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We study the stochastic energetic exchanges in quantum heat engines. Due tomicroreversibility, these obey a fluctuation relation, called the heat enginefluctuation relation, which implies the Carnot bound: no machine can have anefficiency larger than Carnot's efficiency. The stochastic thermodynamics of aquantum heat engine (including the joint statistics of heat and work and thestatistics of efficiency) is illustrated by means of an optimal two-qubit heatengine, where each qubit is coupled to a thermal bath and a two-qubit gatedetermines energy exchanges between the two qubits. We discuss possible solidstate implementations with Cooper pair boxes and flux qubits, quantum gateoperations, and fast calorimetric on-chip measurements of single stochasticevents.

Nonequilibrium fluctuations in quantum heat engines: Theory, example, and possible solid state experiments