--- title: PiecewiseLinearPauliRotations (v2.0) description: API reference for qiskit.circuit.library.PiecewiseLinearPauliRotations in qiskit v2.0 source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.0/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/2.0/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L28-L278) Bases: [`FunctionalPauliRotations`](/docs/api/qiskit/2.0/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 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)`. ### clbits A list of `Clbit`s in the order that they were added. You should not mutate this. **Example** ```python from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit qr1 = QuantumRegister(2) qr2 = QuantumRegister(1) cr1 = ClassicalRegister(2) cr2 = ClassicalRegister(1) qc = QuantumCircuit(qr1, qr2, cr1, cr2) print("List the qubits in this circuit:", qc.qubits) print("List the classical bits in this circuit:", qc.clbits) ``` ```text List the qubits in this circuit: [Qubit(QuantumRegister(2, 'q0'), 0), Qubit(QuantumRegister(2, 'q0'), 1), Qubit(QuantumRegister(1, 'q1'), 0)] List the classical bits in this circuit: [Clbit(ClassicalRegister(2, 'c0'), 0), Clbit(ClassicalRegister(2, 'c0'), 1), Clbit(ClassicalRegister(1, 'c1'), 0)] ``` ### contains\_zero\_breakpoint Whether 0 is the first breakpoint. **Returns** True, if 0 is the first breakpoint, otherwise False. ### cregs A list of `Clbit`s in the order that they were added. You should not mutate this. ### data The circuit data (instructions and context). **Returns** a list-like object containing the [`CircuitInstruction`](/docs/api/qiskit/2.0/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 3.0.0. ### global\_phase The global phase of the current circuit scope in radians. **Example** ```python from qiskit import QuantumCircuit circuit = QuantumCircuit(2) circuit.h(0) circuit.cx(0, 1) print(circuit.global_phase) ``` ```text 0.0 ``` ```python from numpy import pi circuit.global_phase = pi/4 print(circuit.global_phase) ``` ```text 0.7853981633974483 ``` ### instances Default value: `337` ### layout Return any associated layout information about the circuit. This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/2.0/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/2.0/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/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function: an initial layout that permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/2.0/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout, which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/2.0/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing. **Example** ```python from qiskit import QuantumCircuit from qiskit.providers.fake_provider import GenericBackendV2 from qiskit.transpiler import generate_preset_pass_manager # Create circuit to test transpiler on qc = QuantumCircuit(3, 3) qc.h(0) qc.cx(0, 1) qc.swap(1, 2) qc.cx(0, 1) # Add measurements to the circuit qc.measure([0, 1, 2], [0, 1, 2]) # Specify the QPU to target backend = GenericBackendV2(3) # Transpile the circuit pass_manager = generate_preset_pass_manager( optimization_level=1, backend=backend ) transpiled = pass_manager.run(qc) # Print the layout after transpilation print(transpiled.layout.routing_permutation()) ``` ```text [0, 1, 2] ``` ### 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 dictionary of 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. **Example** ```python from qiskit import QuantumCircuit qc = QuantumCircuit(2, 2, metadata={'experiment_type': 'Bell state experiment'}) print(qc.metadata) ``` ```text {'experiment_type': 'Bell state experiment'} ``` ### 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. **Example** ```python from qiskit import QuantumCircuit, QuantumRegister, AncillaRegister # Create a 2-qubit quantum circuit reg = QuantumRegister(2) qc = QuantumCircuit(reg) # Create an ancilla register with 1 qubit anc = AncillaRegister(1) qc.add_register(anc) # Add the ancilla register to the circuit print("Number of ancilla qubits:", qc.num_ancillas) ``` ```text Number of ancilla qubits: 1 ``` ### num\_captured\_stretches The number of stretches in the circuit marked as captured from an enclosing scope. This is the length of the `iter_captured_stretches()` 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\_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. **Example** ```python from qiskit import QuantumCircuit # Create a new circuit with two qubits and one classical bit qc = QuantumCircuit(2, 1) print("Number of classical bits:", qc.num_clbits) ``` ```text Number of classical bits: 1 ``` ### num\_declared\_stretches The number of stretches in the circuit that are declared by this circuit scope, excluding captures. This is the length of the `iter_declared_stretches()` iterable. ### 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\_identifiers The number of real-time classical variables and stretches in the circuit. This is equal to [`num_vars()`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.num_vars "qiskit.circuit.library.PiecewiseLinearPauliRotations.num_vars") + [`num_stretches()`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.num_stretches "qiskit.circuit.library.PiecewiseLinearPauliRotations.num_stretches"). ### 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\_stretches The number of stretches in the circuit. This is the length of the `iter_stretches()` iterable. ### 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. > **Note** > > This attribute computes the estimate starting time of the operations in the scheduled circuit and only works for simple circuits that have no control flow or other classical feed-forward operations. This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit. **Example** ```python from qiskit import QuantumCircuit from qiskit.providers.fake_provider import GenericBackendV2 from qiskit.transpiler import generate_preset_pass_manager qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) qc.measure_all() # Print the original circuit print("Original circuit:") print(qc) # Transpile the circuit with a specific basis gates list and print the resulting circuit backend = GenericBackendV2(2, basis_gates=['u1', 'u2', 'u3', 'cx']) pm = generate_preset_pass_manager( optimization_level=1, backend=backend, scheduling_method="alap" ) transpiled_qc = pm.run(qc) print("Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:") print(transpiled_qc) # Print the start times of each instruction in the transpiled circuit print("Start times of instructions in the transpiled circuit:") for instruction, start_time in zip(transpiled_qc.data, transpiled_qc.op_start_times): print(f"{instruction.operation.name}: {start_time}") ``` ```text Original circuit: ┌───┐ ░ ┌─┐ q_0: ┤ H ├──■───░─┤M├─── └───┘┌─┴─┐ ░ └╥┘┌─┐ q_1: ─────┤ X ├─░──╫─┤M├ └───┘ ░ ║ └╥┘ meas: 2/══════════════╩══╩═ 0 1 Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']: ┌─────────┐ ░ ┌─────────────────┐┌─┐ q_0 -> 0 ───┤ U2(0,π) ├──────■───░─┤ Delay(1255[dt]) ├┤M├ ┌──┴─────────┴───┐┌─┴─┐ ░ └───────┬─┬───────┘└╥┘ q_1 -> 1 ┤ Delay(196[dt]) ├┤ X ├─░─────────┤M├─────────╫─ └────────────────┘└───┘ ░ └╥┘ ║ meas: 2/═══════════════════════════════════╩══════════╩═ 1 0 Start times of instructions in the transpiled circuit: u2: 0 delay: 0 cx: 196 barrier: 2098 delay: 2098 measure: 3353 measure: 2098 ``` **Returns** List of integers representing instruction estimated 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/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/2.0/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/2.0/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/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit. ### prefix Default value: `'circuit'` ### qregs A list of the quantum registers associated with the circuit. ### 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 3.0.0. ### name Type: `str` A human-readable name for the circuit. **Example** ```python from qiskit import QuantumCircuit qc = QuantumCircuit(2, 2, name="my_circuit") print(qc.name) ``` ```text my_circuit ``` ## Methods ### evaluate `evaluate(x)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L174-L190) 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)