approximate_quantum_error(error, *, operator_string=None, operator_dict=None, operator_list=None)[source]

Return a QuantumError object that approximates an error as a mixture of specified operators (channels).

The approximation is done by minimizing the Hilbert-Schmidt distance between the process matrix of the target error channel (\(T\)) and the process matrix of the output channel (\(S = \sum_i{p_i S_i}\)), i.e. \(Tr[(T-S)^\dagger (T-S)]\), where \([p_1, p_2, ..., p_n]\) denote probabilities and \([S_1, S_2, ..., S_n]\) denote basis operators (channels).

See arXiv:1207.0046 for the details.

  • error (QuantumError or QuantumChannel) – the error to be approximated. The number of qubits must be 1 or 2.

  • operator_string (string) – a name for a pre-made set of building blocks for the output channel (Default: None). Possible values are 'pauli', 'reset', 'clifford'.

  • operator_dict (dict) – a dictionary whose values are the building blocks for the output channel (Default: None). E.g. {“x”: XGate(), “y”: YGate()}, keys “x” and “y” are not used in transformation.

  • operator_list (list) – list of building block operators for the output channel (Default: None). E.g. [XGate(), YGate()]


the approximate quantum error.

Return type:


  • NoiseError – if any invalid argument is specified or approximation failed.

  • MissingOptionalLibraryError – if cvxpy is not installed.


The operator input precedence is: list < dict < string. If a string is given, dict is overwritten; if a dict is given, list is overwritten. The string supports only 1- or 2-qubit errors and its possible values are 'pauli', 'reset', 'clifford'. The 'clifford' does not support 2-qubit errors.