Z_N Gauge Theories on a Lattice and Quantum Memory

Details Z_N Gauge Theories on a Lattice and Quantum Memory Z_N Gauge Theories on a Lattice and Quantum Memory

2003-09-19

arxiv.org/abs/quant-ph/0309142v1

Annals Phys. 311 (2004) 152

Physics

Quantum Physics

20 pages, 5 figures

Scientific paper

10.1016/j.aop.2003.11.003

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.

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