# PiecewiseLinearPauliRotations

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

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*(opens in a new tab)*| None*) – The number of qubits representing the state.**breakpoints**(*list*(opens in a new tab)*[**int*(opens in a new tab)*] | None*) – The breakpoints to define the piecewise-linear function. Defaults to`[0]`

.**slopes**(*list*(opens in a new tab)*[**float*(opens in a new tab)*] | np.ndarray | None*) – The slopes for different segments of the piecewise-linear function. Defaults to`[1]`

.**offsets**(*list*(opens in a new tab)*[**float*(opens in a new tab)*] | np.ndarray | None*) – The offsets for different segments of the piecewise-linear function. Defaults to`[0]`

.**basis**(*str*(opens in a new tab)) – The type of Pauli rotation (`'X'`

,`'Y'`

,`'Z'`

).**name**(*str*(opens in a new tab)) – 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}}`

### 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

### global_phase

The global phase of the current circuit scope in radians.

### instances

Default value: `316`

### layout

Return any associated layout information about the circuit

This attribute contains an optional `TranspileLayout`

object. This is typically set on the output from `transpile()`

or `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()`

function, an initial layout which permutes the qubits based on the selected physical qubits on the `Target`

, and a final layout which is an output permutation caused by `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`

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`

must be zero.

### num_parameters

### 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**(opens in a new tab) – When circuit is not scheduled.

### parameters

### 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)`

.

### 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.

### duration

Type: `int | float | None`

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by `unit`

.

### unit

The unit that `duration`

is specified in.

## Methods

### evaluate

`evaluate(x)`

Classically evaluate the piecewise linear rotation.

**Parameters**

**x** (*float*(opens in a new tab)) – Value to be evaluated at.

**Returns**

Value of piecewise linear function at x.

**Return type**