I don't think there is any such branch where you can study both physics and CS in depth. But, I think IITK has a concept of dual major. You can look up on IITK website or contact their students to know how it works.
A compromise branch would be electrical engineering, which is somewhere in between physics and CS.
I like to blog about various topics ranging from education in IITs to social issues in India and US. All opinions and views presented here are my own and not of my employer.