PolynomialPauliRotations

class qiskit.circuit.library.PolynomialPauliRotations(num_state_qubits=None, coeffs=None, basis='Y', name='poly')

Bases: FunctionalPauliRotations

A circuit implementing polynomial Pauli rotations.

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

|i\rangle |0\rangle \mapsto \cos\left(\frac{p(i)}{2}\right) |i\rangle |0\rangle + \sin\left(\frac{p(i)}{2}\right) |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 (int | None) – The number of qubits representing the state.
coeffs (list[float] | None) – 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

coeffs

The coefficients of the polynomial.

coeffs[i] is the coefficient of the i-th power of the function input $x$ , that means that the rotation angles are based on the coefficients value, following the formula

c_j x^j , j=0, ..., d

where $d$ is the degree of the polynomial $p(x)$ and $c$ are the coefficients coeffs.

Returns

The coefficients of the polynomial.

degree

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

Returns

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

name

Type: str

A human-readable name for the circuit.

Example

from qiskit import QuantumCircuit
 
qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)

my_circuit