  Quantum computers will allow calculations beyond existing classical
computers. However, current technology is still too noisy and imperfect to
construct a universal digital quantum computer with quantum error correction.
Inspired by the evolution of classical computation, an alternative paradigm
merging the flexibility of digital quantum computation with the robustness of
analog quantum simulation has emerged. This universal paradigm is known as
digital-analog quantum computing. Here, we introduce an efficient
digital-analog quantum algorithm to compute the quantum Fourier transform, a
subroutine widely employed in several relevant quantum algorithms. We show
that, under reasonable assumptions about noise models, the fidelity of the
quantum Fourier transformation improves considerably using this approach when
the number of qubits involved grows. This suggests that, in the Noisy
Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and
analog quantum computing could be a sensible approach to reach useful quantum
supremacy.
