Here's my code to define the depolarization error using Qiskit, which included both one and two-qubit errors:

def depo_error(one_qubit_error, two_qubit_error):
    noise_model = NoiseModel()

    error_1q = depolarizing_error(one_qubit_error, 1)
    noise_model.add_all_qubit_quantum_error(error_1q, ['u1', 'u2', 'u3'])

    error_2q = depolarizing_error(two_qubit_error, 2)
    noise_model.add_all_qubit_quantum_error(error_2q, ['cx'])

    return noise_model

My question is that after setting up the error rates for one and two-qubit gates, how does the error accumulate? Suppose I have a circuit that looks pretty similar to the Hadamard test:

enter image description here

And I set one_qubit_error = two_qubit_error = 0.5. Is there a way we can estimate how the error accumulates and its effect on the measurement?

  • $\begingroup$ is $U_\psi$ a one-qubit unitary? $\endgroup$
    – forky40
    Commented Oct 16, 2023 at 15:52
  • $\begingroup$ @forky40 I think generally it could be multi-qubit. $\endgroup$
    – IGY
    Commented Oct 17, 2023 at 7:25

1 Answer 1


I think you can find related information in this: http://theory.caltech.edu/~preskill/ph219/chap3_15.pdf

In chapter 3.4.1. Depolarizing channel.

The depolarizing channel is a model of a decohering qubit that has particularly nice symmetry properties. We can describe it by saying that, with probability 1 − p the qubit remains intact, while with probability p an “error” occurs.

You need to learn density matrix representations to walk through the derivation of the error accumulation.


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