Energy-error tradeoff in encoding quantum error correction

While it has been widely recognized that genuine quantum advantage for practical problems might only be achieved with fault-tolerant quantum computers, it is still not entirely clear whether the required quantum error correction will be physically feasible. In the present work, we carefully analyze the required energy resources to encode the logical qubit states for repetition, perfect, and Steane codes. We find that there is a universal trade-off between the target precision and the required energetic resources. Importantly, we find that the energetic resources intimately depend on the specific physical realization of a quantum error correction code, and that the required resources scale exponentially with the targeted precision of the encoding.