Energy Requirements For Fault-Tolerant Quantum Computing

The precise control of qubits is paramount for the implementation of complex algorithms on gate-based quantum computers. Such control is limited by the quantum fluctuations of electromagnetic control fields, which result in errors in the implemented gate operations. The error-correction and qubit number requirements to mitigate the effects of gate errors has been explored at length, but a consistent characterization of their impact on other design resources has been limited. In this work we present a lower bound on the energy required to perform a gate operation as a direct result of the noise in otherwise coherent control fields. This bound allows us to characterize the energy efficiency of quantum algorithms and explore the thermodynamic and control resource costs of quantum computation, which may be necessary for the future design of economical quantum computers.