qsalto 0.1.1

Transformations between quantum weight enumerators

transform your quantum weight enumerators

qsalto provides transformations between several quantum weight enumerators, including

• Shor-Laflamme enumerators $a$, $b$,
• Rains unitary enumerators $a'$,
• and Rains shadow enumerators $a''$.

We provide both

• a python package, available on PyPi: https://pypi.org/project/qsalto,
• a web viewer for visualizing the transformation matrices at https://mc-zen.github.io/qsalto.

Python package

The python package qsalto can be installed via pip install qsalto and features functions to generate nine classes of transformation matrices.

Matrix	Function	Transforms from ...	... to	is self-inverse
$M$	M(n)	$\mathbf{a}$	$\mathbf{b}$	✅
$M'$	M1(n)	$\mathbf{a'}$	$\mathbf{b'}$	✅
$M''$	M2(n)	$\mathbf{a''}$	$\mathbf{b''}$	✅
$T'$	T1(n)	$\mathbf{a}$, $\mathbf{b}$	$\mathbf{a'}$, $\mathbf{b'}$	❌
$T'^{-1}$	iT1(n)	$\mathbf{a'}$, $\mathbf{b'}$	$\mathbf{a}$, $\mathbf{b}$	❌
$T''$	T2(n)	$\mathbf{a}$, $\mathbf{b}$	$\mathbf{a''}$, $\mathbf{b''}$	❌
$T''^{-1}$	iT2(n)	$\mathbf{a''}$, $\mathbf{b''}$	$\mathbf{a}$, $\mathbf{b}$	❌
$T'''$	T3(n)	$\mathbf{a'}$, $\mathbf{b'}$	$\mathbf{a''}$, $\mathbf{b''}$	❌
$T'''^{-1}$	iT3(n)	$\mathbf{a''}$, $\mathbf{b''}$	$\mathbf{a'}$, $\mathbf{b'}$	❌

To compute the full matrices, a special algorithm making use of recursive patterns is employed. Each matrix generator also features the computation of single elements through, e.g., M(100, entry=[3,4]) where entry specifies the row and column of the entry (in that order). This is only faster than computing the entire matrix when merely very few entries are computed.

Single-shot estimators

Furthermore, the function single_shot_estimators(n) generates single-shot estimators for $a$, $b$, $a'$, $b'$, $a''$, and $b''$ for all possible numbers $m=0,...,n$ of singlets as an outcome of a two-copy bell measurement. This function returns six 2D-arrays (one for each quantum weight enumerator in the order as given above) with the estimator for $m$ singlets in the $m$-th column.

License

This library is distributed under the MIT License.

If you want to support work like this, please cite our paper: tba