226 lines
6.5 KiB
Plaintext
226 lines
6.5 KiB
Plaintext
---
|
||
title: PiecewiseChebyshev (v0.31)
|
||
description: API reference for qiskit.circuit.library.PiecewiseChebyshev in qiskit v0.31
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.circuit.library.PiecewiseChebyshev
|
||
---
|
||
|
||
# PiecewiseChebyshev
|
||
|
||
<Class id="qiskit.circuit.library.PiecewiseChebyshev" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/circuit/library/arithmetic/piecewise_chebyshev.py" signature="PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')" modifiers="class">
|
||
Bases: `qiskit.circuit.library.blueprintcircuit.BlueprintCircuit`
|
||
|
||
Piecewise Chebyshev approximation to an input function.
|
||
|
||
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 $d$.
|
||
|
||
The values of the parameters are calculated according to \[1].
|
||
|
||
**Examples**
|
||
|
||
```python
|
||
import numpy as np
|
||
from qiskit import QuantumCircuit
|
||
from qiskit.circuit.library.arithmetic.piecewise_chebyshev import PiecewiseChebyshev
|
||
f_x, degree, breakpoints, num_state_qubits = lambda x: np.arcsin(1 / x), 2, [2, 4], 2
|
||
pw_approximation = PiecewiseChebyshev(f_x, degree, breakpoints, num_state_qubits)
|
||
pw_approximation._build()
|
||
qc = QuantumCircuit(pw_approximation.num_qubits)
|
||
qc.h(list(range(num_state_qubits)))
|
||
qc.append(pw_approximation.to_instruction(), qc.qubits)
|
||
qc.draw(output='mpl')
|
||
```
|
||
|
||
|
||
|
||
**References**
|
||
|
||
**\[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).**
|
||
|
||
Optimizing Quantum Circuits for Arithmetic. [arXiv:1805.12445](http://arxiv.org/abs/1805.12445)
|
||
|
||
**Parameters**
|
||
|
||
* **f\_x** (`Callable`\[\[`int`], `float`]) – the function to be approximated.
|
||
* **degree** (`Optional`\[`int`]) – the degree of the polynomials. Defaults to `1`.
|
||
* **breakpoints** (`Optional`\[`List`\[`int`]]) – the breakpoints to define the piecewise-linear function. Defaults to the full interval.
|
||
* **num\_state\_qubits** (`Optional`\[`int`]) – number of qubits representing the state.
|
||
* **name** (`str`) – The name of the circuit object.
|
||
|
||
## Attributes
|
||
|
||
### ancillas
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.ancillas">
|
||
Returns a list of ancilla bits in the order that the registers were added.
|
||
</Attribute>
|
||
|
||
### breakpoints
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.breakpoints">
|
||
The breakpoints for the piecewise approximation.
|
||
|
||
**Return type**
|
||
|
||
`List`\[`int`]
|
||
|
||
**Returns**
|
||
|
||
The breakpoints for the piecewise approximation.
|
||
</Attribute>
|
||
|
||
### calibrations
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.calibrations">
|
||
Return calibration dictionary.
|
||
|
||
**The custom pulse definition of a given gate is of the form**
|
||
|
||
\{‘gate\_name’: \{(qubits, params): schedule}}
|
||
</Attribute>
|
||
|
||
### clbits
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.clbits">
|
||
Returns a list of classical bits in the order that the registers were added.
|
||
</Attribute>
|
||
|
||
### data
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.data" />
|
||
|
||
### degree
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.degree">
|
||
The degree of the polynomials.
|
||
|
||
**Return type**
|
||
|
||
`int`
|
||
|
||
**Returns**
|
||
|
||
The degree of the polynomials.
|
||
</Attribute>
|
||
|
||
### extension\_lib
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.extension_lib" attributeValue="'include "qelib1.inc";'" />
|
||
|
||
### f\_x
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.f_x">
|
||
The function to be approximated.
|
||
|
||
**Return type**
|
||
|
||
`Callable`\[\[`int`], `float`]
|
||
|
||
**Returns**
|
||
|
||
The function to be approximated.
|
||
</Attribute>
|
||
|
||
### global\_phase
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.global_phase">
|
||
Return the global phase of the circuit in radians.
|
||
</Attribute>
|
||
|
||
### header
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.header" attributeValue="'OPENQASM 2.0;'" />
|
||
|
||
### instances
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.instances" attributeValue="16" />
|
||
|
||
### metadata
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.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.
|
||
</Attribute>
|
||
|
||
### num\_ancillas
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.num_ancillas">
|
||
Return the number of ancilla qubits.
|
||
</Attribute>
|
||
|
||
### num\_clbits
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.num_clbits">
|
||
Return number of classical bits.
|
||
</Attribute>
|
||
|
||
### num\_parameters
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.num_parameters">
|
||
**Return type**
|
||
|
||
`int`
|
||
</Attribute>
|
||
|
||
### num\_qubits
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.num_qubits">
|
||
Return number of qubits.
|
||
</Attribute>
|
||
|
||
### num\_state\_qubits
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.num_state_qubits">
|
||
The number of state qubits representing the state $|x\rangle$.
|
||
|
||
**Return type**
|
||
|
||
`int`
|
||
|
||
**Returns**
|
||
|
||
The number of state qubits.
|
||
</Attribute>
|
||
|
||
### parameters
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.parameters">
|
||
**Return type**
|
||
|
||
`ParameterView`
|
||
</Attribute>
|
||
|
||
### polynomials
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.polynomials">
|
||
The polynomials for the piecewise approximation.
|
||
|
||
**Return type**
|
||
|
||
`List`\[`List`\[`float`]]
|
||
|
||
**Returns**
|
||
|
||
The polynomials for the piecewise approximation.
|
||
</Attribute>
|
||
|
||
### prefix
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.prefix" attributeValue="'circuit'" />
|
||
|
||
### qregs
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.qregs">
|
||
A list of the quantum registers associated with the circuit.
|
||
</Attribute>
|
||
|
||
### qubits
|
||
|
||
<Attribute id="qiskit.circuit.library.PiecewiseChebyshev.qubits">
|
||
Returns a list of quantum bits in the order that the registers were added.
|
||
</Attribute>
|
||
</Class>
|
||
|