# PolynomialPauliRotations¶

class PolynomialPauliRotations(num_state_qubits=None, coeffs=None, basis='Y', name='poly')[source]

A circuit implementing polynomial Pauli rotations.

For a polynomial :mathp(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

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

Return type

List[Clbit]

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 = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

Return type

Union[ParameterExpression, float]

instances = 9

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

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.

parameters
Return type

ParameterView

prefix = 'circuit'
qregs

A list of the quantum registers associated with the circuit.

qubits

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

Return type

List[Qubit]