|
| related topics |
| {energy, state, states} |
| {phase, path, phys} |
| {error, code, errors} |
| {state, algorithm, problem} |
| {temperature, thermal, energy} |
| {operator, operators, space} |
| {force, casimir, field} |
| {measurement, state, measurements} |
| {qubit, qubits, gate} |
| {let, theorem, proof} |
|
Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy
Threshold for a Toric Quantum Memory
Takuya Ohno, Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui
abstract: We study the phase structure of the random-plaquette Z_2 lattice gauge model
in three dimensions. In this model, the "gauge coupling" for each plaquette is
a quenched random variable that takes the value \beta with the probability 1-p
and -\beta with the probability p. This model is relevant for the recently
proposed quantum memory of toric code. The parameter p is the concentration of
the plaquettes with "wrong-sign" couplings -\beta, and interpreted as the error
probability per qubit in quantum code. In the gauge system with p=0, i.e., with
the uniform gauge couplings \beta, it is known that there exists a second-order
phase transition at a certain critical "temperature", T(\equiv \beta^{-1}) =
T_c =1.31, which separates an ordered(Higgs) phase at TT_c. As p increases, the critical
temperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects
with the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The
value p_c is just the accuracy threshold for a fault-tolerant quantum memory
and associated quantum computations. By the Monte-Carlo simulations, we
calculate the specific heat and the expectation values of the Wilson loop to
obtain the phase-transition line T_c(p) numerically. The accuracy threshold is
estimated as p_c \simeq 0.033.
- oai_identifier:
- oai:arXiv.org:quant-ph/0401101
- categories:
- quant-ph cond-mat.dis-nn hep-lat
- comments:
- 24 pages, 14 figures, some clarifications
- doi:
- 10.1016/j.nuclphysb.2004.07.003
- arxiv_id:
- quant-ph/0401101
- journal_ref:
- Nucl.Phys. B697 (2004) 462
- created:
- 2004-01-19
- updated:
- 2004-05-07
Full article ▸
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