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Quantum computers are operated by external driving fields, such as lasers,microwaves or conduction lines, that execute logical operations on multi-qubitregisters, leaving the system in a pure state. However, the drive and thelogical system might become correlated in such a way that, after tracing outthe degrees of freedom of the driving field, the output state will not be pure.Previous works have pointed out that the resulting error scales inversely withthe energy of the drive, thus imposing a limit on the energy-efficiency ofquantum computing. In this study, we show how the same scaling can be seen as aconsequence of two competing phenomena: the entanglement-induced error, whichgrows with time, and a minimal time for computation imposed by quantum speedlimits. This evidence is made possible by quantifying, at any time, thecomputation error via the spectral radius associated to the density matrix ofthe logical qubit. Moreover, we also prove that, in order to attain a giventarget state with the same fidelity, it is energetically more efficient toperform a single driven evolution of the logical qubits rather than to splitthe computation in sub-routines, each operated by a dedicated pulse. Finally,we provide a thermodynamic interpretation of our results.

Time and energy bounds of driven quantum operations for quantum computing