# PolynomialPauliRotations

*class *`PolynomialPauliRotations(num_state_qubits=None, coeffs=None, basis='Y', name='poly')`

Bases: `qiskit.circuit.library.arithmetic.functional_pauli_rotations.FunctionalPauliRotations`

A circuit implementing polynomial Pauli rotations.

For a polynomial :math`p(x)`, a basis state $|i\rangle$ and a target qubit $|0\rangle$ this operator acts as:

$|i\rangle |0\rangle \mapsto \cos(p(i)) |i\rangle |0\rangle + \sin(p(i)) |i\rangle |1\rangle$Let n be the number of qubits representing the state, d the degree of p(x) and q_i the qubits, where q_0 is the least significant qubit. Then for

$x = \sum_{i=0}^{n-1} 2^i q_i,$we can write

$p(x) = \sum_{j=0}^{j=d} c_j x_j$where $c$ are the input coefficients, `coeffs`

.

Prepare an approximation to a state with amplitudes specified by a polynomial.

**Parameters**

**num_state_qubits**(`Optional`

[`int`

]) – The number of qubits representing the state.**coeffs**(`Optional`

[`List`

[`float`

]]) – The coefficients of the polynomial.`coeffs[i]`

is the coefficient of the i-th power of x. Defaults to linear: [0, 1].**basis**(`str`

) – The type of Pauli rotation (‘X’, ‘Y’, ‘Z’).**name**(`str`

) – The name of the circuit.

## Attributes

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

**Return type**

`List`

[`AncillaQubit`

]

### basis

The kind of Pauli rotation to be used.

Set the basis to ‘X’, ‘Y’ or ‘Z’ for controlled-X, -Y, or -Z rotations respectively.

**Return type**

`str`

**Returns**

The kind of Pauli rotation used in controlled rotation.

### calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`

**Return type**

`dict`

### clbits

### coeffs

The multiplicative factor in the rotation angle of the controlled rotations.

The rotation angles are `slope * 2^0`

, `slope * 2^1`

, … , `slope * 2^(n-1)`

where `n`

is the number of state qubits.

**Return type**

`List`

[`float`

]

**Returns**

The rotation angle common in all controlled rotations.

### data

### degree

Return the degree of the polynomial, equals to the number of coefficients minus 1.

**Return type**

`int`

**Returns**

The degree of the polynomial. If the coefficients have not been set, return 0.

### extension_lib

Default value: `'include "qelib1.inc";'`

### global_phase

### header

Default value: `'OPENQASM 2.0;'`

### instances

Default value: `2505`

### metadata

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided `dict`

of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

**Return type**

`dict`

### num_ancilla_qubits

Deprecated. Use num_ancillas instead.

### num_ancillas

Return the number of ancilla qubits.

**Return type**

`int`

### num_clbits

Return number of classical bits.

**Return type**

`int`

### num_parameters

**Return type**

`int`

### num_qubits

Return number of qubits.

**Return type**

`int`

### num_state_qubits

The number of state qubits representing the state $|x\rangle$.

**Return type**

`int`

**Returns**

The number of state qubits.

### op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

**Return type**

`List`

[`int`

]

**Returns**

List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`

.

**Raises**

**AttributeError** – When circuit is not scheduled.

### parameters

**Return type**

`ParameterView`

### prefix

Default value: `'circuit'`

### qregs

A list of the quantum registers associated with the circuit.