Z_N Gauge Theories on a Lattice and Quantum Memory
arXiv:quant-ph/0309142 · doi:10.1016/j.aop.2003.11.003
Abstract
In the present paper we shall study (2+1) dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation modes in the Higgs phase and clarify relationship between the Z_N gauge theories and Kitaev's model for quantum memory and quantum computations. Then we study effects of random gauge couplings(RGC) which are identified with noise and errors in quantum computations by Kitaev's model. By using a duality transformation, it is shown that time-independent RGC give no significant effects on the phase structure and the stability of quantum memory and computations. Then by using the replica methods, we study Z_N gauge theories with time-dependent RGC and show that nontrivial phase transitions occur by the RGC.
20 pages, 5 figures
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- Low-temperature coherence properties of Z_2 quantum memory
- Interplay between lattice gauge theory and subsystem codes
- Quantum engineering for compactly localized states in disordered Lieb lattices
- Population annealing with topological defect driven nonlocal updates for spin systems with quenched disorder
- Construction of Entangled Many-body States via the Higgs Mechanism