PiecewiseLinearPauliRotations

class qiskit.circuit.library.PiecewiseLinearPauliRotations(num_state_qubits=None, breakpoints=None, slopes=None, offsets=None, basis='Y', name='pw_lin')

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Bases: FunctionalPauliRotations

Piecewise-linearly-controlled Pauli rotations.

For a piecewise linear (not necessarily continuous) function $f(x)$ , which is defined through breakpoints, slopes and offsets as follows. Suppose the breakpoints $(x_0, ..., x_J)$ are a subset of $[0, 2^n-1]$ , where $n$ is the number of state qubits. Further on, denote the corresponding slopes and offsets by $a_j$ and $b_j$ respectively. Then f(x) is defined as:

f(x) = \begin{cases} 0, x < x_0 \\ a_j (x - x_j) + b_j, x_j \leq x < x_{j+1} \end{cases}

where we implicitly assume $x_{J+1} = 2^n$ .

Construct piecewise-linearly-controlled Pauli rotations.

Parameters

num_state_qubits (int | None) – The number of qubits representing the state.
breakpoints (list[int] | None) – The breakpoints to define the piecewise-linear function. Defaults to [0].
slopes (list[float] | np.ndarray | None) – The slopes for different segments of the piecewise-linear function. Defaults to [1].
offsets (list[float] | np.ndarray | None) – The offsets for different segments of the piecewise-linear function. Defaults to [0].
basis (str) – The type of Pauli rotation ('X', 'Y', 'Z').
name (str) – The name of the circuit.

Attributes

breakpoints

The breakpoints of the piecewise linear function.

The function is linear in the intervals [point_i, point_{i+1}] where the last point implicitly is 2**(num_state_qubits + 1).

contains_zero_breakpoint

Whether 0 is the first breakpoint.

Returns

True, if 0 is the first breakpoint, otherwise False.

mapped_offsets

The offsets mapped to the internal representation.

Returns

The mapped offsets.

mapped_slopes

The slopes mapped to the internal representation.

Returns

The mapped slopes.

offsets

The breakpoints of the piecewise linear function.

The function is linear in the intervals [point_i, point_{i+1}] where the last point implicitly is 2**(num_state_qubits + 1).

slopes

The breakpoints of the piecewise linear function.

The function is linear in the intervals [point_i, point_{i+1}] where the last point implicitly is 2**(num_state_qubits + 1).

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

Methods

evaluate

evaluate(x)

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Classically evaluate the piecewise linear rotation.

Parameters

x (float) – Value to be evaluated at.

Returns

Value of piecewise linear function at x.

Return type

float