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

# Static MPFs

`qiskit_addon_mpf.static`

Static MPF coefficients.

This module provides the generator function for the linear system of equations ([`LSE`](/docs/api/qiskit-addon-mpf/costs#lse "qiskit_addon_mpf.costs.LSE")) for computing static (that is, time-independent) MPF coefficients.

### setup\_static\_lse

`setup_static_lse(trotter_steps, *, order=1, symmetric=False)`

[GitHub](https://github.com/Qiskit/qiskit-addon-mpf/tree/stable/0.3/qiskit_addon_mpf/static.py#L31-L110)

Return the linear system of equations for computing static MPF coefficients.

This function constructs the following linear system of equations:

$$
A x = b,
$$

with

$$
\begin{split}A_{0,j} &= 1 \\
A_{i>0,j} &= k_{j}^{-(\chi + s(i-1))} \\
b_0 &= 1 \\
b_{i>0} &= 0\end{split}
$$

where \$\chi\$ is the `order`, \$s\$ is \$2\$ if `symmetric` is `True` and \$1\$ oterhwise, \$k\_\{j}\$ are the `trotter_steps`, and \$x\$ are the variables to solve for. The indices \$i\$ and \$j\$ start at \$0\$.

Here is an example:

```python
>>> from qiskit_addon_mpf.static import setup_static_lse
>>> lse = setup_static_lse([1,2,3], order=2, symmetric=True)
>>> print(lse.A)
[[1.         1.         1.        ]
 [1.         0.25       0.11111111]
 [1.         0.0625     0.01234568]]
>>> print(lse.b)
[1. 0. 0.]
```

**Parameters**

- **trotter\_steps** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*] |* [*Parameter*](https://www.cvxpy.org/api_reference/cvxpy.expressions.html#cvxpy.expressions.constants.parameter.Parameter)) – the sequence of trotter steps from which to build \$A\$. Rather than a list of integers, this may also be a [`Parameter`](https://www.cvxpy.org/api_reference/cvxpy.expressions.html#cvxpy.expressions.constants.parameter.Parameter) instance of the desired size. In this case, the constructed [`LSE`](/docs/api/qiskit-addon-mpf/costs#lse "qiskit_addon_mpf.costs.LSE") is parameterized whose values must be assigned before it can be solved.

- **order** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the order of the individual product formulas making up the MPF.

- **symmetric** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) –

  whether the individual product formulas making up the MPF are symmetric. For example, the Lie-Trotter formula is not symmetric, while Suzuki-Trotter is.

  > **Note**
  >
  > Making use of this value is equivalent to the static MPF coefficient description provided by \[1]. In contrast, \[2] disregards the symmetry of the individual product formulas, effectively always setting `symmetric=False`.

**Returns**

The [`LSE`](/docs/api/qiskit-addon-mpf/costs#lse "qiskit_addon_mpf.costs.LSE") to find the static MPF coefficients as described above.

**Return type**

[*LSE*](/docs/api/qiskit-addon-mpf/costs#lse "qiskit_addon_mpf.costs.lse.LSE")

**References**

**\[1]: A. Carrera Vazquez et al., Quantum 7, 1067 (2023).**

[https://quantum-journal.org/papers/q-2023-07-25-1067/](https://quantum-journal.org/papers/q-2023-07-25-1067/)

**\[2]: S. Zhuk et al., Phys. Rev. Research 6, 033309 (2024).**

[https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033309](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033309)