386 citations · 2.1k across the 25 of their papers we have counts for
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Topological Computation without Braiding
H. Bombin, M. A. Martin-Delgado
We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In par…
Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
H. Bombin, M. A. Martin-Delgado
We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin- systems that exhibits topological quantum order. The ground state is a string-net…
Homological Error Correction: Classical and Quantum Codes
H. Bombin, M. A. Martin-Delgado
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a…
Topological Quantum Error Correction with Optimal Encoding Rate
H. Bombin, M. A. Martin-Delgado
We prove the existence of topological quantum error correcting codes with encoding rates asymptotically approaching the maximum possible value. Explicit constructions of thes…