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 $p$ , a basis state $|i\rangle$ of the state register, and a target qubit initialized in $|0\rangle$ , this operator applies a Pauli rotation to the target qubit by the angle $p(i)$ . For the default basis="Y", this acts as:

|0\rangle |i\rangle \mapsto \cos\left(\frac{p(i)}{2}\right) |0\rangle |i\rangle + \sin\left(\frac{p(i)}{2}\right) |1\rangle |i\rangle

For basis="X", the action on the target qubit is:

|0\rangle |i\rangle \mapsto \cos\left(\frac{p(i)}{2}\right) |0\rangle |i\rangle - i\sin\left(\frac{p(i)}{2}\right) |1\rangle |i\rangle

For basis="Z", the action on the target qubit is:

|0\rangle |i\rangle \mapsto e^{-i p(i) / 2} |0\rangle |i\rangle

Let $n$ be the number of qubits representing the state, $d$ the degree of $p$ 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.

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 $x^i$ . 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

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