Landauer's principle laid the main foundation for the development of modern thermodynamics of information. However, in its original inception the principle relies on semiformal arguments and dissipative dynamics. Hence, if and how Landauer's principle applies to unitary quantum computing is less than obvious. Here, we prove an inequality bounding the change of Shannon information encoded in the logical quantum states by quantifying the energetic cost of Hamiltonian gate operations. The utility of this bound is demonstrated by outlining how it can be applied to identify energetically optimal quantum gates in theory and experiment. The analysis is concluded by discussing the energetic cost of quantum error correcting codes with non-interacting qubits, such as Shor's code.

朗道尔原理为现代信息热力学的发展奠定了主要基础。然而，在最初的时候，该原则依赖于半形式论证和耗散动力学。因此，兰道尔原理是否以及如何应用于幺正量子计算并不明显。在这里，我们通过量化哈密顿门操作的能量成本来证明限制在逻辑量子态中编码的香农信息变化的不等式。通过概述如何将其应用于在理论和实验中识别能量最优量子门，证明了该界限的实用性。通过讨论具有非交互量子位的量子纠错码（例如 Shor 码）的能量成本，得出了分析结果。