379 lines
15 KiB
Plaintext
379 lines
15 KiB
Plaintext
---
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title: PiecewiseLinearPauliRotations (latest version)
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description: API reference for qiskit.circuit.library.PiecewiseLinearPauliRotations in the latest version of qiskit
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.PiecewiseLinearPauliRotations
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---
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# PiecewiseLinearPauliRotations
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<Class id="qiskit.circuit.library.PiecewiseLinearPauliRotations" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L27-L277" signature="qiskit.circuit.library.PiecewiseLinearPauliRotations(num_state_qubits=None, breakpoints=None, slopes=None, offsets=None, basis='Y', name='pw_lin')" modifiers="class">
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Bases: [`FunctionalPauliRotations`](qiskit.circuit.library.FunctionalPauliRotations "qiskit.circuit.library.arithmetic.functional_pauli_rotations.FunctionalPauliRotations")
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Piecewise-linearly-controlled Pauli rotations.
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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:
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$$
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f(x) = \begin{cases}
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0, x < x_0 \\
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a_j (x - x_j) + b_j, x_j \leq x < x_{j+1}
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\end{cases}
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$$
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where we implicitly assume $x_{J+1} = 2^n$.
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Construct piecewise-linearly-controlled Pauli rotations.
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**Parameters**
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* **num\_state\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)") *| None*) – The number of qubits representing the state.
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* **breakpoints** ([*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*] | None*) – The breakpoints to define the piecewise-linear function. Defaults to `[0]`.
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* **slopes** ([*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.13)")*\[*[*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")*] | np.ndarray | None*) – The slopes for different segments of the piecewise-linear function. Defaults to `[1]`.
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* **offsets** ([*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.13)")*\[*[*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")*] | np.ndarray | None*) – The offsets for different segments of the piecewise-linear function. Defaults to `[0]`.
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* **basis** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – The type of Pauli rotation (`'X'`, `'Y'`, `'Z'`).
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* **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – The name of the circuit.
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.ancillas">
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A list of `AncillaQubit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### basis
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.basis">
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The kind of Pauli rotation to be used.
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Set the basis to ‘X’, ‘Y’ or ‘Z’ for controlled-X, -Y, or -Z rotations respectively.
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**Returns**
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The kind of Pauli rotation used in controlled rotation.
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</Attribute>
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### breakpoints
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.breakpoints">
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The breakpoints of the piecewise linear function.
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The function is linear in the intervals `[point_i, point_{i+1}]` where the last point implicitly is `2**(num_state_qubits + 1)`.
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.calibrations">
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Return calibration dictionary.
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The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.clbits">
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A list of `Clbit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### contains\_zero\_breakpoint
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.contains_zero_breakpoint">
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Whether 0 is the first breakpoint.
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**Returns**
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True, if 0 is the first breakpoint, otherwise False.
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</Attribute>
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### data
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.data">
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The circuit data (instructions and context).
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**Returns**
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a list-like object containing the [`CircuitInstruction`](qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.
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**Return type**
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QuantumCircuitData
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</Attribute>
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### global\_phase
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.global_phase">
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The global phase of the current circuit scope in radians.
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</Attribute>
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### instances
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.instances" attributeValue="323" />
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### layout
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.layout">
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Return any associated layout information about the circuit
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This attribute contains an optional [`TranspileLayout`](qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation.
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There are two types of permutations caused by the [`transpile()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.
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</Attribute>
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### mapped\_offsets
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.mapped_offsets">
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The offsets mapped to the internal representation.
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**Returns**
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The mapped offsets.
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</Attribute>
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### mapped\_slopes
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.mapped_slopes">
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The slopes mapped to the internal representation.
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**Returns**
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The mapped slopes.
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</Attribute>
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### metadata
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.metadata">
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Arbitrary user-defined metadata for the circuit.
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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.
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</Attribute>
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### num\_ancilla\_qubits
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_ancilla_qubits">
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The minimum number of ancilla qubits in the circuit.
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**Returns**
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The minimal number of ancillas required.
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</Attribute>
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### num\_ancillas
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_ancillas">
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Return the number of ancilla qubits.
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</Attribute>
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### num\_captured\_vars
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_captured_vars">
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The number of real-time classical variables in the circuit marked as captured from an enclosing scope.
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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.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_clbits">
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Return number of classical bits.
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</Attribute>
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### num\_declared\_vars
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_declared_vars">
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The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.
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This is the length of the `iter_declared_vars()` iterable.
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</Attribute>
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### num\_input\_vars
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_input_vars">
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The number of real-time classical variables in the circuit marked as circuit inputs.
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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.
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_parameters">
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The number of parameter objects in the circuit.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_qubits">
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Return number of qubits.
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</Attribute>
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### num\_state\_qubits
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_state_qubits">
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The number of state qubits representing the state $|x\rangle$.
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**Returns**
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The number of state qubits.
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</Attribute>
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### num\_vars
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.num_vars">
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The number of real-time classical variables in the circuit.
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This is the length of the `iter_vars()` iterable.
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</Attribute>
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### offsets
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.offsets">
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The breakpoints of the piecewise linear function.
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The function is linear in the intervals `[point_i, point_{i+1}]` where the last point implicitly is `2**(num_state_qubits + 1)`.
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</Attribute>
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### op\_start\_times
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.op_start_times">
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Return a list of operation start times.
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This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.
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**Returns**
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List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.
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**Raises**
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[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError "(in Python v3.13)") – When circuit is not scheduled.
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</Attribute>
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### parameters
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.parameters">
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The parameters defined in the circuit.
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This attribute returns the [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.
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**Examples**
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The snippet below shows that insertion order of parameters does not matter.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter
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>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
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>>> circuit = QuantumCircuit(1)
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>>> circuit.rx(b, 0)
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>>> circuit.rz(elephant, 0)
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>>> circuit.ry(a, 0)
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>>> circuit.parameters # sorted alphabetically!
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ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
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```
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Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter
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>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
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>>> circuit = QuantumCircuit(1)
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>>> circuit.u(*angles, 0)
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>>> circuit.draw()
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┌─────────────────────────────┐
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q: ┤ U(angle_1,angle_2,angle_10) ├
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└─────────────────────────────┘
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>>> circuit.parameters
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ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
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```
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To respect numerical sorting, a [`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
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>>> x = ParameterVector("x", 12)
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>>> circuit = QuantumCircuit(1)
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>>> for x_i in x:
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... circuit.rx(x_i, 0)
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>>> circuit.parameters
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ParameterView([
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ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
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ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
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..., ParameterVectorElement(x[11])
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])
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```
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**Returns**
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The sorted [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.prefix" attributeValue="'circuit'" />
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### qregs
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.qregs" attributeTypeHint="list[QuantumRegister]">
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A list of the `QuantumRegister`s in this circuit. You should not mutate this.
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</Attribute>
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### qubits
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.qubits">
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A list of `Qubit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### slopes
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.slopes">
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The breakpoints of the piecewise linear function.
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The function is linear in the intervals `[point_i, point_{i+1}]` where the last point implicitly is `2**(num_state_qubits + 1)`.
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.name" attributeTypeHint="str">
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A human-readable name for the circuit.
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</Attribute>
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### cregs
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.cregs" attributeTypeHint="list[ClassicalRegister]">
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A list of the `ClassicalRegister`s in this circuit. You should not mutate this.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.duration" attributeTypeHint="int | float | None">
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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").
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.PiecewiseLinearPauliRotations.unit">
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The unit that [`duration`](#qiskit.circuit.library.PiecewiseLinearPauliRotations.duration "qiskit.circuit.library.PiecewiseLinearPauliRotations.duration") is specified in.
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</Attribute>
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## Methods
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### evaluate
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<Function id="qiskit.circuit.library.PiecewiseLinearPauliRotations.evaluate" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/arithmetic/piecewise_linear_pauli_rotations.py#L173-L189" signature="evaluate(x)">
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Classically evaluate the piecewise linear rotation.
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**Parameters**
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**x** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")) – Value to be evaluated at.
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**Returns**
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Value of piecewise linear function at x.
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**Return type**
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[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")
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</Function>
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</Class>
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