--- title: PiecewiseLinearPauliRotations (v1.0) description: API reference for qiskit.circuit.library.PiecewiseLinearPauliRotations in qiskit v1.0 source: https://quantum.cloud.ibm.com/docs/en/api/qiskit/1.0/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/1.0/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L27-L277) Bases: [`FunctionalPauliRotations`](/docs/api/qiskit/1.0/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 Returns a list of ancilla bits in the order that the registers were added. ### 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 Returns a list of classical bits in the order that the registers were added. ### contains\_zero\_breakpoint Whether 0 is the first breakpoint. **Returns** True, if 0 is the first breakpoint, otherwise False. ### data ### global\_phase Return the global phase of the current circuit scope in radians. ### instances Default value: `266` ### layout Return any associated layout information about the circuit This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/1.0/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/1.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/1.0/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/1.0/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/1.0/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/1.0/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 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. ### 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\_clbits Return number of classical bits. ### 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. ### 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 ### prefix Default value: `'circuit'` ### qregs Type: `list[QuantumRegister]` 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. ### 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)`. ## Methods ### evaluate `evaluate(x)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.0/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)