---
title: PiecewiseLinearPauliRotations (v1.3)
description: API reference for qiskit.circuit.library.PiecewiseLinearPauliRotations in qiskit v1.3
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit/1.3/qiskit.circuit.library.PiecewiseLinearPauliRotations
---

# PiecewiseLinearPauliRotations

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L27-L277)

Bases: [`FunctionalPauliRotations`](/docs/api/qiskit/1.3/qiskit.circuit.library.FunctionalPauliRotations "qiskit.circuit.library.arithmetic.functional_pauli_rotations.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*](https://docs.python.org/3/library/functions.html#int) *| None*) – The number of qubits representing the state.
- **breakpoints** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*] | None*) – The breakpoints to define the piecewise-linear function. Defaults to `[0]`.
- **slopes** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*float*](https://docs.python.org/3/library/functions.html#float)*] | np.ndarray | None*) – The slopes for different segments of the piecewise-linear function. Defaults to `[1]`.
- **offsets** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*float*](https://docs.python.org/3/library/functions.html#float)*] | np.ndarray | None*) – The offsets for different segments of the piecewise-linear function. Defaults to `[0]`.
- **basis** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The type of Pauli rotation (`'X'`, `'Y'`, `'Z'`).
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the circuit.

## Attributes

### ancillas

A list of `AncillaQubit`s in the order that they were added. You should not mutate this.

### 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.

**Returns**

The kind of Pauli rotation used in controlled rotation.

### 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)`.

### calibrations

Return calibration dictionary.

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

> **Deprecated since version 1.3**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations` is deprecated as of Qiskit 1.3. It will be removed in Qiskit 2.0. The entire Qiskit Pulse package is being deprecated and will be moved to the Qiskit Dynamics repository: [https://github.com/qiskit-community/qiskit-dynamics](https://github.com/qiskit-community/qiskit-dynamics). Note that once removed, `qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations` will have no alternative in Qiskit.

### clbits

A list of `Clbit`s in the order that they were added. You should not mutate this.

### contains\_zero\_breakpoint

Whether 0 is the first breakpoint.

**Returns**

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

### data

The circuit data (instructions and context).

**Returns**

a list-like object containing the [`CircuitInstruction`](/docs/api/qiskit/1.3/qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.

**Return type**

QuantumCircuitData

### duration

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.unit "qiskit.circuit.library.PiecewiseLinearPauliRotations.unit").

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.duration` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

### global\_phase

The global phase of the current circuit scope in radians.

### instances

Default value: `313`

### layout

Return any associated layout information about the circuit

This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/1.3/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/1.3/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/1.3/qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the [`transpile()`](/docs/api/qiskit/1.3/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/1.3/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/1.3/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.

### 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.

### metadata

Arbitrary user-defined metadata for the circuit.

Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.

### num\_ancilla\_qubits

The minimum number of ancilla qubits in the circuit.

**Returns**

The minimal number of ancillas required.

### num\_ancillas

Return the number of ancilla qubits.

### num\_captured\_vars

The number of real-time classical variables in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_vars()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.num_input_vars "qiskit.circuit.library.PiecewiseLinearPauliRotations.num_input_vars") must be zero.

### num\_clbits

Return number of classical bits.

### num\_declared\_vars

The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.

This is the length of the `iter_declared_vars()` iterable.

### num\_input\_vars

The number of real-time classical variables in the circuit marked as circuit inputs.

This is the length of the `iter_input_vars()` iterable. If this is non-zero, [`num_captured_vars`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.num_captured_vars "qiskit.circuit.library.PiecewiseLinearPauliRotations.num_captured_vars") must be zero.

### num\_parameters

The number of parameter objects in the circuit.

### num\_qubits

Return number of qubits.

### num\_state\_qubits

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

**Returns**

The number of state qubits.

### num\_vars

The number of real-time classical variables in the circuit.

This is the length of the `iter_vars()` iterable.

### 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)`.

### 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.

**Returns**

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

**Raises**

[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError) – When circuit is not scheduled.

### parameters

The parameters defined in the circuit.

This attribute returns the [`Parameter`](/docs/api/qiskit/1.3/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/1.3/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.

**Examples**

The snippet below shows that insertion order of parameters does not matter.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
```

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
```

To respect numerical sorting, a [`ParameterVector`](/docs/api/qiskit/1.3/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])
```

**Returns**

The sorted [`Parameter`](/docs/api/qiskit/1.3/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.

### prefix

Default value: `'circuit'`

### qregs

Type: `list[QuantumRegister]`

A list of the `QuantumRegister`s in this circuit. You should not mutate this.

### qubits

A list of `Qubit`s in the order that they were added. You should not mutate this.

### 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)`.

### unit

The unit that [`duration`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.duration "qiskit.circuit.library.PiecewiseLinearPauliRotations.duration") is specified in.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.unit` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

### name

Type: `str`

A human-readable name for the circuit.

### cregs

Type: `list[ClassicalRegister]`

A list of the `ClassicalRegister`s in this circuit. You should not mutate this.

## Methods

### evaluate

`evaluate(x)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L173-L189)

Classically evaluate the piecewise linear rotation.

**Parameters**

**x** ([*float*](https://docs.python.org/3/library/functions.html#float)) – Value to be evaluated at.

**Returns**

Value of piecewise linear function at x.

**Return type**

[float](https://docs.python.org/3/library/functions.html#float)