Commuting Pauli Hamiltonians as maps between free modules

DOI10.1007/s00220-013-1810-2zbMath1277.82014arXiv1204.1063OpenAlexW3100008668WikidataQ114230971 ScholiaQ114230971MaRDI QIDQ380335

Jeongwan Haah

Publication date: 13 November 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.1063

zbMATH Keywords

Pauli matricesqubitsClifford operatorsPauli groupPauli Hamiltonianssymplectic transformations

Mathematics Subject Classification ID

Quantum computation (81P68) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Applications of group representations to physics and other areas of science (20C35)

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Invertible subalgebras, Cellular automaton decoders of topological quantum memories in the fault tolerant setting, Nontrivial quantum cellular automata in higher dimensions, Ground subspaces of topological phases of matter as error correcting codes, Fracton phases via exotic higher-form symmetry-breaking, Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices, Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D, Kosaki-Longo index and classification of charges in 2D quantum spin models, Haah codes on general three-manifolds, Gauge structures: from stabilizer codes to continuum models, A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less), A non-commuting stabilizer formalism

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