  Fault-tolerant quantum computation using two-dimensional topological quantum
error correcting codes can benefit from multi-qubit long-range operations. By
using simple commutation rules, a quantum circuit can be transpiled into a
sequence of solely non-Clifford multi-qubit gates. Prior work on fault-tolerant
compilation avoids optimal scheduling of such gates since they reduce the
parallelizability of the circuit. We observe that the reduced parallelization
potential is outweighed by the significant reduction in the number of gates. We
therefore devise a method for scheduling multi-qubit lattice surgery using an
earliest-available-first policy, solving the associated forest packing problem
using a representation of the multi-qubit gates as Steiner trees. Our extensive
testing on random and application-inspired circuits demonstrates the method's
scalability and performance. We show that the transpilation significantly
reduces the circuit length on the set of circuits tested, and that the
resulting circuit of multi-qubit gates has a further reduction in the expected
circuit execution time compared to serial execution.
