---
title: PiecewiseChebyshev (latest version)
description: API reference for qiskit.circuit.library.PiecewiseChebyshev in the latest version of qiskit
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.PiecewiseChebyshev
---

# PiecewiseChebyshev

*class* `qiskit.circuit.library.PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/arithmetic/piecewise_chebyshev.py#L31-L358)

Bases: `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] and see \[2] for a more detailed explanation of the circuit construction and how it acts on the qubits.

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')
```

![Circuit diagram output by the previous code.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/qiskit-circuit-library-PiecewiseChebyshev-1.avif)

References:

\[1] Haener, T., Roetteler, M., & Svore, K. M. (2018). Optimizing Quantum Circuits for Arithmetic. [arXiv:1805.12445](https://arxiv.org/abs/1805.12445)

\[2] Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022). Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. [ACM Transactions on Quantum Computing 3, 1, Article 2](https://doi.org/10.1145/3490631)

**Parameters**

- **f\_x** ([*float*](https://docs.python.org/3/library/functions.html#float) *| Callable\[\[*[*int*](https://docs.python.org/3/library/functions.html#int)*],* [*float*](https://docs.python.org/3/library/functions.html#float)*]*) – the function to be approximated. Constant functions should be specified as `f_x = constant`.
- **degree** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – the degree of the polynomials. Defaults to `1`.
- **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 the full interval.
- **num\_state\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – number of qubits representing the state.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the circuit object.

## Attributes

### breakpoints

The breakpoints for the piecewise approximation.

**Returns**

The breakpoints for the piecewise approximation.

### degree

The degree of the polynomials.

**Returns**

The degree of the polynomials.

### f\_x

The function to be approximated.

**Returns**

The function to be approximated.

### num\_state\_qubits

The number of state qubits representing the state $|x\rangle$.

**Returns**

The number of state qubits.

### polynomials

The polynomials for the piecewise approximation.

**Returns**

The polynomials for the piecewise approximation.

**Raises**

[**TypeError**](https://docs.python.org/3/library/exceptions.html#TypeError) – If the input function is not in the correct format.

### 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
```