  When calculating the overhead of a quantum algorithm made fault-tolerant
using the surface code, many previous works have used defects and braids for
logical qubit storage and state distillation. In this work, we show that
lattice surgery reduces the storage overhead by over a factor of 4, and the
distillation overhead by nearly a factor of 5, making it possible to run
algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits
capable of executing gates with error $p\sim 10^{-3}$. These numbers strongly
suggest that defects and braids in the surface code should be deprecated in
favor of lattice surgery.
