356 lines
14 KiB
Plaintext
356 lines
14 KiB
Plaintext
---
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title: PiecewiseChebyshev (v1.4)
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description: API reference for qiskit.circuit.library.PiecewiseChebyshev in qiskit v1.4
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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.PiecewiseChebyshev
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---
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# PiecewiseChebyshev
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<Class id="qiskit.circuit.library.PiecewiseChebyshev" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.4/qiskit/circuit/library/arithmetic/piecewise_chebyshev.py#L27-L354" signature="qiskit.circuit.library.PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')" modifiers="class">
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Bases: `BlueprintCircuit`
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Piecewise Chebyshev approximation to an input function.
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For a given function $f(x)$ and degree $d$, this class implements a piecewise polynomial Chebyshev approximation on $n$ qubits to $f(x)$ on the given intervals. All the polynomials in the approximation are of degree $d$.
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The values of the parameters are calculated according to \[1] and see \[2] for a more detailed explanation of the circuit construction and how it acts on the qubits.
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**Examples**
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```python
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import numpy as np
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from qiskit import QuantumCircuit
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from qiskit.circuit.library.arithmetic.piecewise_chebyshev import PiecewiseChebyshev
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f_x, degree, breakpoints, num_state_qubits = lambda x: np.arcsin(1 / x), 2, [2, 4], 2
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pw_approximation = PiecewiseChebyshev(f_x, degree, breakpoints, num_state_qubits)
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pw_approximation._build()
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qc = QuantumCircuit(pw_approximation.num_qubits)
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qc.h(list(range(num_state_qubits)))
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qc.append(pw_approximation.to_instruction(), qc.qubits)
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qc.draw(output='mpl')
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```
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**References**
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**\[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).**
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Optimizing Quantum Circuits for Arithmetic. [arXiv:1805.12445](http://arxiv.org/abs/1805.12445)
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**\[2]: Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022).**
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Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. [ACM Transactions on Quantum Computing 3, 1, Article 2](https://doi.org/10.1145/3490631)
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**Parameters**
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* **f\_x** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)") *| Callable\[\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*],* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")*]*) – the function to be approximated. Constant functions should be specified as f\_x = constant.
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* **degree** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)") *| None*) – the degree of the polynomials. Defaults to `1`.
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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 the full interval.
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* **num\_state\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)") *| None*) – number of qubits representing the state.
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* **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – The name of the circuit object.
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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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### breakpoints
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.breakpoints">
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The breakpoints for the piecewise approximation.
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**Returns**
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The breakpoints for the piecewise approximation.
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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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<Admonition title="Deprecated since version 1.3" type="danger">
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The property `qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations` is deprecated as of Qiskit 1.3. It will be removed in Qiskit 2.0. The entire Qiskit Pulse package is being deprecated and will be moved to the Qiskit Dynamics repository: [https://github.com/qiskit-community/qiskit-dynamics](https://github.com/qiskit-community/qiskit-dynamics). Note that once removed, `qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations` will have no alternative in Qiskit.
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</Admonition>
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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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### data
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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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### degree
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.degree">
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The degree of the polynomials.
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**Returns**
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The degree of the polynomials.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.duration">
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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.PiecewiseChebyshev.unit "qiskit.circuit.library.PiecewiseChebyshev.unit").
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<Admonition title="Deprecated since version 1.3.0" type="danger">
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The property `qiskit.circuit.quantumcircuit.QuantumCircuit.duration` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.
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</Admonition>
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</Attribute>
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### f\_x
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.f_x">
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The function to be approximated.
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**Returns**
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The function to be approximated.
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</Attribute>
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### global\_phase
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.instances" attributeValue="268" />
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### layout
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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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### metadata
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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\_ancillas
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.num_input_vars "qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.num_captured_vars "qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.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.PiecewiseChebyshev.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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### op\_start\_times
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.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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### polynomials
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.polynomials">
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The polynomials for the piecewise approximation.
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**Returns**
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The polynomials for the piecewise approximation.
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**Raises**
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[**TypeError**](https://docs.python.org/3/library/exceptions.html#TypeError "(in Python v3.13)") – If the input function is not in the correct format.
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.prefix" attributeValue="'circuit'" />
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### qregs
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.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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### unit
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.unit">
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The unit that [`duration`](#qiskit.circuit.library.PiecewiseChebyshev.duration "qiskit.circuit.library.PiecewiseChebyshev.duration") is specified in.
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<Admonition title="Deprecated since version 1.3.0" type="danger">
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The property `qiskit.circuit.quantumcircuit.QuantumCircuit.unit` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.
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</Admonition>
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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.PiecewiseChebyshev.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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</Class>
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