Quantum Computation with Topological Codes by Keisuke Fujii

Author:Keisuke Fujii
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(3.40)

The binary valuables are transformed into spin variables by . Moreover, we define a coupling constant . Then Eq. (3.40) is rewritten as

(3.41)

where is a normalization factor and m(l) and are end points of the edge . By changing the notation and , the posterior probability is reformulated as a Boltzmann factor of the RBIM:

(3.42)

where . On the edges where the errors are located, anti-ferromagnetic interactions are assigned. The posterior probability of the logical operator Eq. (3.31) is calculated by taking summation over all gauge spin configurations (this corresponds to the summation over all stabilizer operators in Eq. (3.31)):

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