhibitor use.