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class SolovayKitaevDecomposition(basic_approximations=None)

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Bases: object

The Solovay Kitaev discrete decomposition algorithm.

This class is called recursively by the transpiler pass, which is why it is separeted. See qiskit.transpiler.passes.SolovayKitaev for more information.


basic_approximations – A specification of the basic SU(2) approximations in terms of discrete gates. At each iteration this algorithm, the remaining error is approximated with the closest sequence of gates in this set. If a str, this specifies a .npy filename from which to load the approximation. If a dict, then this contains {gates: effective_SO3_matrix} pairs, e.g. {"h t": np.array([[0, 0.7071, -0.7071], [0, -0.7071, -0.7071], [-1, 0, 0]]}. If a list, this contains the same information as the dict, but already converted to GateSequence objects, which contain the SO(3) matrix and gates.




Finds gate in self._basic_approximations that best represents sequence.


sequence (GateSequence) – The gate to find the approximation to.

Return type



Gate in basic approximations that is closest to sequence.



Load basic approximations.


data (list | str | dict) – If a string, specifies the path to the file from where to load the data. If a dictionary, directly specifies the decompositions as {gates: matrix}. There gates are the names of the gates producing the SO(3) matrix matrix, e.g. {"h t": np.array([[0, 0.7071, -0.7071], [0, -0.7071, -0.7071], [-1, 0, 0]]}.

Return type



A list of basic approximations as type GateSequence.


ValueError – If the number of gate combinations and associated matrices does not match.

run, recursion_degree, return_dag=False, check_input=True)

Run the algorithm.


  • gate_matrix (np.ndarray) – The 2x2 matrix representing the gate. This matrix has to be SU(2) up to global phase.
  • recursion_degree (int) – The recursion degree, called nn in the paper.
  • return_dag (bool) – If True return a DAGCircuit, else a QuantumCircuit.
  • check_input (bool) – If True check that the input matrix is valid for the decomposition.

Return type

QuantumCircuit’ | ‘DAGCircuit


A one-qubit circuit approximating the gate_matrix in the specified discrete basis.

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