While recent breakthroughs in quantum computing promise the nascence of the quantum information age, quantum states remain delicate to control. Moreover, the required energy budget for large scale quantum applications has only sparely been considered. Addressing either of these issues necessitates a careful study of the most energetically efficient implementation of elementary quantum operations. In the present analysis, we show that this optimal control problem can be solved within the powerful framework of quantum speed limits. To this end, we derive state-independent lower bounds on the energetic cost, from which we find the universally optimal implementation of unitary quantum gates, for both single and N-qubit operations.

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Among the emerging technologies with prophesied quantum advantage, quantum communications has already led to fascinating demonstrations—including quantum teleportation to and from satellites. However, all optical communication necessitates the use of optical devices, the comprehensive quantum thermodynamic description of which is still severely lacking. In the present analysis, we prove several versions of Landauer’s principle for noisy polarizers, namely, absorbing linear polarizers and polarizing beam splitters. As main results, we obtain statements of the second law quantifying the minimal amount of heat that is dissipated in the creation of linearly polarized light. Our findings are illustrated with an experimentally tractable example, namely, the temperature dependence of a quantum eraser. Published by the American Physical Society 2023