Reduced SpaceTime and Time Costs Using Dislocation Codes and Arbitrary Ancillas
Abstract
We propose two distinct methods of improving quantum computing protocols based on surface codes. First, we analyze the use of dislocations instead of holes to produce logical qubits, potentially reducing spacetime volume required. Dislocations induce defects which, in many respects, behave like Majorana quasiparticles. We construct circuits to implement these codes and present faulttolerant measurement methods for these and other defects which may reduce spatial overhead. One advantage of these codes is that Hadamard gates take exactly $0$ time to implement. We numerically study the performance of these codes using a minimum weight and a greedy decoder using finitesize scaling. Second, we consider state injection of arbitrary ancillas to produce arbitrary rotations. This avoids the logarithmic (in precision) overhead in online cost required if $T$ gates are used to synthesize arbitrary rotations. While this has been considered before, we consider also the parallel performance of this protocol. Arbitrary ancilla injection leads to a probabilistic protocol in which there is a constant chance of success on each round; we use an amortized analysis to show that even in a parallel setting this leads to only a constant factor slowdown as opposed to the logarithmic slowdown that might be expected naively.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 arXiv:
 arXiv:1408.3379
 Bibcode:
 2014arXiv1408.3379H
 Keywords:

 Quantum Physics
 EPrint:
 16 pages, 10 figures