Simulating finite-time quantum isothermal processes with generic superconducting quantum circuit

The finite-time isothermal process is fundamental in quantum thermodynamics yet complicated with combination of changing control parameters and the interaction with the thermal bath. Such complexity prevents the direct application of the traditional thermodynamics measurement of the relevant quantities. In this paper, we provide a discrete-step method to separate the work done and the heat exchange in the isothermal process by decomposing the process into piecewise adiabatic and isochoric processes. The piecewise control scheme makes it possible to simulate the whole process on a generic quantum computer, which provides a new platform to experimentally study quantum thermodynamics. We implement the simulation on ibmqx2 to show the $\mathrm{\mathcal{C}/\tau}$ scaling of the extra work in the finite-time isothermal process.