  Diamond quantum processors consisting of a nitrogen-vacancy (NV) centre and
surrounding nuclear spins have been the key to significant advancements in
room-temperature quantum computing, quantum sensing and microscopy. The
optimisation of these processors is crucial for the development of large-scale
diamond quantum computers and the next generation of enhanced quantum sensors
and microscopes. Here, we present a full model of multi-qubit diamond quantum
processors and develop a semi-analytical method for designing gate pulses. This
method optimises gate speed and fidelity in the presence of random control
errors and is readily compatible with feedback optimisation routines. We
theoretically demonstrate infidelities approaching $\sim 10^{-5}$ for
single-qubit gates and established evidence that this can also be achieved for
a two-qubit CZ gate. Consequently, our method reduces the effects of control
errors below the errors introduced by hyperfine field misalignment and the
unavoidable decoherence that is intrinsic to the processors. Having developed
this optimal control, we simulated the performance of a diamond quantum
processor by computing quantum Fourier transforms. We find that the simulated
diamond quantum processor is able to achieve fast operations with low error
probability.
