Landauer's principle states that the heat generation in an irreversible computation must always be greater than or equal to the information theoretic entropy change and hence sets a fundamental limit on the thermodynamics of information processing, Using concepts and ideas from stochastic thermodynamics several experiments have explored the thermodynamics of information processing at the ultimate limit set by Landauer. In this approach to thermodynamics quantities such as heat and work are described stochastically as fluctuations about average values dominate physics. Turning towards quantum systems no such experiments are yet in operation. This is primarily due to the additional fragility associated with performing measurements on quantum systems. Very recently, interferometric methods have been proposed and used to measure the full statistics of work performed by replacing the necessity of projective measurements by performing phase estimation on an appropriately coupled ancilla qubit. In this talk I will outline how these schemes are modified to allow the extraction of statistics of heat dissipated from an elementary operation on a quantum system has been performed. I will also discuss preliminary experimental results and interesting theoretical extensions.