How to use stim to implement a specific circuit

Question

I'm doing a QEC job, and I want to apply an error like $U_{err}(\theta) = \prod_j e^{-i\frac{\theta_j}{2}P_j} = \prod_j (I\cos(\frac{\theta_j}{2}) - iP_j\sin(\frac{\theta_j}{2}))$, where $\theta_j$ is some given value, and $P_j$ is some Pauli operator. I know that only when $\theta_j = 0$ or $\theta_j = \pm \pi/2$, then $U_err$ is Clifford. I just want to have a function like

def error(Theta, Pauli):
    error_circuit = stim.Circuit()

    TODO!!!

    return error_circuit

to help me to get $U_{err}$, but I don't know how.

Answer 1

For multi-term Pauli errors you can append a correlated error to the circuit:

circuit.append(
    "CORRELATED_ERROR",
    [stim.target_x(2), stim.target_y(3), stim.target_z(5)],
    probability,
)

For Clifford errors, you will need to simulate the circuit by driving a tableau simulator or flip simulator, and probabilistically choosing to do a Clifford gate or not when you want the error. Stim circuits don't have any probabilistic-Clifford instructions.