This is an exciting new area and has begun to attract a lot of attention from students. Indicative of its evolution, many who have crossed the finish line offer varying perspectives on how to go about a Masters in this field. Some suggest doing a graduate degree in Physics with many electives in biology and chemistry, especially if a student is interested in the quantum mechanical aspects (https://www.physicsforums.com/threads/how-to-become-a-quantum-biologist.835068/). Given the composite character of the discipline, it begets many names. Some call it biophysics. Some universities call it ‘Life & Chemical Sciences (Quantum Biology)’. Aspiring candidates will have to search quite a bit to find universities offering quantum biology.
Interested students might consider reading Jim Al-Khalilis’s book, co-authored with Johnjoe McFadden, titled ‘Life on the edge: the coming age of quantum biology’. According to Wikipedia, Jim Al-Khalili is “currently Professor of Theoretical Physics and Chair in the Public Engagement in Science at the University of Surrey”.
The Max Planck Institute for Medical Research is an institution students may explore (http://www.mpimf-heidelberg.mpg.de/en). The Centre of Quantum Technology at The University of Kwazulu-Natal in South Africa could also hold interest for students (http://quantum.ukzn.ac.za/). There is a Quantum University offering a range of courses (http://iquim.org/). Ulm University in Germany offers a Master of Science in Biophysics with an opportunity to do a PhD (https://www.daad.de/deutschland/studienangebote/international-programs/en/?p=d&s=kr&id=4277).
Students might also like to look at the Hokkaido University, Graduate School of Science, School of Science in Japan (https://www.sci.hokudai.ac.jp/english/history.html).
Students could also look at The Institute for Advanced Studies at The University of Surrey (http://www.surrey.ac.uk/subjects/biosciences-and-medicine). Or the Paris Diderot Physics Department (http://www.physique.univ-paris-diderot.fr/IMG/pdf/plaquettem2__ang_nov_2012.pdf).