Classical computing works by processing bits, or 0s and 1s representing electrical signals of on and off. Quantum computing employs a very different technique for information processing. It uses qubits, which can exist as both a 1 and 0 at the same time, and uses the properties of subatomic particles in quantum physics such as interference, entanglement, and superposition to extend computational capabilities to hitherto unprecedented levels. The efficacy of quantum computing for important verticals such as healthcare where quantum computing can enable important breakthroughs in the development of life-saving drugs, performing quick DNA sequencing, detecting diseases in early stages, and performing other compute-intensive healthcare related tasks is not yet fully explored. Furthermore, implementations of quantum computing for healthcare scenarios such as these have their own unique set of requirements. Unfortunately, existing literature that address all of these dimensions is largely unstructured. This research is intended to be the first systematic analysis of the capabilities of quantum computing in enhancing healthcare systems. This article is structured with the help of taxonomies developed from existing literature to provide a panoramic view of the background and enabling technologies, applications, requirements, architectures, security and open issues, and future research directions. We believe the paper will aid both new and experienced researchers working in both quantum computing and the healthcare domains in visualizing the diversity in current research, in better understanding both pitfalls and opportunities, and coming up with informed decisions when designing new architectures and applications for quantum computing in healthcare.