Thermodynamics of fast quantum gates*

Quantum computation gates rely on the possibility to perform qubit rotations in the Bloch sphere faster than decoherence. Strikingly, a thermodynamic description analyzing the coherent energy exchanges between the qubit and the driven field is still missing. Previous studies have focused on long timescales [1-2], much larger than one Rabi period, blurring out any coherent phenomenon, and are therefore inadequate to study e.g. the work cost of fast gates. Here we propose a thermodynamic description that is valid at short time-scales, where the dynamics is captured by the Optical Bloch Equations, featuring coherent excitation exchanges between qubit and the field. We identify the first and second law and their quantum components. The derivation of an integral and a detailed Crooks quantum fluctuation theorems ensures the thermodynamic consistency of our theory. Predictions from earlier Floquet-based (long time-scale) approaches are recovered in relevant regimes. Our results contribute to bridge the gap between quantum thermodynamics on the one hand, and quantum optics and quantum computation on the other hand.
[1] K. Szczygielskli et al., Phys. Rev. E 87, 012120 (2013).
[2] B. Donvil, J. Stat. Mech. 043104 (2018).