  Magic state distillation, which is a probabilistic process used to generate
magic states, plays an important role in universal fault-tolerant quantum
computers. On the other hand, to solve interesting problems, we need to run
complex programs on fault-tolerant quantum computers, and hence, the system
needs to use hardware resources efficiently. Taking advantage of parallelism is
a major optimization strategy and compilers are responsible for performing
optimizations to allow parallel processing. However, the probabilistic nature
of magic state distillation is not compatible with compile-time optimizations
and results in an additional run-time delay. To reduce the additional run-time
delay, we propose introducing a pool of magic states. We run simulations of
quantum circuits to verify the magnitude of the run-time delay and the
usefulness of the mitigation approach. The experimental results show that the
run-time delay is amplified by parallel processing, and pooling effectively
reduces the run-time delay with a small spatial cost.
