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We propose two distinct methods of improving quantum computing protocolsbased on surface codes. First, we analyze the use of dislocations instead ofholes to produce logical qubits, potentially reducing spacetime volumerequired. Dislocations induce defects which, in many respects, behave likeMajorana quasi-particles. We construct circuits to implement these codes andpresent fault-tolerant measurement methods for these and other defects whichmay reduce spatial overhead. One advantage of these codes is that Hadamardgates take exactly $0$ time to implement. We numerically study the performanceof these codes using a minimum weight and a greedy decoder using finite-sizescaling. Second, we consider state injection of arbitrary ancillas to producearbitrary rotations. This avoids the logarithmic (in precision) overhead inonline cost required if $T$ gates are used to synthesize arbitrary rotations.While this has been considered before, we consider also the parallelperformance of this protocol. Arbitrary ancilla injection leads to aprobabilistic protocol in which there is a constant chance of success on eachround; we use an amortized analysis to show that even in a parallel settingthis leads to only a constant factor slowdown as opposed to the logarithmicslowdown that might be expected naively.

Reduced Space-Time and Time Costs Using Dislocation Codes and Arbitrary Ancillas