  The fragile nature of quantum information limits our ability to construct
large quantities of quantum bits suitable for quantum computing. An important
goal, therefore, is to minimize the amount of resources required to implement
quantum algorithms, many of which are serial in nature and leave large numbers
of qubits idle much of the time unless compression techniques are used.
Furthermore, quantum error-correcting codes, which are required to reduce the
effects of noise, introduce additional resource overhead. We consider a
strategy for quantum circuit optimization based on topological deformation in
the surface code, one of the best performing and most practical quantum
error-correcting codes. Specifically, we examine the problem of minimizing
computation time on a two-dimensional qubit lattice of arbitrary, but fixed
dimension, and propose two algorithms for doing so.
