# SolovayKitaevDecomposition

`qiskit.synthesis.SolovayKitaevDecomposition(basic_approximations=None)`

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Bases: `object`

(opens in a new tab)

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.

**Parameters**

**basic_approximations** (*str*(opens in a new tab) *|**dict*(opens in a new tab)*[**str*(opens in a new tab)*, np.ndarray] |* *list*(opens in a new tab)*[GateSequence] | None*) – 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.

## Methods

### find_basic_approximation

`find_basic_approximation(sequence)`

Finds gate in `self._basic_approximations`

that best represents `sequence`

.

**Parameters**

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

**Returns**

Gate in basic approximations that is closest to `sequence`

.

**Return type**

### load_basic_approximations

`load_basic_approximations(data)`

Load basic approximations.

**Parameters**

**data** (*list*(opens in a new tab) *|**str*(opens in a new tab) *|**dict*(opens in a new tab)) – 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]]}`

.

**Returns**

A list of basic approximations as type `GateSequence`

.

**Raises**

**ValueError**(opens in a new tab) – If the number of gate combinations and associated matrices does not match.

**Return type**

list(opens in a new tab)[GateSequence]

### run

`run(gate_matrix, recursion_degree, return_dag=False, check_input=True)`

Run the algorithm.

**Parameters**

**gate_matrix**(*np.ndarray*) – The 2x2 matrix representing the gate. This matrix has to be SU(2) up to global phase.**recursion_degree**(*int*(opens in a new tab)) – The recursion degree, called $n$ in the paper.**return_dag**(*bool*(opens in a new tab)) – If`True`

return a`DAGCircuit`

, else a`QuantumCircuit`

.**check_input**(*bool*(opens in a new tab)) – If`True`

check that the input matrix is valid for the decomposition.

**Returns**

A one-qubit circuit approximating the `gate_matrix`

in the specified discrete basis.

**Return type**

QuantumCircuit’ | ‘DAGCircuit