A stabilizer code for uncorrelated errors can correct spatially correlated ones
Tsuyoshi Hayashi, Toshihico Arimitsu, Sachiko Kitajima, Fumio Shibata · Journal of Physics A Mathematical and Theoretical · 2007
It is shown that errors on qubits caused by spatially correlated noise of quantum Brownian motion can be corrected with a stabilizer code (a quantum error correction code) and recovery operations prepared for uncorrelated noise without modifications. The analysis is made by means of the quantum stochastic Liouville equation approach which has been developed within the canonical operator formalism for dissipative systems called non-equilibrium thermo field dynamics. This approach yields a transparent procedure to derive completely positive maps describing errors on qubits under given statistics of noise.