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Quantum circuits implementing fault-tolerant quantum error correction (QEC)for the three qubit bit-flip code and five-qubit code are studied. To describethe effect of noise, we apply a model based on a generalized effectiveHamiltonian where the system-environment interactions are taken into account byincluding stochastic fluctuating terms in the system Hamiltonian. This noisemodel enables us to investigate the effect of noise in quantum circuits underrealistic device conditions and avoid strong assumptions such as maximalparallelism and weak storage errors. Noise thresholds of the QEC codes arecalculated. In addition, the effects of imprecision in projective measurements,collective bath, fault-tolerant repetition protocols, and level of parallelismin circuit constructions on the threshold values are also studied with emphasison determining the optimal design for the fault-tolerant QEC circuit. Theseresults provide insights into the fault-tolerant QEC process as well as usefulinformation for designing the optimal fault-tolerant QEC circuit for particularphysical implementation of quantum computer.Comment: 9 pages, 9 figures; to be submitted to Phys. Rev.

Microscopic quantum dynamics study on the noise threshold of fault-tolerant quantum error correction