I have a Pauli channel with disjoint probabilities $P_I$, $P_X$, $P_Y$, $P_Z$ (meaning $P_I + P_X + P_Y + P_Z = 1$) corresponding to Pauli errors I, X, Y, Z. Is there some way apply this Pauli channel in Stim?

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    $\begingroup$ Note: this is a question I received by email. I put the answer here for posterity. $\endgroup$ Commented May 11, 2021 at 0:42

1 Answer 1


Update: Since v1.4, stim supports custom pauli channels PAULI_CHANNEL_1(px, py, pz) and PAULI_CHANNEL_2(pix, piy, ..., pzz).

Before v1.4

If $P_x = P_y = P_z$ then DEPOLARIZE1 is what you need. If $P_y = P_z = 0$ then X_ERROR is what you need (ditto Y_ERROR, Z_ERROR). Otherwise you can use CORRELATED_ERROR and ELSE_CORRELATED_ERROR.

For example, suppose $P_x = 0.1$, $P_y = 0.2$, $P_z = 0.3$ and your target is qubit $5$. You can do this:

ELSE_CORRELATED_ERROR(0.22222222222) Y5  # note: P(Y|not X) = 20%/(100% - 10%)
ELSE_CORRELATED_ERROR(0.42857142857) Z5  # note: P(Z|not X and not Y) = 30%/(100% - 10% - 20%)

The else-case probabilities are conditioned on the earlier cases not happening, which is why they are larger than the original probabilities.

Here's the general case, implemented as python code:

def append_generic_single_qubit_error_channel_to_circuit(
        circuit: stim.Circuit,
        target: int,
        px: float,
        py: float,
        pz: float):
        circuit: The circuit to append the error channel to.
        target: The qubit to hit with the error channel.
        px: The disjoint probability of an X error.
        py: The disjoint probability of a Y error.
        pz: The disjoint probability of a Z error.

        0 <= px <= 1
        0 <= py <= 1
        0 <= pz <= 1
        px+py+pz <= 1
    circuit.append_operation("CORRELATED_ERROR", [stim.target_x(target)], px)
    circuit.append_operation("ELSE_CORRELATED_ERROR", [stim.target_y(target)], py / (1 - px))
    circuit.append_operation("ELSE_CORRELATED_ERROR", [stim.target_z(target)], pz / (1 - px - py))

Note that it agrees with the example case:

import stim
c = stim.Circuit()
    circuit=c, target=5, px=0.1, py=0.2, pz=0.3)
E(0.1) X5

(E is an abbreviation for CORRELATED_ERROR)


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