Joint mitigation of quantum gate and measurement errors via the Z-mixed-state expression of the Pauli channel

Quantum error mitigation is becoming increasingly crucial. We have reformulated the expression of the Pauli channel, termed as the Z-mixed-state expression of the Pauli channel (ZMSEPC). Based on this expression, we have studied the changes of measurement expectation values after composing multiple Pauli channels and proposed related theorems. Afterward, we proposed a method called quantum error mitigation based on the Z-mixed-state expression of the Pauli channel (QEM-ZMSEPC) that can mitigate both quantum gate noise and quantum measurement noise, which offers a lower complexity compared to traditional measurement error mitigation methods. We have conducted experiments for the QEM-ZMSEPC method on classical computers and real quantum computers. The results demonstrate that compared to zero noise extrapolation method, QEM-ZMSEPC has superior error mitigation effects. Furthermore, our experimental results demonstrate the potential of the QEM-ZMSEPC combining other error mitigation techniques such as Pauli twirling. These positive results imply the significance of QEM-ZMSEPC.