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# PiecewiseLinearPauliRotations

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

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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:

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

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

Construct piecewise-linearly-controlled Pauli rotations.

Parameters

• num_state_qubits (Optional[int]) – The number of qubits representing the state.
• breakpoints (Optional[List[int]]) – The breakpoints to define the piecewise-linear function. Defaults to [0].
• slopes (Optional[List[float]]) – The slopes for different segments of the piecewise-linear function. Defaults to [1].
• offsets (Optional[List[float]]) – 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.

## Methods Defined Here

### evaluate

PiecewiseLinearPauliRotations.evaluate(x)

Classically evaluate the piecewise linear rotation.

Parameters

x (float) – Value to be evaluated at.

Return type

float

Returns

Value of piecewise linear function at x.

## Attributes

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

Return type

List[AncillaQubit]

### 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.

Return type

str

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).

Return type

List[int]

### calibrations

Return calibration dictionary.

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

Return type

dict

### clbits

Returns a list of classical bits in the order that the registers were added.

Return type

List[Clbit]

### contains_zero_breakpoint

Whether 0 is the first breakpoint.

Return type

bool

Returns

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

### extension_lib

Default value: 'include "qelib1.inc";'

### global_phase

Return the global phase of the circuit in radians.

Return type

Union[ParameterExpression, float]

Default value: 'OPENQASM 2.0;'

### instances

Default value: 2591

### mapped_offsets

The offsets mapped to the internal representation.

Return type

List[float]

Returns

The mapped offsets.

### mapped_slopes

The slopes mapped to the internal representation.

Return type

List[float]

Returns

The mapped slopes.

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

Return type

dict

### num_ancilla_qubits

The minimum number of ancilla qubits in the circuit.

Return type

int

Returns

The minimal number of ancillas required.

### num_ancillas

Return the number of ancilla qubits.

Return type

int

### num_clbits

Return number of classical bits.

Return type

int

### num_parameters

Return type

int

### num_qubits

Return number of qubits.

Return type

int

### num_state_qubits

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

Return type

int

Returns

The number of state qubits.

### 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).

Return type

List[float]

### 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.

Return type

List[int]

Returns

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

Raises

AttributeError – When circuit is not scheduled.

### parameters

Return type

ParameterView

### prefix

Default value: 'circuit'

### qregs

A list of the quantum registers associated with the circuit.

### qubits

Returns a list of quantum bits in the order that the registers were added.

Return type

List[Qubit]

### 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).

Return type

List[int]