This paper introduces the detector error model as a powerful framework for designing fault-tolerant quantum circuits. The detector error model fully captures fault-tolerance at the circuit level, unlike the stabilizer formalism commonly used for quantum error-correcting codes. The authors demonstrate the utility of this framework at three levels of abstraction in the engineering cycle of fault-tolerant circuit design: (1) finding robust syndrome extraction circuits, (2) identifying efficient measurement schedules, and (3) constructing fault-tolerant procedures. They enhance the surface code's resistance to measurement errors, devise short measurement schedules for color codes, and implement a more efficient fault-tolerant method for measuring logical operators. The detector error model is a binary matrix that captures the relationship between errors and detectors. It allows for the identification of errors by interpreting measurement outcomes. The framework is applied to three different levels of abstraction: (1) designing syndrome extraction circuits for high measurement noise, (2) designing measurement schedules for color codes, and (3) designing fault-tolerant logical measurement procedures. The authors show that the detector error model can be used to design fault-tolerant circuits that are robust to various types of errors, including measurement errors and data qubit errors. The paper also discusses the use of detector error models in the context of fault-tolerant quantum computing. It shows that the detector error model can be used to design fault-tolerant procedures that are robust to a wide range of errors. The authors demonstrate that the detector error model can be used to design fault-tolerant circuits that are efficient in terms of resource requirements and have high fault tolerance. The paper concludes that the detector error model is a powerful framework for designing fault-tolerant quantum circuits and that it has the potential to significantly improve the performance of quantum error-correcting codes.This paper introduces the detector error model as a powerful framework for designing fault-tolerant quantum circuits. The detector error model fully captures fault-tolerance at the circuit level, unlike the stabilizer formalism commonly used for quantum error-correcting codes. The authors demonstrate the utility of this framework at three levels of abstraction in the engineering cycle of fault-tolerant circuit design: (1) finding robust syndrome extraction circuits, (2) identifying efficient measurement schedules, and (3) constructing fault-tolerant procedures. They enhance the surface code's resistance to measurement errors, devise short measurement schedules for color codes, and implement a more efficient fault-tolerant method for measuring logical operators. The detector error model is a binary matrix that captures the relationship between errors and detectors. It allows for the identification of errors by interpreting measurement outcomes. The framework is applied to three different levels of abstraction: (1) designing syndrome extraction circuits for high measurement noise, (2) designing measurement schedules for color codes, and (3) designing fault-tolerant logical measurement procedures. The authors show that the detector error model can be used to design fault-tolerant circuits that are robust to various types of errors, including measurement errors and data qubit errors. The paper also discusses the use of detector error models in the context of fault-tolerant quantum computing. It shows that the detector error model can be used to design fault-tolerant procedures that are robust to a wide range of errors. The authors demonstrate that the detector error model can be used to design fault-tolerant circuits that are efficient in terms of resource requirements and have high fault tolerance. The paper concludes that the detector error model is a powerful framework for designing fault-tolerant quantum circuits and that it has the potential to significantly improve the performance of quantum error-correcting codes.