<p>Quantum computing uses fundamentally different ways of information processing compared to traditional computing systems such as the use of qubits (quantum bits) and the quantum properties of subatomic particles such as interference, entanglement and superposition to extend the computational capabilities to hitherto unprecedented levels. Although quantum computing systems promise to provide exponential performance benefits in processing, the field is still in an embryonic phase with active ongoing research and development. The efficacy of quantum computing for important verticals such as healthcare---where quantum computing can enable important breakthroughs such as developing drugs, quick DNA sequencing, processing big healthcare data, and performing other compute-intensive tasks---is not yet fully explored. Keeping in view, this article explores this area and analyzes the potential of quantum computing for healthcare systems. We explore various dimensions within healthcare ecosystem where quantum computing could introduce new possibilities through higher computational speed to perform complex healthcare computations. Implementations of quantum computing in the healthcare scenarios have their own unique set of requirements. And therefore, we not only identify those key elements but also present a taxonomy of existing literature around quantum-based healthcare ecosystem, distinguishing cryptography in classical vs modern era along the way. Finally, we explore current challenges, their causes, and future research directions in implementing quantum computing systems in healthcare. </p>