I will give an overview of one of my long-standing research strands on how to exploit randomness in the design of quantum compilers and algorithms. This will include the general idea of mixing different unitaries to obtain a quadratic reduction in compilation errors without any increase in average gate count. I will then review work by myself and other groups on incorporating randomization into Trotterisation approaches to Hamiltonian simulation and phase estimation, including the qDrift algorithm. Lastly, I will describe more recent work on mitigated magic dilution for non-Clifford logic, where we showed how randomisation can enable us to dilute high magic gates (like the T gate) to achieve a larger number of low magic gates (such as small angle rotations) while also mitigating errors. The approach of mitigated magic dilution is benchmarked against the Hubbard model, where we see evidence that it is orders of magnitude more resource-efficient in the early error-corrected setting where algorithms are of low depth.
