  The question of the energetic efficiency of quantum computers has gained some
attention only recently. A precise understanding of the resources required to
operate a quantum computer with a targeted computational performance and how
the energy requirements can impact the scalability is still missing. In this
work, one implementation of the quantum Fourier transform (QFT) algorithm in a
trapped ion setup was studied. The main focus was to obtain a theoretical
characterization of the energetic costs of quantum computation. The energetic
cost of the experiment was estimated by analyzing the components of the setup
and the steps involved in a quantum computation, from the cooling and
preparation of the ions to the implementation of the algorithm and readout of
the result. A potential scaling of the energetic costs was argued and used to
find a possible threshold for an energetic quantum advantage against
state-of-the-art classical supercomputers.
