Markovian heat engine boosted by quantum coherence

We evaluate the role of quantum coherence as a thermodynamic resource in a noisy, Markovian one-qubit heat engine. We demonstrate that, when operating according to a quantum Otto cycle, can surpass the classical efficiency limit by consuming the coherence of noisy quantum states. Computed Leggett-Garg temporal correlations imply the engine's non-classical nature. Amplitude damping significantly reduces efficiency and extractable work. In contrast, phase damping has no significant impact on the extractable work. We implement the entire Otto cycle in a quantum circuit, simulating realistic amplitude and phase damping channels, as well as gate-level noise. We introduce an operational measure of the circuit's thermodynamic cost, establishing a direct link between energy consumption and information processing in quantum heat engines.