Quantum compiling with low overhead

I will present a scheme to compile complex quantum gates that uses significantly fewer resources than existing schemes. In standard fault-tolerant protocols, a magic state is distilled from noisy resources, and copies of this magic state are then assembled into produced complex gates using the Solovay-Kitaev theorem or variants thereof. In our approach, we instead directly distill magic states associated to complex gates from noisy resources, leading to a reduction of the compiling overhead of several orders of magnitude.