Static MPFs (qiskit_addon_mpf.static
)¶
Static MPF coefficients.
This module provides the generator function for the linear system of equations (LSE
) for
computing static (that is, time-independent) MPF coefficients.
- setup_static_lse(trotter_steps, *, order=1, symmetric=False)[source]¶
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 $2$ ifsymmetric
isTrue
and $1$ oterhwise, $k_{j}$ are thetrotter_steps
, and $x$ are the variables to solve for. The indices $i$ and $j$ start at $0$.Here is an example:
>>> 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[int] | Parameter) – the sequence of trotter steps from which to build $A$. Rather than a list of integers, this may also be a
Parameter
instance of the desired size. In this case, the constructedLSE
is parameterized whose values must be assigned before it can be solved.order (int) – the order of the individual product formulas making up the MPF.
symmetric (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
to find the static MPF coefficients as described above.- Return type:
References
- [1]: A. Carrera Vazquez et al., Quantum 7, 1067 (2023).
- [2]: S. Zhuk et al., Phys. Rev. Research 6, 033309 (2024).
https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033309