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

Low overhead quantum computation using lattice surgery