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Quantum computation with generalized dislocation codes
Published in American Physical Society
2020
Volume: 102
   
Issue: 4
Abstract
In this paper, we study quantum computing with twists. Twists are yet another form of defects in a lattice. They arise from dislocations in the lattice and can be used to encode and process quantum information. Surface codes with twists are also called dislocation codes. Hastings and Geller showed that dislocation codes could provide gains in space-time complexity of quantum computation. In this paper, we undertake a detailed study of generalized dislocation codes. We develop the theory of qubit dislocation codes over arbitrary four-valent and bicolorable lattices. We give a construction to introduce twists in such lattices and also study the structure of logical operators. We then study dislocation codes over odd prime dimensions in square lattices. Using the theory developed, we present protocols for implementing a universal gate set in qubit dislocation codes. We also show how to implement the generalized Clifford group in qudit dislocation codes in odd prime dimensions. © 2020 American Physical Society.
About the journal
JournalData powered by TypesetPhysical Review A
PublisherData powered by TypesetAmerican Physical Society
Open AccessNo