Despite its societal and industrial relevance, how energy consumption will impact the scalability of quantum computers remains a scarcely explored question. Properly addressing it mandates synergies between fundamental research and enabling technologies, the former (resp. the latter) managing the computing performances (resp. the macroscopic resource consumption). This effort requires to set up common methodologies and languages.
Here we propose such methodology and apply it to the case of a superconducting, full-stack quantum computer operating in the NISQ, then in the fault-tolerant paradigm.
Based on a comprehensive modeling, we study the impact of various parameters on the global power consumption, ranging from the software (computing architecture and choice of code) to the hardware (quality of qubits) and engineering parameters (cryogeny, controlling electronics, wiring). We propose a quantum energy efficiency as a new benchmark that can be further used to rank quantum processors, and define a quantum energy advantage in the execution of a useful quantum algorithm. We provide realistic estimations of the minimal energetic bill for fault-tolerant quantum computations. Our findings reveal that the quantum energy advantage can be reached before the quantum computational advantage, providing a new and strong argument for the practical interest of quantum computing. Our approach also allows to exhibit some conceptual differences in the way energy is being used in quantum compared to classical computers. Finally, our methodology is general and extendable to other qubits, codes and quantum technologies.
[1] A. Auffèves, Quantum technologies need a Quantum Energy Initiative, arXiv:2111.09241
[2] M Fellous-Asiani, JH Chai, RS Whitney, A Auffèves, HK Ng, Limitations in quantum computing from resource constraints, PRX Quantum 2 (4), 040335
[3] M Fellous-Asiani, The resource cost of large scale quantum computing, arXiv:2112.04022
[4] M Fellous-Asiani, JH Chai, Y Thonnart, HK Ng, RS. Whitney, A Auffèves, Optimizing quantum energy efficiency for scalable full-stack quantum computers [To appear]

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This work has been done in collaboration with Marco Fellous-Asiani$^{1,7}$, Jing Hao Chai$^{1,2}$, Yvain Thonnart$^{3}$, Hui Khoon Ng$^{4,2,5}$, Robert S. Whitney$^6$, Alexia Auffèves$^1$

$^1$Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France
$^2$Centre for Quantum Technologies, National University of Singapore, Singapore
$^3$Université Grenoble Alpes, CEA-LIST, F-38000 Grenoble, France
$^4$Yale-NUS College, Singapore
$^5$MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d’Azur, Sorbonne
Université, National University of Singapore, Nanyang Technological University, Singapore
$^6$LPMMC, Université Grenoble Alpes and CNRS, Grenoble, France
$^7$Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Warsaw, Poland