  Despite significant overhead reductions since its first proposal, magic state
distillation is often considered to be a very costly procedure that dominates
the resource cost of fault-tolerant quantum computers. The goal of this work is
to demonstrate that this is not true. By writing distillation circuits in a
form that separates qubits that are capable of error detection from those that
are not, most logical qubits used for distillation can be encoded at a very low
code distance. This significantly reduces the space-time cost of distillation,
as well as the number of qubits. In extreme cases, it can cost less to distill
a magic state than to perform a logical Clifford gate on full-distance logical
qubits.
